text:
# Retinal S-opsin dominance in Ansell’s mole-rats (Fukomys anselli) is a consequence of naturally low serum thyroxine

## Abstract

Mammals usually possess a majority of medium-wavelength sensitive (M-) and a minority of short-wavelength sensitive (S-) opsins in the retina, enabling dichromatic vision. Unexpectedly, subterranean rodents from the genus Fukomys exhibit an S-opsin majority, which is exceptional among mammals, albeit with no apparent adaptive value. Because thyroid hormones (THs) are pivotal for M-opsin expression and metabolic rate regulation, we have, for the first time, manipulated TH levels in the Ansell’s mole-rat (Fukomys anselli) using osmotic pumps. In Ansell’s mole-rats, the TH thyroxine (T4) is naturally low, likely as an adaptation to the harsh subterranean ecological conditions by keeping resting metabolic rate (RMR) low. We measured gene expression levels in the eye, RMR, and body mass (BM) in TH-treated animals. T4 treatment increased both, S- and M-opsin expression, albeit M-opsin expression at a higher degree. However, this plasticity was only given in animals up to approximately 2.5 years. Mass-specific RMR was not affected following T4 treatment, although BM decreased. Furthermore, the T4 inactivation rate is naturally higher in F. anselli compared to laboratory rodents. This is the first experimental evidence that the S-opsin majority in Ansell’s mole-rats is a side effect of low T4, which is downregulated to keep RMR low.

## Introduction

### Unusual cone proportion in the mole-rat retina – adaptive or not?

The ability to perceive light was presumably one key advantage in animal evolution explaining the great variability of visual systems found across all animal taxa which have evolved in response to different visual requirements1. The mammalian retina possesses two types of photoreceptors, rods for dim light vision and cones for daylight and high acuity vision. Light-sensitive proteins, i.e. opsins, determine the spectral sensitivity of different photoreceptor types. While rods express rhodopsin as the only opsin type, most mammals express two cone opsin types with different spectral properties, namely short-wavelength sensitive (S-) opsins (detecting light in the UV to blue wavelength range, depending on species; encoded by Opn1sw, from here: S-opsin) and medium-wavelength sensitive (M-) opsins (green wavelength range; encoded by Opn1mw, from here: M-opsin). Spectral separation of the cone types enables dichromatic vision. Thus far, many exceptions from the mammalian retinal blueprint are known2,3, of which one will be addressed in the present study.

African mole-rats from the genus Fukomys (formerly known as Cryptomys4, family Bathyergidae) live in subterranean burrow systems, an ecotope characterised by almost constant darkness. These animals show typical sensory adaptations to the subterranean ecotope5, but have retained small, structurally functional eyes. The rod-dominated retina of Ansell’s mole-rats has a high cone proportion of about 10% which is higher than those of nocturnal surface dwellers6,7,8,9,10, and can perceive monochromatic light in the blue and green wavelength range11. However, while all mammals studied thus far possess a majority of M-opsins in their retina3,12, Fukomys mole-rats exhibit a clear majority of S-opsins8. The retina of the Ansell’s mole-rat (Fukomys anselli) contains about 10% pure M-cones, 20% pure S-cones, and 70% dual pigment cones expressing mainly S-opsin and small amounts of M-opsin as determined by immunohistochemistry8. Thus, in total, approximately 90% of cones showed a predominant S-opsin expression. The large S-/M-opsin ratio is exceptional in the animal kingdom and has raised questions about a possible adaptive value. However, Kott et al.13 have shown that blue light propagates less efficiently than green light in natural burrow systems of F. anselli, and light intensities drop quickly to scotopic levels, by which only rods are activated13. These findings make it unlikely that the S-opsin rich retina has any adaptive value for life in subterranean burrow systems. Moreover, brain regions involved in visual orientation in three-dimensional environments are severely reduced in bathyergid mole-rats14 explaining recent behavioural data15. These findings suggest that the mole-rats’ visual system serves simple light detection rather than high acuity image forming or colour discrimination. Yet, the mechanisms leading to the unique opsin ratio remain unclear.

### Low M-opsin expression might be a side effect of low thyroxine levels

THs, in particular, the transcriptionally active 3,5,3′-triiodothyronine (T3) and the precursor thyroxine (T4), are mainly associated with neural development, growth, metabolism, and the cardiac system, but are also one major factor influencing cone opsin expression16,17,18,19,20,21. Only a small fraction of T4 and T3 secreted by the thyroid gland is circulating freely, while the rest is bound to transport proteins. Only the free fraction (FT4, FT3) is biologically active22. In the retina, T3 binds to the TH receptor isoform β2 (TRβ2), a nuclear receptor expressed in cones. This suppresses S-opsin expression and instead activates M-opsin expression17,23,24. Low serum TH levels, a state referred to as hypothyroid, thus leads to downregulation of M-opsin expression with a high plasticity throughout adulthood, at least in mice, rats, and likely also in humans19,25. Interestingly, we have previously shown that Ansell’s mole-rats have serum FT4 levels which are approximately 10-fold lower compared to other rodents, while FT3 levels are in the rodent-typical range26. Total TH levels (free and bound fraction; TT4 and TT3) appeared to be downregulated as well. Moreover, the bound T4 and T3 fraction is significantly higher compared to other rodents, resulting in a lower free fraction relative to total TH levels. These measurements indicate that in F. anselli, FT4 is downregulated by reduced T4 synthesis and increased protein binding rate. We have interpreted our results in view of the low resting metabolic rate (RMR) of F. anselli27, a typical trait among bathyergid mole-rats28. Low RMR is a pivotal adaptation of African mole-rats because in (sealed) underground burrows oxygen availability is low, risk of overheating is high, and food availability is scarce27,28. THs regulate metabolic pathways by which the balance between energy expenditure and storage is maintained. Excess THs increase energy expenditure by central and peripheral mechanisms. By the same token, low TH levels reduce energy expenditure29. Thus, it appears reasonable that natural selection has favoured low T4 in F. anselli to maintain low RMR. In contrast, as stated above, there is no reason to assume that a similar selective pressure was acting on colour vision properties. Instead, the S-opsin majority found in Fukomys mole-rats is likely to be only a side effect of low T4 levels.

Nevertheless, there is a major contradiction in this model. The normal T3 levels found in Ansell’s mole-rats should be sufficient to upregulate both, RMR and M-opsin expression. However, TH signalling is not only dependent on circulating TH levels but also on various other factors. First, THs cannot passively diffuse through cell membranes, thus several transmembrane transporters are required for TH supply of target cells30. The monocarboxylate transporter 8 (MCT8) and the organic anion transporting peptide 1c1 (OATP1C1) are well described as high-affinity TH transporters31. MCT8 transports T4 as well as T3, with a higher affinity for T332,33, and OATP1C1 has the highest T4 affinity compared to other TH transporters34. While MCT8 is widely expressed, including metabolically active organs such as liver and kidney33, OATP1C1 is predominantly expressed at blood-tissue barriers35,36. Second, intracellular conversion of the prohormone T4 into the receptor-active T3 is catalysed by deiodinases type 1 and 2 (DIO1, DIO2). A third deiodinase type (DIO3) is mostly responsible for TH inactivation into TH metabolites, such as reverse T3 (rT3) or T237. Third, TH action is mediated by binding to TH receptors which are nuclear receptors regulating gene expression. Availability of different receptor isoforms encoded by the genes Thra and Thrb is cell- and age-specific.38. Consequently, availability and function of these regulatory components finally determine cellular TH effects.

In the present study, we treated Ansell’s mole-rats with T4 using subcutaneous osmotic pumps for 12 weeks, to study the effects on opsin expression, RMR, and body mass (BM). We treated another group with T3, to control for T3-specific effects, because T4 treatment leads to a slight upregulation of T3 via deiodination. We aimed to test two scenarios: i.) if M-opsin expression, RMR, or BM are upregulated by T4 treatment, the respective target tissues are likely to be T4-dependent (e.g. through T4-specific transporters), and ii.) if T4 treatment has no impact on one of these traits, either THs are inactivated in target tissues or the TH signalling pathway is interrupted. By T4 treatment, we successfully achieved rodent-typical TH levels, which allowed us to draw conclusions on these two scenarios, as well as to infer adaptive implications for life underground.

## Results

### T4 administration results in a euthyroid T4 level

We treated Ansell’s mole-rats with T4 (n = 5), T3 (n = 5) or the vehicle solution (VH) (n = 3), in which T3 and VH treatments served as controls. We measured serum levels of FT4, FT3, TT4, and TT3 using commercially available ELISA kits (see Supplementary Table S1), and statistically compared pre- and post-treatment levels to assess successful treatment in each treatment group (only p-values adjusted for multiple comparisons are given in this section, unless otherwise stated). In the T4 animals where we aimed to achieve rodent-typical T4 serum levels, FT4 was significantly elevated after treatment (t = 40.91, p = 0.0012) (Fig. 1a). Mean FT4 levels were in the rodent-typical range26 (3.12 ± 0.75 ng/dl). FT3 was elevated by a factor of 1.42 (t = 2.86, adjusted p = 0.0687, unadjusted p = 0.046) which can be attributed to T4 deiodination (Fig. 1b). Taken together, T4 supplement resulted in an FT4:FT3 ratio of approximately 9:1, which can be considered rodent-typical39. Furthermore, TT4 was also significantly upregulated following T4 treatment (TT4: t = 8.87, adjusted p = 0.005) (Fig. 1c,d). In the T3 group, we aimed to achieve a slight FT3 upregulation as observed in the T4 group, to control for FT3 effects. Following T3 treatment, FT3 levels were significantly elevated (t = 6.53, adjusted p = 0.0084) (Fig. 1b) by a factor of 1.45 which is very close to the elevation factor of 1.42 observed in the T4 group. TT3 was also significantly elevated in the T3 group (t = 8.39, adjusted p = 0.004) (Fig. 1d), but FT4 and TT4 were not affected (Fig. 1a,c). In the VH group, FT4 and FT3 levels did not differ between the two samplings (Fig. 1a,b). Surprisingly, TT4 and TT3 levels were significantly upregulated at the end of the treatment period (TT4: t = 10.46, adjusted p = 0.022; TT3: t = 10.36, adjusted p = 0.018) (Fig. 1c,d). Post-treatment levels of rT3, the inactivated form of T4, were compared between the treatment groups, to get an impression of T4 inactivation rates. One-way ANOVA revealed that rT3 was significantly upregulated in the T4 group compared to the other groups (one-way ANOVA, F = 20.28, p = 0.0003) (Fig. 1e). We further analysed the respective rT3:TT4 ratios (in %), as a measure of relative T4 inactivation rates, but found no significant difference between the three groups (Fig. 1f), indicating that relative conversion rates remain stable despite T4 treatment.

