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The SPECTRA Procedure

Overview: SPECTRA Procedure

The SPECTRA procedure performs spectral and cross-spectral analysis of time series. You can use spectral analysis techniques to look for periodicities or cyclical patterns in data.

The SPECTRA procedure produces estimates of the spectral and cross-spectral densities of a multivariate time series. Estimates of the spectral and cross-spectral densities of a multivariate time series are produced using a finite Fourier transform to obtain periodograms and cross-periodograms. The periodogram ordinates are smoothed by a moving average to produce estimated spectral and cross-spectral densities. PROC SPECTRA can also test whether or not the data are white noise.

PROC SPECTRA uses the finite Fourier transform to decompose data series into a sum of sine and cosine waves of different amplitudes and wavelengths. The finite Fourier transform decomposition of the series is

where

t

is the time subscript,

are the equally spaced time series data

n

is the number of observations in the time series

m

is the number of frequencies in the Fourier decomposition: if n is even, if n is odd

k

is the frequency subscript,

is the mean term:

are the cosine coefficients

are the sine coefficients

are the Fourier frequencies:

Functions of the Fourier coefficients and can be plotted against frequency or against wave length to form periodograms. The amplitude periodogram is defined as follows:

Several definitions of the term periodogram are used in the spectral analysis literature. The following discussion refers to the sequence as the periodogram.

The periodogram can be interpreted as the contribution of the kth harmonic to the total sum of squares (in an analysis of variance sense) in the decomposition of the process into two-degree-of-freedom components for each of the m frequencies. When n is even, is zero, and thus the last periodogram value is a one-degree-of-freedom component.

The periodogram is a volatile and inconsistent estimator of the spectrum. The spectral density estimate is produced by smoothing the periodogram. Smoothing reduces the variance of the estimator but introduces a bias. The weight function used for the smoothing process, W(), often called the kernel or spectral window, is specified with the WEIGHTS statement. It is related to another weight function, w(), the lag window, that is used in other methods to taper the correlogram rather than to smooth the periodogram. Many specific weighting functions have been suggested in the literature (Fuller, 1976; Jenkins and Watts, 1968; Priestley, 1981). Table 26.3 later in this chapter gives the relevant formulas when the WEIGHTS statement is used.

Letting i represent the imaginary unit , the cross-periodogram is defined as follows:

The cross-spectral density estimate is produced by smoothing the cross-periodogram in the same way as the periodograms are smoothed using the spectral window specified by the WEIGHTS statement.

The SPECTRA procedure creates an output SAS data set whose variables contain values of the periodograms, cross-periodograms, estimates of spectral densities, and estimates of cross-spectral densities. The form of the output data set is described in the section OUT= Data Set.


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# DAVIDSTUTZ

12thJANUARY2015

A. Vedaldi, S. Soatto. Quick Shift and Kernel Methods for Mode Seeking. European Conference on Computer Vision, 2008.

Proposed in 2008, Quick Shift is a segmentation algorithm based on mode seeking which can also be used to generate superpixels. In general, a mode seeking algorithm starts from a Parzen density estimate $p(x_n)$ for all pixels $x_n \in \{1,\ldots,W\} \times \{1,\ldots,H\}$ (here, $W$ and $H$ are the width and height of the image, respectively) and each pixel is assigned to a mode by following the density $p(x_n)$ upwards, that is in the direction of the gradient. Therefore, Quick Shift may be categorized as gradient ascent method. In particular, Quick Shift pre-computes $p(x_n)$ for all pixels using a Gaussian kernel. In practice, given an image $I$, the distance $d(x_n, x_m)$ used within the Gaussian kernel consists of a color term and a spatial term:

$d(x_n, x_m) = α \| I(x_n)−I(x_m)\|_2 + \|x_n −x_m\|_2$

where $α$ weights the influence of the color term. Subsequently, each pixel $x_n$ gets assigned to the pixel $x_m \in N_R(x_n) = \{x_m : \|x_n −x_m\|_\infty \leq R/2\}$ such that $p(x_m) > p(x_n)$ or is left unassigned. These assignments correspond to the modes, which represent the final superpixels. The algorithm is summarized in algorithm 1.

function quickshift(
$I$ // Color image.
)
for $n = 1$ to $W\cdot H$
initialize $t(x_n) = 0$
for $n = 1$ to $W\cdot H$
// $N_R(x_n)$ is the set of all pixels in the neighborhood of size $N$ around $x_n$.
calculate $p(x_n) = \sum_{x_m \in N_R(x_n)} \exp\left(\frac{-d(x_n, x_m)}{(2/3)R}\right)$
for $n = 1$ to $W\cdot H$
set $t(x_n) = \arg \max_{x_m \in N_R(x_n):p(x_m) > p(x_n)}\{p(x_m)\}$
// $t$ can be interpreted as forest, where all pixels $x_n$ with $t(x_n) = 0$ are roots.
derive superpixel segmentation $S$ from $t$
return $S$

Algorithm 1: The superpixel algorithm Quick Shift.