### M-opsin expression is markedly lower expressed than S-opsin on transcriptional level

We measured expression levels of S-opsin and M-opsin in eyecups containing the retina of untreated Ansell’s mole-rats to determine, if the S-opsin dominance found on protein level8 is already set on gene expression level. Real-time Quantitative Reverse Transcription PCR (qRT-PCR) revealed that S-opsin was expressed 42 ± 22-fold higher than M-opsin as determined by the 2−ΔΔCT method40, which indicates that M-opsin expression is significantly lower expressed already on transcriptional level (t = 24.5, p < 0.001, n = 13).

### Opsin expression was upregulated following T4 treatment only in young animals

To test if T4 treatment influenced M-opsin expression, we measured gene expression levels of M-opsin and S-opsin in eyecups containing the retina by qRT-PCR. To determine treatment effects, we extirpated one eye prior to treatment and the other eye post-treatment. By this, we could calculate treatment effects pairwise in each animal (Fig. 2). Relative expression levels of both opsins did not differ significantly between untreated and treated eyes in any of the treatment groups (Fig. 2a,c,d). However, calculation of fold changes revealed a potential difference between young and old animals (boundary arbitrarily set to 1,000 days of age based on fold changes) in the T4 group. While T4 treatment led to an increase of M-opsin expression between 6.42–16.34-fold in young animals (n = 3), expression in old animals increased only 1.03 and 1.31-fold (n = 2). Such a differential effect is not seen in the T3 or VH group (see Supplementary Table S2). In a second approach, we therefore analysed the data of young animals only (n = 3). In young animals M-opsin expression significantly increased following T4 treatment (Table 1), and also S-opsin expression (Table 1;Fig. 2b), indicating that these effects were masked by old animals in the pooled analysis.

To control for the possibility that opsins are expressed at different baseline levels in each eye, we normalised the data by calculating the ratio between M- and S-opsin expression levels for each eye in pre- and post-treatment samples. By this, we could compare M-opsin expression levels in pre- and post-treatment samples relative to S-opsin expression as an alternative measure for changes in M-opsin expression. An increase of this ratio would further indicate that M-opsin expression is upregulated by a higher degree than S-opsin and vice versa. We found a significant increase in M-opsin/S-opsin ratio in the pooled data (t = 2.86, p = 0.046, n = 5) as well as in data of young animals only (t = 5.86, p = 0.028, n = 3) (Fig. 3). Here again, the effect in pooled data is lower than in data of young animals. Thus, expression of both opsins is upregulated following T4 treatment, but expression of M-opsin is upregulated at a higher degree than S-opsin (Fig. 3).

### Expression differences of TH transporters and TH signalling components following T4 treatment

We were further interested if components involved in TH signalling, namely Mct8, Oatp1c1, Dio2, Dio3, and Thrb are i. expressed in eyecup/retina samples, and ii. influenced by T4 or T3 treatment. We also measured expression levels of the Rhodopsin-encoding gene (Rho) and chicken ovalbumin upstream promoter transcription factor 1 (Coup-TF1), a nuclear receptor involved in spatial patterning of cone opsins across the retina41. We found that none of the tested components were differentially expressed in the three treatment groups after correction for multiple comparisons (without correction, Oatp1c1 and Coup-TF1 were significantly upregulated following T4 treatment; Table 1; Fig. 2a,c,d). In order to test if treatment effects on gene expression are age-dependent, as was the effect on opsin expression, we performed a second, separate analysis in which animals older than 1,000 days were excluded. In young animals, we found a significant upregulation of Mct8, Thrb, and Coup-TF1 after correcting for multiple comparisons (Table 1; Fig. 2b). In T3-treated old animals no significant changes in gene expression were found. Unfortunately, we could not statistically analyse treatment effects separately in T4-treated old animals and T3-treated young animals, respectively, because the sample sizes (n = 2) were not sufficient (see Supplementary Table S2).

### Application of T4 decreased body mass but TH treatment did not influence RMR

At start of the treatments, BM did not differ between treatment groups (one-way ANOVA, F = 1.08, p = 0.375, n = 3). To reveal possible treatment effects on BM, we calculated a repeated measures one-way ANOVA on weekly BM. In the T4 treatment group, BM differed significantly between week 1 (baseline) and weeks 6, 10, 11, and 12, respectively (F = 3.29, p = 0.002, n = 12) (Fig. 4). No significant changes in BM were observed in the T3 and VH group. We further measured RMR in all treatment cohorts and an additional untreated control cohort between weeks 10 and 12. No significant differences could be observed in mass-specific RMR (msRMR) between any of the four cohorts (one-way ANOVA, F = 2.77, p = 0.081, n = 4) (Fig. 5).

## Discussion

In the present study, we investigated how upregulation of T4 impacts retinal gene expression, msRMR, and BM in F. anselli. The purpose was to investigate the molecular basis of the exceptionally low M-opsin expression and to challenge its adaptive viewpoint in a proximate context considering low RMR of mole-rats.

As the basis for the present study, we needed to upregulate serum FT4 levels into a rodent-typical range. A slight upregulation of FT4 by cold acclimation was achieved in naked mole-rats (Heterocephalus glaber), a close relative of Ansell’s mole-rats42, but this is the first time TH levels were exogenously upregulated under controlled conditions in a mole-rat species. To achieve normal FT4 levels, we treated the animals with a higher T4 dose than recommended by the American Thyroid Association for the treatment of hypothyroid mice43, to compensate for the higher protein binding rate in Ansell’s mole-rats26. Although total rT3 levels were highly elevated in T4-supplemented animals, the rT3:TT4 ratio, a measure for relative T4 inactivation rate, did not differ between the experimental groups, suggesting that the balance between T4 levels and T4 inactivation stayed equilibrated under T4 treatment. It was instead severalfold higher in all experimental groups (range: 0.91 ± 0.33–1.43 ± 0.93%) compared to rats (0.29%44, 0.14%45) and mice (0.17%46) (rT3:TT4 ratios for rats and mice were calculated with mean values from the cited publications). This indicates that T4 inactivation is naturally upregulated in F. anselli compared to other rodent species, which might represent one mechanism leading to the naturally low T4 levels. While T4 and T3 treatments yielded the desired results, VH treatment led to an unexpected upregulation of TT4 and TT3. The VH solution contained BSA, i.e. albumin, which is the main serum TH binding protein in rodents39 and therefore often used as a stabilising agent to overcome the short half-life of THs during long-term treatments. We assume that artificial administration of BSA could have led to an elevated binding of endogenous T4 and T3 to BSA. This in turn could have led to a drop in free serum TH, which decreases negative feedback to the hypothalamus and pituitary, stimulating endogenous TH release. This explanation is supported by our observation that FT4 and FT3 were unaffected in the VH group, pointing out that only the bound fraction has increased. This finding does not influence our experimental outcomes, since the bound fraction is physiologically inactive, but it should be considered in long-term hormone treatments where BSA is used as a stabiliser.

Advanced short-wavelength sensitivity in Ansell’s mole-rats has no evident adaptive value in underground burrow systems, as suggested by Kott et al.13 based on light propagation data in burrow systems. In fact, sensory systems of subterranean mammals have adapted to the almost lightless ecotope5, thus vision plays a subordinate role. Nevertheless, we were able to upregulate M-opsin expression by T4 treatment. This finding reveals that the expression regulation of mole-rat’s M-opsin is comparable to the regulation in other mammals, and the S-opsin majority is a systemic effect of low serum T4 levels. However, M-opsin expression was only upregulated in young animals up to an age of approximately 2.2 years (fold change: 9.94 ± 5.6; Supplementary Table S2). In older animals (>2.9 years, referred to as old animals), no effect on opsin expression was observed following T4 treatment (fold change: 1.17 ± 0.2; Supplementary Table S2). In the T4 group, we had a gap of approximately 0.7 years between the oldest “young” animal and the youngest “old” animal. Therefore, we could not determine the exact age where M-opsin does not respond to T4 treatment anymore, but it is likely to be around 2.5 years. In salmonid fish, TH treatment shows no effect on opsin expression in older animals as well, but this observation is linked to different developmental stages47. In F. anselli, TH sensitivity of cones drops at an age where the animals are fully grown48, rendering a developmental cue unlikely. Interestingly, the age-dependent effects we observed in the mole-rat retina are in contrast to Glaschke et al.19 who, for the first time, showed that M-opsin expression is still prone to TH manipulation in fully maturated photoreceptors of adult mice and rats. A similar effect was reported in adult hypothyroid human patients treated with T4, based on a colour contrast sensitivity test25. It can be argued that the contradicting observation is a consequence of prolonged natural TH deprivation experienced by the mole-rat retina. The resulting long-term lack of TH signalling might lead to permanent downregulation of redundant components of the TH signalling pathway (e.g. through gene silencing by nuclear orphan receptors49), from which Mct8 and Thrb might be promising candidates. Expression of both genes was upregulated in the T4 group, but only in young animals (≤2.2 years). MCT8 plays a role in photoreceptor and interneuron supply with TH, as indicated by immunohistochemical data50, and TRβ2 is a transcriptional activator of M-opsin expression16. Insufficient availability of these two components in old animals might thus impede TH signalling in photoreceptors. But note, the specific role of TRβ2 in mole-rats could not be tested due to insufficient information on the existence and/or structure of the β1 and β2 receptor isoforms. Furthermore, Arbogast et al.51, who used a reporter mouse line to visualize T3 signalling sites in the retina, have suggested that most T3 signalling is likely to take place in the inner retina16. Therefore, expressional changes of Mct8 and Thrb do not automatically reflect changes in T3 signalling within cone cells, but our results revealed promising targets which might be involved in the observed effects on opsin expression.

Unexpectedly, not only M-opsin, but also S-opsin was upregulated through T4 supplement. This observation is quite puzzling, because in several mammals, S-opsin is expressed independently from T3 signalling via TRβ216,18,19. TRβ2 is the isoform responsible for M-opsin expression, but it cannot be excluded that T3 initiates other signalling pathways via other receptor isoforms or transcription factors involved in upstream mechanisms. One promising candidate is the retinoic acid receptor-related orphan receptor α (RORα) which transactivates multiple cone genes. RORα also binds to the promoter of S-opsin and the locus control region of M-opsin and thereby enhances the expression of both genes. RORα-deficient mice do not completely lack opsin expression, but S- and M-opsins are significantly downregulated52. Moreover, expression of the RORα gene may be regulated by TH, because expression levels were partly downregulated in brains of hypothyroid mice compared to T4-replaced controls53. Taken together, the naturally hypothyroid mole-rat retina might not only lead to low M-opsin expression levels, but rather to a general downregulation of both cone opsins (and other cone-specific genes) due to missing RORα signalling. T4 treatment of F. anselli could thus have augmented expression of both cone opsins via higher RORα availability, while M-opsin expression was further enhanced by additional TRβ2 signalling. The latter assumption is further supported by M-opsin/S-opsin expression ratio, which revealed a significantly higher upregulation of M-opsin compared to S-opsin expression. We also observed Coup-TF1 upregulation following T4 supplement. In the retina, the encoded nuclear receptor is pivotal for spatiotemporal patterning of cone opsins41. In cultured adipocytes, Coup-TF1 expression is upregulated by T3, which is in line with our findings54. This observation indicates that T4 supplement not only enhances opsin expression in F. anselli, but might also activate regulatory pathways involved in spatiotemporal patterning. Unfortunately, the sample size available in the present study did not allow us to conduct immunohistochemical studies on retinal flatmounts to resolve this issue on protein level. Note, that in contrast to laboratory mice and rats, mole-rats cannot be purchased from commercial breeders and wild captures cannot be easily imported. The animals have a very slow breeding rate (1–2 litters with on average two pups per litter per year), very low growth rates (0.36 g per day)48, and reach full maturity only at >1 year of age. The availability of animals is thus extremely limited, which made us choose qRT-PCR as the method of choice for analysing treatment effects in the eye. This enabled us to screen a broad spectrum of genes for treatment effects and to infer regulatory mechanisms underlying opsin expression. Surely, histological and electrophysiological experiments are needed to support our findings also from functional side, but based on our gene expression data, it can be concluded that the signalling pathways involved in opsin expression are largely inactivated, but can be readily restored by T4 supplement, supporting our main hypothesis of the unusual opsin phenotype in F. anselli being a side effect of low serum T4. Further support for the hypothesis comes from the RMR measurements. T4 supplement in F. anselli did not induce changes in msRMR compared to T3 and VH treatment, as well as the untreated control group. This is somewhat surprising, because in mammals, metabolic rate is usually positively correlated with TH serum levels29,55. As stated above, T4 inactivation was upregulated following T4 treatment, and overall T4 inactivation rates in F. anselli are higher than those in the rat. These findings raise the possibility that F. anselli has evolved tissue-specific resistance to TH signalling. Resistance to TH is usually a pathologic state with different molecular causes, including TH transporters, deiodinases, and TH receptors56. However, when mechanisms like elevated TH inactivation are restricted to metabolically active organs such as the liver and kidney, an animal could maintain a low metabolic rate while other TH-dependent tissues are not necessarily influenced. This predicted mechanism could also account for T3 being ineffective in upregulating RMR in mole-rats. Support for this model comes from other animal species, e.g. the blind mole-rat (Spalax ehrenbergi superspecies)57 inhabiting subterranean burrow systems, and the African striped mouse (Rhabdomys pumilio)58 inhabiting semi-arid regions with pronounced climatic changes. In both species, a climate-dependent inverse relationship between TH levels and metabolic rate was reported. Thus, organ-specific resistance to TH might represent a shared trait to adapt to challenging environmental conditions. In naked mole-rats, upregulation of FT4 and basal metabolic rate were achieved by prolonged cold exposure (5 °C below normal temperature for >1 year)42,59, suggesting that metabolic regulation by T4 is possible in bathyergid mole-rats, when environmental conditions change. In our study, influencing factors such as ambient temperature or food availability were kept constant. Nevertheless, we observed a significant decrease in BM in T4-treated animals, while the T3 and VH group were unaffected. In human, daily T3 administration was shown to upregulate genes related to glucose and lipid metabolism, energy metabolism, and catabolism (among others) in skeletal muscle60. If these genes are also upregulated in mole-rats following T4 treatment, this could have led to higher energy expenditure (e.g. through increased activity) and loss of energy stores which might then be causative for weight loss observed in F. anselli. While the significant drop in BM was established in week 10 (being even more pronounced in week 11 and 12), we also observed a single significant drop in week 6, which we cannot explain thus far. To address these open questions regarding TH effects on metabolic physiology, we are currently planning to investigate the underlying molecular mechanisms in metabolically relevant organs such as liver, kidney, brown adipose tissue, and skeletal muscle in Fukomys mole-rats.

In summary, we have, for the first time, manipulated TH levels in a bathyergid species with naturally low T4 serum levels by exogenous TH administration. The finding that T4 treatment led to an upregulation of opsin expression and other regulatory components suggests that retinal TH supply is T4-dependent, supporting previous studies50,61. Therefore, the S-opsin majority which was suggested to have no adaptive value in underground burrows13, is likely to be a side effect of low T4 serum levels. A low RMR is pivotal to cope with the harsh subterranean conditions, hence we assume that a low T4 serum level is an ecophysiological adaptation to downregulate RMR. Our finding that RMR was the only trait assessed in the present study that was not affected by T4 supplement, supports this assumption. Elevated T4 inactivation is indicative for tissue-specific compensatory mechanisms to keep RMR low. THs regulate animal physiology on many levels, and the present study again emphasizes the need of promoting research in different animal species to understand the full spectrum of TH function.

## Methods

### Animals

We tested a total of 18 Ansell’s mole-rats (8 females, 10 males) which were all born and maintained at the animal facility of the Department of General Zoology, University of Duisburg-Essen, Germany, and hence were of known age (Table 2). The mean age of all animals was 2.6 ± 0.92 years (range: 1.45–4.17 years) at start of treatment, which represents a fully matured adult stage where the prevalence of age-related health impairments are usually not observed in these long-lived rodents with an average lifespan of 7 years and a maximum lifespan of around 20 years62. The animals were housed as family groups in glass terraria of appropriate size with wood shavings as litter. Light cycle, room temperature, and humidity were kept constant at 12/12, 25 ± 1 °C and 40 ± 3 %, respectively. The diet consisted of carrots and potatoes fed ad libitum, supplemented with apples and grain provided once per week. All animals remained in their families after completion of the experiments. All animal experiments were conducted in accordance with the German Regulations for Laboratory Animal Science (GV-SOLAS) and were approved by the North Rhine-Westphalia State Environment Agency (LANUV; permit number: 84-02.04.2016.A176).

### Thyroid hormone treatment

Ansell’s mole-rats were randomly assigned to one of three treatment groups (Table 2) and were treated with a daily dosage of either 90 ng/g BM T4 (T2501, Sigma-Aldrich, Taufkirchen, Germany), 2 ng/g BM T3 (T2877, Sigma-Aldrich) or the vehicle (VH) solution containing 15 mM NaOH, 50% propylenglycol and PBS containing 5% BSA (T844.2, Carl Roth, Karlsruhe, Germany) as monotherapies. Osmotic pumps (pump model 2006, ALZET®, DURECT Corporation, Cupertino, CA, USA) were filled with the respective solution through a 0.22 µm syringe-end filter (Carl Roth, P666.1) and primed in sterile 0.9% NaCl for 60 h at 37 °C before implantation to achieve immediate pumping. Osmotic pumps deliver the test agents with a constant flow rate, thus being well-suited for long-term hormone treatments. Constant administration further overcomes the short half-life of THs in rodents39. For implantation, we deeply anesthetized the animals with an intramuscular injection of 6 mg/kg ketamine (Medistar, Ascheberg, Germany) and 2.5 mg/kg xylazine (Medistar)63, and implanted the pumps subcutaneously slightly below the scapulae through a small incision. The animals received daily pain medication (Carprofen, 5 mg/kg s.c., Norbrook Laboratories, Newry, UK) for at least 3 days, and were isolated in a sterile terrarium for 24–48 h for recovery before they were returned to their family group. We replaced the implanted pumps after 6 weeks with new pumps.

### Enucleation

Prior to pump implantation, we extirpated the left eye. The right eye was extirpated together with explantation of the second pump after 12 weeks of treatment (end of treatment). By this, pairwise comparisons of treatment effects on gene expression were possible. For enucleation, eyes were lubricated with local anaesthetics (Xylocain, AstraZeneca, Wedel, Germany) to relax the ocular muscles. Afterwards, the eyeball was gently pushed out of the orbit, grasped with a curved forceps at the optic nerve, and pulled out of the orbit by twisting the optic nerve. We immediately removed the cornea, lens, and vitreous from the freshly isolated eyes. The eyecup containing the retina and RPE was transferred into RNA stabilising reagent RNAlater (Qiagen, Hilden, Germany), incubated for 24 h at 4 °C, and stored at −20 °C for expression analyses. Removal of the eyes does not impair the life of mole-rats, because these animals are adapted to the dark subterranean habitat and apart from the capability to distinguish between light and darkness, they do not orient visually10,14.

### Quantification of serum TH levels

For monitoring of serum TH levels, we collected blood samples before treatment (baseline), after six weeks of treatment, and at the end of treatments (post-treatment). Blood samples (on average 0.9 ml per sample) were obtained from the vena saphena of the hindpaw under ketamin/xylazine anaesthesia as described above and centrifuged at 10,000 × g at 20 °C. Serum aliquots were stored at −20 °C until use. Serum levels of FT4, FT3, TT4, TT3, and rT3 were determined with commercial ELISA kits according to manufacturer’s instructions (DRG Diagnostics, Marburg, Germany: FT4 – EIA 2386; FT3 – EIA 2385; TT4 – EIA 4568; TT3 – EIA 4569; BioVendor, Brno, CZ: rT3 – RCD029R). We measured hormone concentrations of baseline and post-treatment samples, except for rT3 where we only measured post-treatment levels, because baseline serum samples were depleted. In case, FT4 levels were under detection limit of the assay, values are depicted as <0.05 ng/dl, which represents the detection limit of the FT4 ELISA kit used in this study.

### Isolation of RNA and qRT-PCR

Eyecups were immersed in 350 µl lysis buffer (Buffer RLT, Qiagen) and homogenized with a TissueLyser II (Qiagen). Total RNA from eyecup lysates was extracted by using the RNeasy Mini Kit (Qiagen) according to manufacturer’s instructions. An on-column DNase digestion step was further included in the extraction procedure with RNase-Free DNase Set (Qiagen). Total RNA was quantified by using a NanoDrop ND-1000 (Peqlab, Erlangen, Germany). RNA was reverse-transcribed into complementary DNA (cDNA) using AMV Reverse Transcription System (A3500, Promega, Mannheim, Germany) according to manufacturer’s instructions. We further added 10 µg BSA per reaction to reduce the inhibitory effect of melanin on reverse transcriptase and DNA polymerase efficiencies64. qRT-PCR was performed using SybrGreen premix (Invitrogen, Carlsbad, CA, USA) in 30 µl final reactions and an iCycler iQ Real Time PCR Detection System (Bio-Rad, Hercules, CA, USA). The PCR program consisted of an initializing step (95 °C for 3 min) and 40 amplification cycles comprising 95 °C for 45 s, 56 °C for 25 s, and 72 °C for 30 s. Each sample/primer combination was measured in triplicate and the Ct values were averaged before normalisation. To obtain normalised mRNA data, we selected two reference genes Hprt and Hexb, which were shown to be stably expressed in the rodent retina regardless of age and sex50,65. Based on the expression levels of the two reference genes, relative expression levels and fold changes of the target genes were calculated following the 2−ΔΔCT method40. DNA primer pairs (metabion international, Planegg, Germany) for Mct8, Oatp1c1, Dio2, Dio3, Thrb, S-opsin, M-opsin, Rho, Coup-TF1, Hprt, and Hexb are listed in Table 3.