The original implementation is part of the VLFeat Library. Generated superpixel segmentations can be found in figure 1.

• [1] P. Arbeláez, M. Maire, C. Fowlkes, J. Malik. Contour detection and hierarchical image segmentation. Transactions on Pattern Analysis and Machine Intelligence, volume 33, number 5, pages 898–916, 2011.

What is your opinion on the summarized work? Or do you know related work that is of interest? Let me know your thoughts in the comments below:

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I don’t know about you, but my world is somewhat dark right now. Actually, it is really dark. It’s like being in a Leonard Cohen dream. You can’t want it darker. There are plagues that surround us—plagues of the body and of the soul. Darkness in the streets. In just the last nine months, in my world at least, we have lost the light of four feminist legal giants of the profession—Barbara Babcock, Ruth Bader Ginsburg, Shirley Abrahamson and, more recently, Deborah Rhode. How could it get much darker? January 6, 2021.1 That dark may be the darkest.

It has been quite the experience reading Michael Sandel’s book, The Tyranny of Merit: What’s Become of the Common Good?,2 during this dark period. Chapter 1 begins: “These are dangerous times for democracy.”3 How chilling to go back to these words after the events of January 6, 2021. And he is not alone in this thought. My friend and colleague from the University of Iowa, Linda Kerber, said early in her Charles Haskins lecture for the American Council of Learned Societies (ACLS): “We are facing the most serious threat to our democracy.”4

And, although the Sandel book offers some useful explanations for what is most likely happening in these dark times, the explanation is hardly comforting. I agree with much of what Sandel says, especially his emphasis that our focus on individual merit can result in the creation of apparent winners and losers. To blame the insurrection on the anger of a racist mob is too simple, although surely some of that is true. But these are not the types of racists that tried to keep Mary Means Monk out of their white neighborhood and then bombed her house when that attempt failed.5 Nor are they racists like Mrs. Hodge, trying to keep her one block in D.C. purely white and testifying that, even if she had thought a person were white but then learned that the person had a drop of Black blood, she would be overcome with hate.6 The anger of the insurrectionists is more complex. The racists to be feared in modern times are the white supremacy terrorists. But they are aided by all the “losers”7 that President Trump both loathes and loves.

Sandel tries to explain all of this to his readers, even before it unfolds before our eyes. Although in truth it has been unfolding for years. The premise of his book is quite simple. It is that, by embracing a meritocracy (you can succeed if you just try hard and, oh, by the way, have sufficient talent), we are creating winners and losers. The winners think they deserve what they reap (they have “hubris,” a favorite term of Sandel—one that he uses 56 times throughout the book). And the losers feel bad, are ashamed, and become resentful.8

This is not a new idea. As Sandel points out early in his book, it was the thesis of a 1958 book called The Rise of the Meritocracy by Michael Young.9 Sandel cites to Young throughout his own book. It is also the primary theme of a 2019 book, The Meritocracy Trap: How America’s Foundational Myth Feeds Inequality, Dismantles the Middle Class, and Devours the Elite,10 written by Yale law professor Daniel Markovits. Sandel also cites to this work, although less often than I think he should have.11

Sandel then builds his case on these earlier writings. In fact, he builds his case, and then he builds it again and again. He asserts that the notions that equal opportunity is enough and that one’s ability to “rise to the top” is what is most important in this country are just plain wrong. For those who doubt his thesis, you are Sandel’s intended audience and you should read this book.

But Sandel also adds some interesting context, especially for those of us who have lived through these times leading to the triumph of the rhetoric of the possibility of “rising,” which in turn leads to the concept that there are some losers who deserve their fate and others who lose “through no fault of their own.” Ronald Reagan is credited by Sandel as the first president to contribute to the rhetoric of rising and the concept of the deservedly poor. But these concepts were similarly embraced by more recent Presidents, such as Bill Clinton and Barack Obama.12 Republicans and Democrats alike have contributed to the current structure of the meritocracy, creating winners and losers—those who deserve their fates and the handful who do not and, therefore, may be justifiably aided by the state.