### Measurement of resting metabolic rates

RMR were determined by measuring oxygen consumption (VO2) during rest by means of an open-flow respirometry system based on our protocol described elsewhere27. Briefly, the animals were food deprived for at least 4 h before they were individually placed in a custom-made stainless steel chamber with an airtight acrylic glass (Plexiglas) lid. The chamber was submerged into a temperature-controlled water bath to ensure that all measurements were conducted at 29 °C (within the thermoneutral zone27). Each individual was in the respiratory chamber for a minimum duration of 2 h and 3 h maximum. Ambient air was pushed through the chamber with a flow rate of 258 ± 5 ml/min regulated by a flow meter (Model 35830, Analyt-MTC, Müllheim, Germany). Carbon dioxide and water were filtered from the incurrent as well as excurrent air using Soda Lime and Indicating Drierite (Hammond Drierite, Xenia, OH, USA), respectively. Oxygen content of the depleted air was measured by an oxygen sensor (Servomex Type 5200 Multi Purpose, Crowborough, UK) and recorded at intervals of 2 s by DIAdem 8.0 (National Instruments, München, Germany). The lowest 150 consecutive readings (equal to 5 min of measurement) of oxygen consumption were used to calculate RMR following the appropriate equation from Lighton66. All measurements were corrected for BM, flow rate, ambient air pressure and temperature.

### Statistical analyses

Statistical analyses were performed using GraphPad Prism 5 (GraphPad Software, Inc., La Jolla, CA, USA). Relative gene expression data were statistically analysed with two-tailed paired t-test67 to compare gene expression levels in pre- and post-treatment samples from the same animal. In an alternative approach, we excluded data from old animals (boundary arbitrarily set to 1,000 days of age based on fold changes, see results section for details) and analysed expression data from young animals (n = 3) separately for an age-dependent analysis of T4-treated animals. For analysis, data were kept in Ct scale (log2), except for M-opsin/S-opsin ratios, which were calculated from Ct data prior to analysis. The Benjamini-Hochberg procedure was used to adjust p-values for multiple comparisons with the false discovery rate set to 0.0568. Figures are presented as fold changes. ELISA data were compared with two-tailed paired t-test for differences between pre- and post-treatment hormone levels, except for rT3 data, which were analysed with one-way ANOVA followed by Bonferroni correction for multiple comparisons to compare intergroup differences at end of treatment. BM data were analysed by comparing weekly BM with repeated measures ANOVA followed by Bonferroni correction for multiple comparisons. Figures are presented as ΔBM, which was calculated by subtraction of weekly BM from baseline BM (baseline equals 0). msRMR data were analysed with one-way ANOVA followed by Bonferroni correction for multiple comparisons. qRT-PCR, ELISA, BM, and msRMR values were log-transformed prior to analysis, but non-logarithmic values are presented in figures. All data are shown as $$\bar{x}$$ or median ± S.D. or interquartile range, as indicated in figure legends, and significance was defined as *p < 0.05, **p < 0.01, ***p < 0.001.

### Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

## References

1. 1.

Land, M. F. & Nilsson, D.-E. Animal Eyes. (Oxford University Press, 2012).

2. 2.

Peichl, L. Diversity of mammalian photoreceptor properties: Adaptations to habitat and lifestyle? Anat. Rec. A Discov. Mol. Cell. Evol. Biol. 287A, 1001–1012, https://doi.org/10.1002/ar.a.20262 (2005).

3. 3.

Hunt, D. M. & Peichl, L. S cones: Evolution, retinal distribution, development, and spectral sensitivity. Vis. Neurosci. 31, 115–138, https://doi.org/10.1017/s0952523813000242 (2014).

4. 4.

Kock, D., Ingram, C. M., Frabotta, L. J., Honeycutt, R. L. & Burda, H. On the nomenclature of Bathyergidae and Fukomys n. gen. (Mammalia: Rodentia). Zootaxa, 51–55 (2006).

5. 5.

Burda, H., Bruns, V. & Müller, M. Sensory adaptations in subterranean mammals. Prog. Clin. Biol. Res. 335, 269–293 (1990).

6. 6.

Oelschläger, H. H. A., Nakamura, M., Herzog, M. & Burda, H. Visual system labeled by c-fos immunohistochemistry after light exposure in the ‘blind’ subterranean Zambian mole-rat (Cryptomys anselli). Brain. Behav. Evol. 55, 209–220 (2000).

7. 7.

Cernuda-Cernuda, R., Garcia-Fernandez, J. M., Gordijn, M. C., Bovee-Geurts, P. H. & DeGrip, W. J. The eye of the African mole-rat Cryptomys anselli: to see or not to see? Eur. J. Neurosci. 17, 709–720 (2003).

8. 8.

Peichl, L., Němec, P. & Burda, H. Unusual cone and rod properties in subterranean African mole-rats (Rodentia, Bathyergidae). Eur. J. Neurosci. 19, 1545–1558, https://doi.org/10.1111/j.1460-9568.2004.03263.x (2004).

9. 9.

Němec, P., Burda, H. & Peichl, L. Subcortical visual system of the African mole-rat Cryptomys anselli: to see or not to see? Eur. J. Neurosci. 20, 757–768, https://doi.org/10.1111/j.1460-9568.2004.03510.x (2004).

10. 10.

Wegner, R. E., Begall, S. & Burda, H. Light perception in ‘blind’ subterranean Zambian mole-rats. Anim. Behav. 72, 1021–1024, https://doi.org/10.1016/j.anbehav.2006.02.018 (2006).

11. 11.

Kott, O., Šumbera, R. & Němec, P. Light perception in two strictly subterranean rodents: life in the dark or blue? PLoS One 5, e11810, https://doi.org/10.1371/journal.pone.0011810 (2010).

12. 12.

Ahnelt, P. K. & Kolb, H. The mammalian photoreceptor mosaic-adaptive design. Prog. Retin. Eye Res. 19, 711–777 (2000).

13. 13.

Kott, O., Moritz, R. E., Šumbera, R., Burda, H. & Němec, P. Light propagation in burrows of subterranean rodents: tunnel system architecture but not photoreceptor sensitivity limits light sensation range. J. Zool. 294, 67–75, https://doi.org/10.1111/jzo.12152 (2014).

14. 14.

Němec, P. et al. The visual system in subterranean African mole-rats (Rodentia, Bathyergidae): retina, subcortical visual nuclei and primary visual cortex. Brain Res. Bull. 75, 356–364, https://doi.org/10.1016/j.brainresbull.2007.10.055 (2008).

15. 15.

Kott, O., Němec, P., Fremlová, A., Mazoch, V. & Šumbera, R. Behavioural tests reveal severe visual deficits in the strictly subterranean African mole-rats (Bathyergidae) but efficient vision in the fossorial rodent coruro (Spalacopus cyanus, Octodontidae). Ethology 122, 1–13, https://doi.org/10.1111/eth.12515 (2016).

16. 16.

Ng, L. et al. A thyroid hormone receptor that is required for the development of green cone photoreceptors. Nat. Genet. 27, 94–98 (2001).

17. 17.

Roberts, M. R., Srinivas, M., Forrest, D., Morreale de Escobar, G. & Reh, T. A. Making the gradient: thyroid hormone regulates cone opsin expression in the developing mouse retina. Proc. Natl. Acad. Sci. USA 103, 6218–6223, https://doi.org/10.1073/pnas.0509981103 (2006).

18. 18.

Applebury, M. L. et al. Transient expression of thyroid hormone nuclear receptor TRbeta2 sets s opsin patterning during cone photoreceptor genesis. Dev. Dyn. 236, 1203–1212, https://doi.org/10.1002/dvdy.21155 (2007).

19. 19.

Glaschke, A. et al. Thyroid hormone controls cone opsin expression in the retina of adult rodents. J. Neurosci. 31, 4844–4851, https://doi.org/10.1523/jneurosci.6181-10.2011 (2011).

20. 20.

Forrest, D. & Swaroop, A. Minireview: the role of nuclear receptors in photoreceptor differentiation and disease. Mol. Endocrinol. 26, 905–915, https://doi.org/10.1210/me.2012-1010 (2012).

21. 21.

Swaroop, A., Kim, D. & Forrest, D. Transcriptional regulation of photoreceptor development and homeostasis in the mammalian retina. Nat. Rev. Neurosci. 11, 563–576, https://doi.org/10.1038/nrn2880 (2010).

22. 22.

Mendoza, A. & Hollenberg, A. N. New insights into thyroid hormone action. Pharmacol. Ther. 173, 135–145, https://doi.org/10.1016/j.pharmthera.2017.02.012 (2017).

23. 23.

Glaschke, A., Glösmann, M. & Peichl, L. Developmental changes of cone opsin expression but not retinal morphology in the hypothyroid Pax8 knockout mouse. Invest. Ophthalmol. Vis. Sci. 51, 1719–1727, https://doi.org/10.1167/iovs.09-3592 (2010).

24. 24.

Roberts, M. R., Hendrickson, A., McGuire, C. R. & Reh, T. A. Retinoid x receptor γ is necessary to establish the s-opsin gradient in cone photoreceptors of the developing mouse retina. Invest. Ophthalmol. Vis. Sci. 46, 2897–2904, https://doi.org/10.1167/iovs.05-0093 (2005).

25. 25.

Cakir, M. et al. The effect of hypothyroidism on color contrast sensitivity: a prospective study. Eur. Thyroid J. 4, 43–47, https://doi.org/10.1159/000371549 (2015).

26. 26.

Henning, Y. et al. Unusual ratio between free thyroxine and free triiodothyronine in a long-lived mole-rat species with bimodal ageing. PLoS One 9, e113698, https://doi.org/10.1371/journal.pone.0113698 (2014).

27. 27.

Schielke, C. K. M., Burda, H., Henning, Y., Okrouhlík, J. & Begall, S. Higher resting metabolic rate in long-lived breeding Ansell’s mole-rats (Fukomys anselli). Front. Zool. 14, https://doi.org/10.1186/s12983-017-0229-6 (2017).

28. 28.

Zelová, J., Sumbera, R., Sedlácek, F. & Burda, H. Energetics in a solitary subterranean rodent, the silvery mole-rat, Heliophobius argenteocinereus, and allometry of RMR in African mole-rats (Bathyergidae). Comp. Biochem. Physiol. A Mol. Integr. Physiol. 147, 412–419, https://doi.org/10.1016/j.cbpa.2007.01.002 (2007).

29. 29.

Mullur, R., Liu, Y.-Y. & Brent, G. A. Thyroid hormone regulation of metabolism. Physiol. Rev. 94, 355–382, https://doi.org/10.1152/physrev.00030.2013 (2014).

30. 30.

Bernal, J., Guadano-Ferraz, A. & Morte, B. Thyroid hormone transporters - functions and clinical implications. Nat. Rev. Endocrinol. 11, 406–417, https://doi.org/10.1038/nrendo.2015.113 (2015).

31. 31.

Mayerl, S. et al. Transporters MCT8 and OATP1C1 maintain murine brain thyroid hormone homeostasis. J. Clin. Invest. 124, 1987–1999, https://doi.org/10.1172/JCI70324 (2014).

32. 32.

Friesema, E. C. H. et al. Identification of monocarboxylate transporter 8 as a specific thyroid hormone transporter. J. Biol. Chem. 278, 40128–40135, https://doi.org/10.1074/jbc.M300909200 (2003).

33. 33.

Kinne, A., Schulein, R. & Krause, G. Primary and secondary thyroid hormone transporters. Thyroid Res. 4, S7 (2011).

34. 34.

Hagenbuch, B. Cellular entry of thyroid hormones by organic anion transporting polypeptides. Best Pract. Res. Clin. Endocrinol. Metab. 21, 209–221, https://doi.org/10.1016/j.beem.2007.03.004 (2007).

35. 35.

Müller, J. & Heuer, H. Expression pattern of thyroid hormone transporters in the postnatal mouse brain. Front. Endocrinol. (Lausanne) 5, https://doi.org/10.3389/fendo.2014.00092 (2014).

36. 36.

Pizzagalli, F. et al. Identification of a novel human organic anion transporting polypeptide as a high affinity thyroxine transporter. Mol. Endocrinol. 16, 2283–2296, https://doi.org/10.1210/me.2001-0309 (2002).

37. 37.

Bianco, A. C. & Kim, B. W. Deiodinases: implications of the local control of thyroid hormone action. J. Clin. Invest. 116, 2571–2579, https://doi.org/10.1172/jci29812 (2006).

38. 38.

Bernal, J. Thyroid hormone receptors in brain development and function. Nat. Clin. Pract. Endocrinol. Metab. 3, 249–259, https://doi.org/10.1038/ncpendmet0424 (2007).

39. 39.

Davies, D. T. Assessment of rodent thyroid endocrinology - Advantages and pit-falls. Comp. Haematol. Int. 3, 142–152, https://doi.org/10.1007/bf00186098 (1993).

40. 40.

Livak, K. J. & Schmittgen, T. D. Analysis of relative gene expression data using real-time quantitative PCR and the 2−ΔΔCT method. Methods 25, 402–408, https://doi.org/10.1006/meth.2001.1262 (2001).

41. 41.

Satoh, S. et al. The spatial patterning of mouse cone opsin expression is regulated by BMP signaling through downstream effector COUP-TF nuclear receptors. J. Neurosci. 29, 12401–12411, https://doi.org/10.1523/jneurosci.0951-09.2009 (2009).

42. 42.

Buffenstein, R., Woodley, R., Thomadakis, C., Daly, T. J. M. & Gray, D. A. Cold-induced changes in thyroid function in a poikilothermic mammal, the naked mole-rat. Am. J. Physiol. Regul. Integr. Comp. Physiol. 280, R149–R155 (2001).

43. 43.

Bianco, A. C. et al. American Thyroid Association guide to investigating thyroid hormone economy and action in rodent and cell models. Thyroid 24, 88–168, https://doi.org/10.1089/thy.2013.0109 (2014).

44. 44.

Banovac, K., Zakarija, M. & Rabinovitch, A. A study of hepatic metabolism of thyroxine in BB/W rats treated with L-thyroxine. Horm. Metab. Res. 21, 69–72, https://doi.org/10.1055/s-2007-1009153 (1989).

45. 45.

Keck, F. S., Wolf, C. F. & Pfeiffer, E. F. The influence of circulating thyroxine serum concentration on hepatic thyroxine deiodinating activity in rats. Exp. Clin. Endocrinol. 96, 269–277, https://doi.org/10.1055/s-0029-1211019 (1990).

46. 46.

Schoenmakers, C. H., Pigmans, I. G., Poland, A. & Visser, T. J. Impairment of the selenoenzyme type I iodothyronine deiodinase in C3H/He mice. Endocrinology 132, 357–361, https://doi.org/10.1210/endo.132.1.8419134 (1993).

47. 47.

Cheng, C. L., Gan, K. J. & Flamarique, I. N. Thyroid hormone induces a time-dependent opsin switch in the retina of salmonid fishes. Invest. Ophthalmol. Vis. Sci. 50, 3024–3032, https://doi.org/10.1167/iovs.08-2713 (2009).

48. 48.

Burda, H. Reproductive biology (behaviour, breeding, and postnatal development) in subterranean mole-rats. Cryptomys hottentotus (Bathyergidae). Z. Säugetierkunde 54, 360–376 (1989).

49. 49.

Zhang, Y. & Dufau, M. L. Gene silencing by nuclear orphan receptors. Vitam. Horm. 68, 1–48, https://doi.org/10.1016/S0083-6729(04)68001-0 (2004).

50. 50.

Henning, Y. & Szafranski, K. Age-dependent changes of monocarboxylate transporter 8 availability in the postnatal murine retina. Front. Cell. Neurosci. 10, https://doi.org/10.3389/fncel.2016.00205 (2016).

51. 51.

Arbogast, P., Flamant, F., Godement, P., Glösmann, M. & Peichl, L. Thyroid hormone signaling in the mouse retina. PLoS One 11, e0168003, https://doi.org/10.1371/journal.pone.0168003 (2016).

52. 52.

Fujieda, H., Bremner, R., Mears, A. J. & Sasaki, H. Retinoic acid receptor-related orphan receptor α regulates a subset of cone genes during mouse retinal development. J. Neurochem. 108, 91–101, https://doi.org/10.1111/j.1471-4159.2008.05739.x (2009).

53. 53.

Koibuchi, N., Yamaoka, S. & Chin, W. W. Effect of altered thyroid status on neurotrophin gene expression during postnatal development of the mouse cerebellum. Thyroid 11, 205–210, https://doi.org/10.1089/105072501750159534 (2001).

54. 54.

Singh, S., Rajput, Y. S., Barui, A. K., Sharma, R. & Grover, S. Expression of developmental genes in brown fat cells grown in vitro is linked with lipid accumulation. In Vitro Cell. Dev. Biol. Anim. 51, 1003–1011, https://doi.org/10.1007/s11626-015-9930-y (2015).

55. 55.

Kim, B. Thyroid hormone as a determinant of energy expenditure and the basal metabolic rate. Thyroid 18, 141–144, https://doi.org/10.1089/thy.2007.0266 (2008).

56. 56.

Dumitrescu, A. M. & Refetoff, S. The syndromes of reduced sensitivity to thyroid hormone. Biochim. Biophys. Acta 1830, 3987–4003, https://doi.org/10.1016/j.bbagen.2012.08.005 (2013).

57. 57.

Avivi, A. et al. They live in the land down under: thyroid function and basal metabolic rate in the blind mole rat. Spalax. Endocr. Res. 39, 79–84, https://doi.org/10.3109/07435800.2013.833216 (2014).

58. 58.

Rimbach, R., Pillay, N. & Schradin, C. Both thyroid hormone levels and resting metabolic rate decrease in African striped mice when food availability decreases. J. Exp. Biol. 220, 837–843, https://doi.org/10.1242/jeb.151449 (2017).

59. 59.

Woodley, R. & Buffenstein, R. Thermogenic changes with chronic cold exposure in the naked mole-rat (Heterocephalus glaber). Comp. Biochem. Physiol. A Mol. Integr. Physiol. 133, 827–834 (2002).

60. 60.

Clement, K. et al. In vivo regulation of human skeletal muscle gene expression by thyroid hormone. Genome Res. 12, 281–291, https://doi.org/10.1101/gr.207702 (2002).

61. 61.

Akanuma, S., Hirose, S., Tachikawa, M. & Hosoya, K. Localization of organic anion transporting polypeptide (Oatp) 1a4 and Oatp1c1 at the rat blood-retinal barrier. Fluids Barriers CNS 10, https://doi.org/10.1186/2045-8118-10-29 (2013).

62. 62.

Dammann, P. & Burda, H. Sexual activity and reproduction delay ageing in a mammal. Curr. Biol. 16, R117–R118, https://doi.org/10.1016/j.cub.2006.02.012 (2006).

63. 63.

Garcia Montero, A., Burda, H. & Begall, S. Chemical restraint of African mole-rats (Fukomys sp.) with a combination of ketamine and xylazine. Vet. Anaesth. Analg. 42, 187–191, https://doi.org/10.1111/vaa.12180 (2015).

64. 64.

Opel, K. L., Chung, D. & McCord, B. R. A study of PCR inhibition mechanisms using real time PCR. J. Forensic Sci. 55, 25–33, https://doi.org/10.1111/j.1556-4029.2009.01245.x (2010).

65. 65.

Adachi, H. et al. Stage-specific reference genes significant for quantitative PCR during mouse retinal development. Genes Cells 20, 625–635, https://doi.org/10.1111/gtc.12254 (2015).

66. 66.

Lighton, J. R. B. Measuring Metabolic Rates – A Manual for Scientists. (Oxford University Press, 2008).

67. 67.

de Winter, J. C. F. Using the Student’s t-test with extremely small sample sizes. Pract. Assess. Res. Eval. 18 (2013).

68. 68.

Benjamini, Y. & Hochberg, Y. Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. R. Stat. Soc. Series B Stat. Methodol. 57, 289–300 (1995).

## Acknowledgements

Y.H. was supported by a scholarship by Hanno & Gudrun Fiedler (UDE scholarship) and by a grant of the German Research Foundation (DFG-grant DA992/3-1) to Philip Dammann (Central Animal Laboratory, University Hospital, Essen). N.M. and H.B. acknowledge financial support by the Grant Agency of the Czech Republic (project no.: 31-17-19896S). The authors thank Ivonne Görlich (FLI, Jena) for excellent assistance with gene expression analyses, and Sandra Malewski, Patricia Gerhardt, and Marzena Nowak for help with animal care.

## Author information

Authors

### Contributions

Conceived the study and designed the experiments: Y.H., H.B., K.S. and S.B. Conducted experiments: Y.H. (hormone treatments/measurements, expression analyses, metabolic rate measurements) and N.M. (metabolic rate measurements). Analysed the data: Y.H., N.M. and K.S. Wrote the manuscript: Y.H., with significant input from all co-authors. Contributed reagents, materials, analysis tools: H.B., S.B. and K.S. All authors reviewed and approved the manuscript.

### Corresponding author

Correspondence to Yoshiyuki Henning.

## Ethics declarations

### Competing Interests

The authors declare no competing interests.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Rights and permissions

Reprints and Permissions

Henning, Y., Mladěnková, N., Burda, H. et al. Retinal S-opsin dominance in Ansell’s mole-rats (Fukomys anselli) is a consequence of naturally low serum thyroxine. Sci Rep 8, 4337 (2018). https://doi.org/10.1038/s41598-018-22705-y

• Accepted:

• Published:

• ### The topography of rods, cones and intrinsically photosensitive retinal ganglion cells in the retinas of a nocturnal (Micaelamys namaquensis) and a diurnal (Rhabdomys pumilio) rodent

• Ingrid van der Merwe
• , Ákos Lukáts
• , Veronika Bláhová
• , Maria K. Oosthuizen
• , Nigel C. Bennett
• , Pavel Němec
•  & Gianluca Tosini

PLOS ONE (2018)


text:
Tag Info

11

It's probably impossible to prevent chromatic aberration, since there is no such thing as a perfectly achromatic lens. but you can certainly minimize it. As you have mentioned, for a given spectral range, the best way is to choose a lens that is said to be "achromatic" even though the correction is never perfect. But if you want to use a lens that is not ...