Sandel and I are in agreement about the problems created by an overarching meritocracy. And, personally, I needed no convincing on the matter. I think it is abhorrent for any of us to think that we made it to the top because we deserve it. The song that actually kept going through my head as I read this book was not Leonard Cohen’s darkness song. Rather it was “There but for Fortune,” by Phil Ochs:

Show me the prison, show me the jail.

Show me the prisoner whose life has gone stale.

And I’ll show you a young man with so many reasons why.

There but for fortune go you or I.13

And it does occur to me that one’s experience of success and how one views the role of luck in that success may be gendered. Noted historian Linda Kerber, the 2020 Haskins lecturer selected by the ACLS, began her talk with the following notation: “The late historian Mary Maples Dunn often repeated the findings of a survey of new PhDs: Men ascribe success to their own brilliance. Women ascribe success to luck.”14

I think the Ochs lyrics pretty much sum up Sandel’s point. Luck, not merit, is the great decider: luck of family, luck of natural-born talent, luck at each precipice on the journey of life. Speaking personally, I had the great luck to have been born white and to have been born into a respected and valued family. But I had the bad luck to have been born in Columbus, Georgia, which is a small city in the South. It was a place that, in the 1950s and 1960s, did not value women except as wives of powerful men, which my grandmother was (luck!). But there was no way it could have allowed me to be who I was as a lesbian (bad luck regarding time and place). One day in a high school class, my plane geometry teacher wanted to congratulate the star of the school play. Very dramatically, he said “She is a fine …” (and then he went over to pick up a dictionary and pretended to thumb through it) “… thespian,” he concluded. “You have to be very careful about saying the right word here.” And the whole class giggled. I was 16. I felt very awkward and I certainly felt like I didn’t belong.

I had a friend who showed me the way to escape from Columbus, Georgia. She had gone to Vassar and told me that I should do the same (luck!). I got in (luck!). But Vassar turned out to be a less-than-ideal escape. I loved the campus when I first visited it as a junior in high school (1962). What clinched my choice, though, was that the Vassar Experimental Theater was doing a production of Lillian Hellman’s The Children’s Hour that weekend. The fact that Vassar was willing to produce a play about hidden lesbian love made a huge impression on me. Of course, the two leading parts in that play were for women, which probably made it attractive to the Drama Department at an all-women’s college. And, as I learned later, although Vassar tolerated lesbians when they were on stage in a play, the reality was that lesbians were not welcome in the student body. If they were discovered, they were expelled. Consequently, I learned early on the value of the closet. (This was disappointing, but probably “good luck” at the time.) Again, I was being told that I didn’t belong.

Not belonging is a sadness. And although my own experience is perhaps minor compared to that of others, it is real. If you have ever experienced “not belonging,” you can begin to understand the sadness—a sadness that can sometimes turn to resentment. Again, I was lucky. For years, I didn’t belong in my family. For a time, I was not even sure about old friends. But, in the end, I was able to reconnect with all these people (luck).

Ever since college, at every corner, every turn in my life, and even though I was striving hard at times, I have seen my successes as involving a great deal of luck. For example, my Vassar A.B. helped me immensely in acquiring my first law school teaching job at the University of Texas, which occurred shortly after I graduated from the University of Georgia School of Law. I think the Vassar credential more or less upped the value of graduating at the top of the class at a state law school. I am a firm believer in the value of state schools, like the University of Georgia, and I feel that luck again intervened to place me there, in Athens, Georgia.15

What Sandel wants us to realize is that even if we work hard, even if we are smart, it is luck more than “just deserts” that got us to where we are. And that means that the “losers” are the luckless ones. “There but for fortune…” The “winners” have no right to look down on the “losers.” The luckless ones are not worthless; they are not to be despised. They need not only our support but also our admiration for both their survival skills and for their contributions. They don’t need our handouts. “They” should not even be thought of as “other than us.” As much as I believe we need a stronger safety net for all of us, the one thing Sandel convinced me of was that a safety net is not enough. We need to find a way to make everyone feel proud of what he or she is contributing to the common good.