11

All telescopes have in common that they gather and focus light from far away objects. They use a primary opical element, such as a concave mirror or a (planar- or bi-)convex lense (or lense system), and they use an eyepiece with another lense system (for viewing) or a camera in their primary focus. A refractor telescope does not sharpen the image per se. ...

9

The first question anyone asks about a telescope is "what is the magnification?" It is almost always not the most important thing. Any telescope can magnify a million times, given a short enough eyepiece - the problem is, how good the image is. For observing planets, the main thing is resolving power - the ability of the telescope to discern tiny details. ...

7

Yes, stacking Barlow lenses is a common practice to effectively increase focal length by multiplying their individual focal lengths. When I say common, most advanced eyepieces actually have many glass elements and are a type of a Barlow lens themselves, so just by using a single Barlow lens in front of your eyepiece you'd already be, technically, stacking ...

5

The Moon is the easiest target to start with. After that, try whichever bright planets are currently in the sky: Jupiter, Saturn, Mars, Venus. Then get a star map and try to find some of the brighter star clusters, nebulas, and galaxies. I recommend the monthly sky maps and object lists at Skymaps.com. Latitude 19°N falls midway between their northern ...

5

Canon camera has another method to reduce or cancel chromatic abberation they call Diffractive Optics. The idea is to use a lens with a diffraction pattern in it that causes the chromatic aberration to bend the opposite way from normal lenses. So if blue is bending the most through the normal lens, then it will bend the least when going through the ...

5

A fouth approach to add to @Uhoh's 3 others, is to make the lens of extra low dispersion glass. Dispersion is a measure of how refractive index varies with colour. However such glass is relatively difficult to make, in the quality required for lenses, and so rather expensive. Further information about dispersion can be found on this wikipedia page https:/...

4

An 18.5 inch telescope is easily large enough to collect the photons you require. So long as you have a good CCD camera, with a pixel size on the sky that is considerably smaller than the "seeing" and you take a great deal of care in how you make and analyse the observations. Exposure times can be minutes if necessary, because a typical transit lasts a ...

4

A bright, nearby star with a large exoplanet would be best. For example, the first star to have a transiting planet observed was HD 209458, in Pegasus. It has a magnitude of 7.65. When the large "hot jupiter" transits the star it dims by a relative flux of 0.984. That corresponds to a change in magnitude of about 0.016. I.e. it changes from a magnitude 7.65 ...

3

This is a really interesting question! The Dragonfly telescope described below takes advantage of the fact that on Earth, the optical surfaces of some lenses can generate less diffuse scattering than the optical surfaces of reflecting telescopes. If you were worrying about scattering from secondary mirrors you could make an off-axis primary, but at a ...

3

Further would a Barlow lens solve the chromatic aberration issues with a f/5 refractor. I suppose in theory they could, but they would have to be designed to do so. In practice, they vary widely in quality, and either don't have an effect on chromatic aberration, or actually make it worse. Which would be a better option? There is no objective way of ...

3

1. Resolving power and diffraction Diffraction happens anywhere there's an edge. "It is defined as the bending of light around the corners of an obstacle or aperture into the region of geometrical shadow of the obstacle." (Wikipedia) So all you need for diffraction is an obstacle of any shape - at the edge of the obstacle, the light will bend a little. In ...

3

I'll attempt to answer as many of these questions, to the best of my abilities, as I can at this late hour. 1) Lenses have an index of refraction that is different than vacuum, and air, and they are curved. ie: corners when light is concerned. 2) The entrance and exit pupils are the pupil size required to pass an "extreme" ray through an optic. Meaning ...

3

Actually, your Newtonian may run the risk of suffering from the projection method. The secondary, planar mirror in the Newtonian will be subject to heating. Although it is not in the prime focal point, the light rays are already pretty much bundled up, and this may lead to heating and ultimately to failure of the secondary mirror! With refractors, you don't ...

3

You would be better off using lens 5 and 3. Though don't expect much, a simple single lens for the objective and for the eyepiece will give a lot of chromatic aberration (false colour). Refracting telescopes usually use at least two lens of different glass types (crown & flint often in a doublet) and eyepieces usually have 4+ lens. You should be able to ...

2

I generally agree with the answer above, but have a couple more insights which might help you if you decide to proceed with trying to make your own scope... The lens pairs that James mentioned (crown and flint) are known as a doublet. Glass has two key properties in play here - its index of refraction (how much it bends light) and its dispersion (how much ...

2

It depend where vibration are. Often (if you have a good mount for the telescope) all the structure vibrate and there are some good anti-vibration feet that can be useful. If the tripod isn't the problem and the vibration are only near the telescope, probably the problem is the mount that is under-sized for you telescope. In this case the only good way is ...

2

The refractor will be better for wide-field observing of starfields and big nebula and galaxies. For planets and small to medium (also larger with 2" eyepieces or just 1.25" eyepieces with a low magnification and big apparent field of view) sized DSOs (nebulae, galaxies and star clusters) the reflector will have an advantage due to its aperture. The only ...

2

Item B is called a visual back. The new focuser would just replace this, and screw onto item A. The focuser you link to is designed for a refractor, but you need one for a SCT, like this https://www.firstlightoptics.com/skywatcher-focusers/dual-speed-2-crayford-focuser-for-sct-telescopes.html There are lots of different makes and prices. Regarding the ...

1

It's 70mm aperture, so the maximum useful magnification will be 165x. If you have a 4mm eyepiece, you will have 75x magnification, and at that, you can expect to see rings of Saturn, moons of Jupiter in good conditions. Venus will show phases. I can't say much about Mercury. You can see many surface features of the Moon. The view will be particularly good at ...

1

There is a wide variety of telescopes, so it's a bit difficult to give a general answer, but here are some pointers: If there is an open-end, it likely is a reflector telescope (perhaps a Newton). In this case, you can see the secondary mirror attached inside. When you look through the place where you set the eyepiece, are you facing the same direction as ...

1

I have viewed through many telescopes over the years and in doing so have met many people like yourself. To suggest a F/12.5 Maksutov will satisfy you would be the equivalent of telling someone to dive into the deep end of a swimming pool without knowing if that person can swim. If it's bang for buck that motivated your question I think you would get the ...

1

First off I want to say I am a complete amateur when it comes to stars and even bigger when it comes to optics. I was looking at sky from indoors and my windows have double glass. It turns out that this was the problem or maybe the glass on the window is not some good quality. In any case, all works well now and I am thrilled at what I'm seeing in the ...

1

Meade make the 497 auto star hand controller, which plugs in where your existing hand controller goes. This turns your mount into a fully computerised one. Alternatively you should be able to use a laptop to control the mount via the aux ports. It’s all in the manual. If your telescope did not originally come with the auto star hand controller, here is a ...

1

Depending on the root cause, vibration damping pads may or may not help. Some telescope vendors sell sets of three for $50 or so; an Internet search also yields a few do-it-yourself recipes using silicone caulk, sorbothane insoles, etc. Other home remedies are possible, such as adding weight or shims to the mount, or hanging a chain from the optical tube ... 1 You already have an answer but there are a few interesting Physics things in your question that are linked: 1) Diffraction and the fact that telescopes have no "slit". 5) Stars don't appear as a sphere, they appear as dots. The telescope has a round aperture (of say 60mm or so) and this behaves as a slit in some ways. It causes diffraction patterns (an ... 1 There are a few rules of thumb you will need: Maximum useful magnification$M_{max}\approx D\times 50$where$D$is the diameter of the objective is in inches, and magnification$M=l_{obj}/l_{eye}$, where$l_{obj}$and$l_{eye}\$ are the focal lengths of the objective and eye piece respectively.

Only top voted, non community-wiki answers of a minimum length are eligible

format: plain


text:
# Problem with units

1. Oct 14, 2005

### Henk

I'm having great difficulties with CGS-units. In an experiment involving NMR I have to calculate the proton-proton distance in CaSO4.2H2O.

I have done the measurements and they are, I think, pretty good however I have some problems with the calculations because of the units.

The formula I have to use is the following:

a = (3/2)(u*u0)/r^3

where u = 2.79*5.05*10^-27 J/T = 2.79*5.05*10^-24 erg/Gauss and u0 is the Permeability of vacuum. a is something I measured and has a value of 4.5 Gauss.

I know that r should be about 1.5 Angstrom (spelling?). My instructor told me to use CGS-units (thus putting u0=1) but does that mean that the rest of the formula stays the same? Or are there other changes like an additional 4pi or something. If I just put u0=1 I get r = 1.67*10^-8 (but I don't know the units, I believe the CGS-unit for distance is cm in which case r=1.67*10^-10 m = 1.67 A which is pretty close to 1.5 A).

2. Oct 15, 2005

### vanesch

Staff Emeritus
Why don't you do the calculations first in SI units, and convert in the end in CGS ? I also get confused often between CGS, Gaussian, Natural,... etc units concerning EM quantitities because indeed, some include a 4 pi, others don't etc...

So I then do everything in SI units, and fill in the 4 pi in the other units in order to obtain the same result


text:
# Realization of divide by 78 counter

I am unable to pick the right option from the below

A divide by 78 counter can be realized using?
a) 6 number of mod 13 counters
b) 13 number of mod 6 counters
c) one mod-13 counter followed by one mod 6 counter
d) 13 number of mod-13 counters

I know a divide by 78 counter has 78 states so I decided that answer cannot be C because a mod-13 counter has 13 states and mod-6 has 6 states total making up only 20 states and then the next option is D that has 13 *13 = 169 states more than required. I think it must be a or b and the is b according to the book I solved but my question is why it can't be a?

  mod-6 counter has 6 states so total 13*6 = 78 . this was the explanation
but mod-13 counter has 13 states so total 6*13 = 78 both are same

Iam unable to find out the reason why the answer is B. kindly help me with this. Thanks

The book is wrong. The right answer is C. 78=13*6. The mod-13 counter will be incremented with each pulse of the incoming signal, and will overflow every 13 counts of such pulses. The mod-6 counter will be incremented each time that the mod-13 counter overflows. The mod-6 counter will overflow every 6 of its counts. Therefore, the mod-6 counter will overflow every 6*13=78 pulses of the incoming signal.

In other words, for each state of the mod-6 counter, the mod-13 counter counts 13 states. So, in total, you will have 6*13=78 different "global" states. That's why, if you have them one after the other (so that counter k increments one unit when counter k-1 overflows), you have to multiply the numbers of states, not add them.

These will be the count values for each of the two counters, before each pulse at the input.

{(mod-13 counter value) (mod-6 counter value)}
{0 0}
{1 0}
...
{12 0}
{0 1}
{1 1}
...
{12 1}
{0 2}
{1 2}
...
...
{12 5}
<-- Here is the overflow for the global counter formed. Above this line, there are 78 different states.
{0 0}
...

Also:
a) and d) are wrong, because there is no integer N such that $13^N=78$.
b) is wrong, because there is no integer N such that $6^N=78$.

• Incidentally, because six and thirteen are relatively prime, one could also have both counters increment on every clock cycle, and have the output go high when both counters are simultaneously zero. – supercat May 22 '12 at 21:09
• @supercat Right, but then you would need an extra gate, which is not offered. – Telaclavo May 22 '12 at 21:36
• The approach is a useful one to know when designing logic to go in a PLD, since large-fan-in gates are cheap, but simulating count-enable or latch-enable signals is expensive. If one needs to use a separate macrocell to produce the output anyway (e.g. because one wants an output which is high for one pulse out of 78) it may be worthwhile to simplify all the other counters and just watch for them to fire 'in sync'. – supercat May 22 '12 at 22:06


text:
# Math Digest

## Summaries of Media Coverage of Math

Edited by Allyn Jackson, AMS
Contributors:
Mike Breen (AMS), Claudia Clark (freelance science writer), Lisa DeKeukelaere (2004 AMS Media Fellow), Annette Emerson (AMS), Brie Finegold (University of California, Santa Barbara)

### September 2007

"Sorting Out the Genome," by Brian Hayes. American Scientist, September-October 2007, pages 386-391.

One way to measure the evolutionary distance between species is by examing their genetic codes and counting the number of reversals in genetic strings between the two. For example, badcef is two reversals away from abcdef. Is there an algorithm to find the minimum number of reversals in much longer strings? The answer is yes, and it involves signed permutations, for which the problem is easier to solve than it is for unsigned permutations. In this article Hayes describes the development of the algorithm and its relevance to genetics. Near the end of the article, he writes that "The decade-long effort to solve the sorting-by-reversals problem stands as a model of interdisciplinary collaboration. The question that inspired the work in the first place was of genuine importance to biology, but it also turned out to hold real interest for mathematicians and computer scientists, who might well have tackled the problem even if it didn't have an appealing application."

--- Mike Breen

"The fine art of painting by the numbers," by Kyle MacMillan. Denver Post, 30 September 2007.
"Math adds unique dimension to show," by Mary Voelz Chandler. Rocky Mountain News, 5 October 2007.

 A/C Kepler, 70 inches by 70 inches, acrylic on canvas, 2007, by Clark Richert. Image courtesy of Clark Richert. The Museum of Contemporary Art in Denver invited Clark Richert to create a design to be incised into the driveway of the institution's new building. Richert's work is also featured in the "Quasi-Symmetries" solo exhibition at Denver's Rule Gallery. He tells reporter Chandler that his father and a brother are mathematicians, another brother is a physicist and his sister is a doctor, and notes that although he trained in fine art he "seem[s] to have gravitated to mathematics." His works incorporate mathematical and scientific concepts such as tiling and patterns. One work is titled Riemannian Tangencies, in tribute to the great 19th-century German mathematician G. F. B. Riemann. Chandler concludes, "Happily for us, he has combined the two---mathematics and art---into work that for a change really merits the word unique." --- Annette Emerson

"Les demoiselles d'Avignon", by Arthur L. Miller. New Scientist, 29 September 2007, pages 50-51.

This article describes the mathematical influences that led to Picasso's conception of his 1907 painting Les Demoiselles d'Avignon, which marks the birth of cubism. Picasso was very interested in photography and alternative ways to project reality onto a two-dimensional space. The mathematical influences came through an insurance actuary named Maurice Princet, who showed Picasso a book by Esprit Jouffret about complex polyhedra in four dimensions. Jouffret was also a friend of the great mathematician Henri Poincaré, and Princet gave Picasso and his circle of friends lectures about Poincaré's ideas. The face of the squatting figure in the painting is "a projection from the fourth dimension, in which front and profile views are seen simultaneously, her head swiveled 180 degrees," Miller writes. "The seeds of cubism had been planted."

--- Allyn Jackson

"Mathematician puts people back into the equation", by Peggy Curran. The Gazette (Montreal, Canada), 29 September 2007.

William Byers, the author of How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox, celebrates the chaotic rather than systematic nature of mathematical thinking. A mathematics professor at Concordia University in Canada, Byers says "Zero is clearly a paradox." And although the article states that the book has garnered good reviews in math journals, a reviewer for the Mathematical Association of America, computer scientist David J. Stucki, writes that the book "fails to deliver on many levels." A more complimentary review by mathematician Gregory Chaitin appeared in New Scientist (see July Math Digest). Peggy Curran writes, "As someone who wouldn't know a dodecahedron if I met one on the street, I was in no position to quibble when Byers cited irregularities from the simplest 1+1=2 through the complexities of Euclidean Geometry."

--- Brie Finegold

"2007 Visualization Challenge." Science, 28 September 2007, pages 1857-1863.
"A Video That's Worth a Million Words," by Julie J. Rehmeyer. Science News Online, 17 November 2007.
"U of M math video is a Web hit," by Tom Crann. Minnesota Public Radio: All Things Considered, 28 November 2007.
"UMinn Profs' Math Video is YouTube Phenom; 1M Hits." WCCO-TV, 5 December 2007.
"Mathematics Professors' Video About Möbius Transformations Is a YouTube Hit", The Wired Campus, Chronicle of Higher Education, 19 December 2007.

 Visualization of a Möbius transformation. (Image courtesy of Douglas Arnold, Institute for Mathematics and its Applications, University of Minnesota.) "Möbius Transformations Revealed," a video by Douglas Arnold and Jonathan Rogness (University of Minnesota), won Honorable Mention in the 2007 Science and Engineering Visualization Challenge, sponsored by Science and the National Science Foundation (NSF). The video shows transformations in the plane and then relates them to movements of a sphere. When this item was first posted, "Möbius Transformations Revealed" had over 50,000 hits on YouTube, which is pretty impressive, but by December the video had collected more than one million hits at the site. All of the winning entries in the challenge appear in the issue and online. The winning entry, a photo of seaweed Irish moss, was featured on this issue's cover. The NSF site has details on how to enter the 2008 Challenge. Rehmeyer's article has some stills from the video and explains some of the video's geometry. --- Mike Breen

"Local Politics, Web Money," by Amy Schatz. The Wall Street Journal, 28 September 2007, page A6.

 Daniel Biss. (Photo: Jill Norton Photography) In this article, writer Amy Schatz discusses how the Democratic fund-raising site ActBlue.com is affecting political races. Created in 2004, ActBlue has raised more than US$28 million for Democratic candidates. Last year it began widening its focus to include local as well as national races. Enter Daniel Biss, a 30-year-old University of Chicago mathematics professor running for a seat in the Illinois state legislature. He decided to become politically active after 9/11 and the beginning of the Iraq war. Biss has raised over US$37,000 online. In fact, the level of funds raised on ActBlue for Biss over one recent week came in second only to funds raised for Democratic presidential candidate John Edwards. However, the incentives for people to donate to his campaign are not likely to be used by the Edwards campaign: John Green, a friend of Biss, raised more than US\$3,200 online by promising to eat a liquefied Happy Meal, to wax one leg, and then to post the video on YouTube, if at least 200 people donated to Biss's campaign online. They did, and the video of Green making good on those promises has been watched over 16,000 times on YouTube. (Biss is the 1999 winner of the Morgan Prize and is on the Editorial Board of the Notices of the AMS.) --- Claudia Clark

"Bellas geheimes Seminar (Bella's secret seminar)", by George Szpiro. Die Zeit, 27 September 2007.

 Bella Subbotovskaya. (Photo courtesy of Ilya Muchnik. Picture quality improved by Poline Tylevich.) This article describes the life of an extraordinary woman, Bella Subbotovskaya, who in Soviet-era Moscow founded an underground university for Jewish mathematics students in 1978. Many such students were prevented due to anti-Semitism from studying at state universities. Subbotovskaya, a strong-minded mathematician and musician, founded the "Jewish People's University" out of a selfless desire to help others have educational opportunities they were unfairly denied. Her university ran until 1983, when Subbotovskaya died in a mysterious hit-and-run accident. The original English version of this article appears in the November 2007 issue of the AMS Notices. --- Allyn Jackson

"Ups and downs of a senator scientist": Review of The Volterra Chronicles: The Life and Times of an Extraordinary Mathematician 1860-1940 by Judith R. Goodstein. Reviewed by Salvatore Coen. Nature, 27 September 2007, pages 406-407.

 Judith Goodstein's The Volterra Chronicles: The Life and Times of an Extraordinary Mathematician 1860-1940 offers a look at Vito Volterra, the man who gave the world the predator-prey model, now learned by math students everywhere as a way to describe the way populations interact. His mathematical achievements are set against the backdrop of World War II Europe, where he suffered for his anti-fascist politics. As a mathematics professor at multiple Italian universities, Volterra contributed to mathematical research in a variety of fields, but his most well-known work was in biological modeling. An Italian Jew, he was also a senator who dared to speak out against Mussolini and to collaborate on military action and scientific research with scientists in allied countries. Goodstein's biography of Volterra also details his correspondence with other famous mathematicians of his time and includes translations of his letters in order to offer a unique insight into his personality and contributions. --- Lisa DeKeukelaere

"Business by numbers." The Economist, 25 September 2007, pages 85-87.

The subject of this article is the importance of algorithms to business. Businesses use algorithms to improve processes, such as product delivery, and to analyze data, such as records of consumer purchases. An example of the first type is UPS's VOLCANO algorithm that UPS uses to schedule its airline fleet. UPS estimates that the algorithm has saved the company tens of millions of dollars since 2000. Examples of the second type are algorithms to detect consumer fraud and Internet search algorithms. Algorithms still depend on humans, though. The article cites a case of a UPS planning model that routed all packages through Iowa because of a data error that made it appear that sending packages to Iowa was free.

--- Mike Breen

"Microsoft Says Excel 2007 Produces Math Errors," by Paul McDougall. Information Week, 26 September 2007.
"Excel 2007 flunks some math problems," by Gregg Keizer. Computerworld, 26 September 2007.

The original version of Excel 2007 has trouble with calculations that result in numbers near 216. Molham Serry discovered that when he asked Excel 2007 to do 850 times 77.1, the program returned 100,000 instead of 65,535 (216 - 1). Microsoft manager David Gainer said that the problem, peculiar to Excel 2007 and not to earlier versions of Excel, is not in the calculation, but in the code that formats the displayed result. He noted that if a user does the previous calculation and then asks Excel to multiply that result by two, the final result displayed will be 131,070 (which is correct), not 200,000. The bug reportedly was fixed in the second week of October.