Now, for me, this is a problem with respect to many of the “losers” who stormed the Capitol on January 6, 2021. I cannot forgive most of them for their actions. But I must try to understand the plight of those who have been downtrodden by the meritocracy and by this economy that is not working for them. And we all need to work together to make their lives better so that this never happens again. Those who feel left out and are angry need to feel like they belong.

Sandel’s final chapters offer two possible suggestions for improving the current state of affairs. One suggestion centers on education. It is always the solution, right? We need more equal access to education. Poppycock! We have been trying for decades to make access to education be more equitable. But the problem is that we have been using the myth of meritocracy as our means. And it is a myth. Rely on the SAT rather than your family connections? Great idea! But have you ever noticed how skewed the SAT results are toward the families with connections?16 We in the education industry know this best. Good families beget good standardized tests, which beget admissions to good institutions, which beget good jobs.

One of Sandel’s proposed solutions to the educational admissions problem is to throw all application files into the air, once, of course, you have narrowed them to a universe of potentially able students. Personally, I can’t see how this helps. And even if it could, it comes too late. I fear that the credentialing necessary to get into the universe of files to be thrown into the air will cut out most of the “losers.” Furthermore, in his proposal, Sandel focuses too heavily on the prestigious institutions. Many folks can get ahead in the world without attending prestigious institutions (even in these days that overemphasize the importance of a four-year college education). Sandel too often seems to conflate prestigious institutions with all four-year colleges.

If we want to solve this current problem through the route of higher education, I do not think our energies should be spent on trying to get “losers” into Yale or Harvard or Stanford. We should, of course, continue to break down the barriers to entry into these elite schools. But what we need to do, if indeed a college education is necessary to success, is to increase the funding of state universities and community colleges.17 And we need to start the equalization process at about age 4, by means of publicly funded preschools.18 We may even need to reimagine the entire educational process. Sandel doesn’t rule this out. He just doesn’t talk about it much.

Sandel’s final chapter offers his other solution: the value of work. All of us, the lucky and the unlucky, need to feel useful. We need to feel that we are contributing to the common good. We need to be connected to the things that make this country great.

Too often, Sandel’s choice of words in this section of the book focuses on paid work. The paycheck that you bring home is evidence that you are part of the production class and not just a consumer. You are contributing to the common good, or more specifically, to the GDP. But if you are underpaid, then you appear to be undervalued as a producer. If the pandemic has taught us nothing else, surely it has taught us the value of those underpaid workers—the trash collectors, the grocery store clerks, the home healthcare workers, and especially the EMT personnel and the ambulance drivers. Why in the world should they be paid so much less than I am being paid? They are the ones who make my life possible.19

Sandel seems a bit too ready to accept this fact of underpayment, of undervaluation. That is because what he really cares about is how each of us, regardless of how we are participating in this world, understands our own value. The evil meritocracy, by branding some of us as “losers,” prevents many of us from feeling like we are essential contributors to the “common good.” And that is a bad way for us to structure our society. And although Sandel’s discussion of how to improve education and to value work are useful, I don’t think any of his proposals will accomplish the goal that he has in mind.

If the “losers” could only feel connected, if they could only feel like they were “active participants” in the American project, then perhaps we could all be “one”: “one” with differences of opinions (that is good), “one” with the ability to debate our differences (that is good), “one” in a world where there is no class of winners or losers. Then we could all aspire to live in a world where we are sometimes led in one direction and sometimes in another direction, based on equal debate and participation. That is the true American Dream. The possibility of “rising” is a good thing. Equal educational opportunity and meaningful work opportunities are also good. But even more importantly, we need to find a way for all Americans to attain a sense of personal worth and belonging. To use a phrase that was coined by a president who served before we developed the rhetoric of “rising” based on equal opportunity, what we need is a theory that “will make all boats rise.” That phrase is attributed to President John F. Kennedy, who is said to have used it first in a 1963 speech in which he said “a rising tide lifts all boats.”20 In my view, that phrase remains an excellent beacon to help guide us toward a world in which we all feel that we belong.

## Notes

1

This was the date of the siege of the Capitol, the insurrection presumably incited by President Trump.

2

Michael J. Sandel, The Tyrannyof Merit: Whats Becomeofthe Common Good? (2020).

3

Id. at 3.

4

ACLS, 2020 A Life of Learning by Linda K. Kerber. The Charles Homer Haskins Prize Lecture, YouTube (Dec. 22, 2020), https://www.youtube.com/watch?v=oVVyQg9QHtY&feature=youtu.be.