--- Mike Breen

"Report: Mixed Grades for No Child Left Behind," by Peg Tyre. Newsweek, 25 September 2007.
"On a Nationwide Test, Improving Math Scores Outpace Reading Gains," by Eddy Ramírez. U.S. News and World Report, 26 September 2007.
"Math Scores Up for 4th and 8th Graders," by Nancy Zuckerbrod. Associated Press, 26 September 2007.
"U.S. Test Results Show Growth in Math, Not Reading," by Claudio Sanchez. All Things Considered (NPR), 26 September 2007.

The National Assessment of Educational Progress (NAEP) released its "report card" on the progress of U.S. fourth- and eighth-grade students in math and reading. The percentage of fourth graders rated proficient or better went up three points to 39% and the percentage of eighth graders rated similarly went up two points to 32%. Some people, such as Secretary of Education Margaret Spellings, attributed the progress to No Child Left Behind (NCLB) programs, while others, such as the director of the Cato's Institute Center for Educational Freedom, said that the improvements are the result of measures taken before NCLB went into effect. The U.S. News and World Report article begins with a question from the test taken by fourth graders: The Ben Franklin Bridge was 75 years old in 2001. In what year was the bridge 50 years old? Thirty-six percent of the fourth graders chose the correct answer. The NAEP report on math scores is online.

--- Mike Breen

"In Theory, Diamondbacks Are Winning Way Too Often," by Dan Rosenheck. New York Times, 23 September 2007, Sports page 6.
"Why a dead Greek mathematician says the D-Backs won't win it all," by Kyle Wright. Pensacola News Journal, 5 October 2007.

Baseball statisticians use a statistic they call the Pythagorean Theorem ([runs scored2 + runs allowed2]/runs allowed2) because of its similarity to the theorem about right triangles. Since 1901, 95 percent of teams' won-lost records in Major League Baseball have been within eight games of the formula's projection. At the time of the publication of the New York Times article, the number of wins by the Arizona Diamondbacks exceeded the number predicted by the theorem by the largest amount recorded since 1901. The Diamondbacks scored fewer runs than they allowed, yet won their division, mostly because of the team's record in games decided by one run: 32-20. Baseball statisticians expect a team's record in such games to be much closer to 50-50. Some of the Diamondbacks' success is attributed to luck, and some to the performance of its bullpen. Kyle Wright, author of the second article, was right: After sweeping the Chicago Cubs in the Divisional Series, the Diamondbacks themselves were swept by the Colorado Rockies in the National League Championship Series. The Diamondbacks' record in the playoffs was 3-4, scoring 24 runs and giving up 24. Their only one-run game was a loss.

--- Mike Breen

"Women, Girls, and Math," hosted by Ira Flatow. NPR Science Friday, 21 September 2007.

This one-hour-long NPR piece features conversations with former Wonder Years star and math major Danica McKellar, Harvey Mudd College President Maria Klawe, and two women involved with the US team that competed in the 2007 China Girls Math Olympiad. All four women spoke to the importance of teachers reaching out in the classroom to math students of both genders by providing real-world examples and encouraging students not to be frustrated by a certain type or level of mathematics---there is no math gene, and practice makes perfect. McKellar, who is promoting her new book Math Doesn't Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail, noted that most math students are drawn to the subject by one special teacher who provides a comfortable environment for doing math. In doing research for the book, she discovered that girls today are still inhibited by a sense of needing to "be nice" or "play dumb" in the classroom, which prevents them from asking questions and learning more.

--- Lisa DeKeukelaere

"Fast Computers and the Music of Math" by Caroline Evans. Song of the Day on National Public Radio, 20 September 2007.

The song of the day on 20 September was "Sweden Hasn't Changed, You Have," by the band named Fast Computers. The band's first album, Heart Geometry, includes song titles "Math Predictions" and "Gravity/Love," which "betray the band's interest in the mathematical." Although the vocals "concentrate only fleetingly on math" reviewer Evans notes that "the group also uses math to trace intricate musical patterns and ornate designs." Hear the segment and the featured song on NPR.

--- Annette Emerson

"A Lust for Numbers": Review of The Indian Clerk, by David Leavitt. Reviewed by Nell Freudenberger. New York Times, 16 September 2007.

David Leavitt's new novel has as its main characters two historical figures from twentieth century mathematics: the Briton G. H. Hardy, a Cambridge don and one of the leading number theorists of his time, and the young Srinivasa Ramanujan, brilliant, self-taught Indian mathematician. The novel explores the relationship between these two very different mathematicians---a relationship that, at least for Hardy, had romantic overtones. The reviewer writes: "[W]hat [Leavitt] makes of their relationship is much more subtle than a love affair. Initially frustrated by the young genius's tendency to pursue several ideas in an associative fashion, Hardy eventually realizes he has come in contact with a mind that expands his notion of their discipline." The review does not discuss mathematics much, beyond saying that Hardy was working on the Riemann Hypothesis. For citations of other reviews of this book, visit the Reviews page on the AMS web site.

--- Allyn Jackson

"Reality by numbers," by Max Tegmark. New Scientist, 15 September 2007, pages 38-41.

In this article, MIT physicist Max Tegmark makes a case for what he calls "the mathematical universe hypothesis". The idea is to strip away from our description of the universe all human-defined concepts---Tegmark offers protons, stars, and molecules as examples of such concepts---in order to lay bare the mathematical structure they embody. Without such human-defined "baggage", Tegmark claims, "a sufficiently large supercomputer could calculate how the state of the universe evolves over time without interpreting it in human terms." The article contains some baffling passages. For example, Tegmark likens a physicist's outside overview of external reality to the viewpoint of a bird surveying the landscape from high above; the inside view of an observer living in that reality is like the viewpoint of a frog that is part of the landscape the bird is seeing. "[F]rom the bird's perspective, trajectories of objects moving in four-dimensional space-time resemble a tangle of spaghetti," Tegmark writes. "Where the frog sees something moving with constant velocity, the bird sees a straight strand of uncooked spaghetti. Where the frog sees the moon orbit the Earth, the bird sees two intertwined spaghetti strands. To the frog, the world is described by Newton's laws of motion and gravitation. To the bird, the world is the geometry of the pasta." Tegmark says that the biggest objection to the mathematical universe hypothesis is that it is "counter-intuitive and disturbing", a reaction that he dismisses "as a failure to appreciate Darwinian evolution."

--- Allyn Jackson

"Penetrating the mumbo-jumbo": Review of The Tiger that Isn't, by Michael Blastland and Andrew Dilnot. Reviewed by Mike Holderness. New Scientist, 15 September 2007, page 57.

This book is an extension of the authors' BBC radio program More or Less, which aims to raise the level of mathematical literacy among the general public. One reason bogus numbers and statistics make their way so frequently into public discourse is that so many people do not understand even basic mathematics. The reviewer states that, according to surveys, one in three people "do not understand percentages at all" (and then he parenthetically quips: "Hang on: one-third of which population?"). Thus the authors of this book have taken on a daunting task. They "succeed engagingly," the review says, "even providing some very accesible critiques of quite advanced statistics."

--- Allyn Jackson

"Using Math to Track Terrorists," by Joe Palca. Science Friday (NPR), 14 September 2007.

In the first half hour of the program, Rochester Institute of Technology mathematics professor Bernard Brooks and University of Arizona professor of management information systems Hsinchun Chen speak with Palca about the ways that mathematics and computer science are being used to track down terrorists. Brooks discussed how patterns of terrorist communications have been studied and modeled using graph theory. For example, given that one member of a terrorist cell has been identified on a network that can be monitored, Brooks stated that "we can use some of the algorithms useful for searching social networks to identify the clique of the terrorist cell" without necessarily even having to listen to the content. Chen noted how "tech mining" and "opinion mining" can be used along with language processing and mathematical models to identify "the most critical members and the most critical messages that you really need to pay more attention to" on existing forums.

--- Claudia Clark

"Ein Neuling in der Walhalla (A newbie in the Valhalla)". Süddeutsche Zeitung, 13 September 2007, page 46.

The Walhalla, located near Regensburg, Germany, is a collection of marble busts depicting outstanding Germans. This year a bust of Carl Friedrich Gauss (1777-1855) was the 128th addition to the collection. The short item in the Süddeutsche Zeitung is basically a caption for a photo of the bust of Gauss. The item describes Gauss as "one of the most important mathematicians of all time" but gives no hint of his achievements beyond saying that he "developed many formulas".

--- Allyn Jackson

"Kristalle für Köln (Crystals for Cologne)", by Ulf von Rauchhaupt. Frankfurter Allgemeine Zeitung, 9 September 2007, page 67.

Taking the new stained-glass windows in the renowned cathedral in Cologne, Germany, as its starting point, this article discusses how mathematical notions of randomness can be used to create tiling patterns similar to those used in stained-glass windows.

--- Allyn Jackson

"May the Best Team Win," by Julie Rehmeyer. Science News Online, 8 September 2007.

Luck is a much more important player on the baseball field than you might think, according to a physicist from Los Alamos National Laboratory who recently computed that the team with the best record wins only 56 percent of the time. He found that playing a season of continuous play-off style elimination rounds would increase the odds that the best team would win the World Series, but this system probably will never be implemented because fans like to see the underdog win---an event bolstered by the importance of luck over skill on the field. In both baseball and football, the strongest team ends up with the best record only 30 percent of the time. This indicates not only that chance is a bigger factor in baseball than in football, which plays far fewer games per season, but also that this number---30 percent---may be the ideal balance of luck and skill needed to please the fans.

--- Lisa DeKeukelaere

"Beautiful Minds," by Virginia Postrel. The Atlantic, September 2007, pages 140-141.

The public's stereotypes mad scientists and mathematicians are not easy ones to dispel. So how to explain the success of the television shows CSI and NUMB3RS, whose stars are a scientist and a mathematician, respectively? Neither show resorts to science fiction or conspiratorial cover-ups of alien sightings, so what makes the characters so compelling? Postrel thinks that the shows "align scientific curiosity with justice." The shows promise that the use of science and mathematics will lead to the truth, untainted by external pressures. She writes that the series' main characters' eccentricity does not alienate them from the viewer but instead "makes them more perceptive and, in many cases, more empathetic." The special quality of Charlie Eppes, the mathematician in Numb3rs, is that he sees patterns that others don't.

--- Mike Breen

"D'où viennent les maths? (Where does math come from?)", by Mathieu Grousson. Science et Vie, September 2007, pages 50-67.

This three-part article explores questions about the origin of mathematical ideas. The first part of the article discusses recent research showing that the human brain has an innate sense of numbers, and the second part looks at mathematical artifacts from ancient civilizations. The third part is titled "Math: Reality or pure mental construction?" and features interviews with two French mathematicians, J.-P. Delahaye and J.-P. Bourguignon. Delahaye comes down on the side of math having a separate reality: "When I do mathematics, I am convinced of having encountered a reality that is apart from me and that has not waited until I am there to take the form that I discover." Bourguignon, by contrast, argues that mathematics is a product of human minds. Asked if math has an independent existence, he replies: "No, I think that the cultural context determines the emergence of certain concepts." There are also interviews with historian of science A. Dahan and philosopher A. Barberousse.

--- Allyn Jackson