5

See City of Birmingham v. Monk, 185 F.2d 859 (5th Cir. 1950), cert. denied, 341 U.S. 940 (1951). For a vivid photo of the bombed home, see https://www.al.com/news/birmingham/2016/06/bombings.html.

6

Hurd v. Hodge, 334 U.S. 24 (1948), discussed in Clement E. Vose, Caucasians Only: The Supreme Court, the NAACP, andthe Restrictive Covenant Cases 82 (1959).

7

Core Trump supporters are often described as persons who are not college educated and have lost their jobs (or fear losing them). In general, they are said to feel they deserve more and have been shortchanged by the elites who are in power. At the same time, studies show that the median income of a Trump supporter is higher than that of the average American. See Nate Silver, The Mythology of Trump’s “Working Class” Support, FiveThirtyEight (May 3, 2016), https://fivethirtyeight.com/features/the-mythology-of-trumps-working-class-support/.

8

To be clear, when I refer to “losers” who are created by the meritocracy, I am not including the “Oath Keepers,” who clearly played a role in the recent insurrection, or other seditionists like them. I am worried about the more general underclass, those who feel rejected by the promise of this country, many of whom also appear to have participated in the insurrection.

9

Michael Young, The Riseofthe Meritocracy (1958).

10

Daniel Markovits, The Meritocracy Trap: How Americas Foundational Myth Feeds Inequality, Dismantlesthe Middle Class, and Devoursthe Elite (2019).

11

For an excellent excerpt relaying principles from his book, see Daniel Markovits, How Life Became an Endless, Terrible Competition, Atlantic (Sept. 2019), https://www.theatlantic.com/magazine/archive/2019/09/meritocracys-miserable-winners/594760/.

12

See Sandel, supra note 2, at 22–23.

13

Phil Ochs, “There but for Fortune,” as sung by Joan Baez (Vanguard 1964).

14

ACLS, supra note 4.

15

Strange luck, in my view, because in 1960, I had been visiting a friend on the campus (I was a sophomore in high school) at the time that Charlayne Hunter and Hamilton Holmes were desegregating the campus. The Red and Black, the school newspaper, had some fairly offensive letters and an awful cartoon. I swore at the time that I would never set foot on that campus again. But times change—and change brings hope.

16

On average, children whose parents make more than $200,000 a year score about 250 points higher on the SAT than children whose parents make$40,000 to $60,000. See Markovits, supra note 10. 17 According to the Center for American Progress, there is a$78 billion gap between funds to support four-year colleges and funds to support two-year community colleges. The total gap is due to many factors in addition to underfunding by state legislatures. The problem of underfunding is extremely serious as to community colleges, whose students tend to come from lower-income and lower-wealth families and, therefore, need more support. See Victoria Yuen, The \$78 Billion Community College Funding Shortfall, Ctr. Am. Progress (Oct. 7, 2020), https://www.americanprogress.org/issues/education-postsecondary/reports/2020/10/07/491242/78-billion-community-college-funding-shortfall/.

18

There is a drastic undersupply of affordable childcare and early education in this country, despite the widespread demonstration of the benefits that such early intervention would produce both for the child and for society. For a recent report on the state of this undersupply, see Steven Jessen-Howard & Simon Workman, Early Learning in the United States: 2019, Ctr. Am. Progress (Sept. 16, 2019), https://www.americanprogress.org/issues/early-childhood/reports/2019/09/16/474487/early-learning-united-states-2019/.

19

See “The World’s Scariest Economist” on Coronavirus, Innovation, and Purpose, Vox Conversations (May 18, 2020), https://podcasts.apple.com/us/podcast/worlds-scariest-economist-on-coronavirus-innovation/id1081584611?i=1000474928034.

20

The phrase did not arise with Kennedy, according to his speechwriter, Ted Sorensen. But Kennedy embraced it and used it numerous times. See Ted Sorensen, Counselor: A Lifeatthe Edgeof History (2008).

## Author notes

*

Patricia A. Cain is Professor of Law at Santa Clara University and is the Aliber Family Chair in Law, Emerita, at the University of Iowa. She is a graduate of Vassar College and received her J.D. from the University of Georgia. Professor Cain is a member of the American Law Institute and a fellow of the American College of Trust and Estate Counsel. She teaches courses in federal taxation, property, wills and trusts, estate planning, torts, and sexuality and the law.

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits you to copy and redistribute in any medium or format, for non-commercial use only, provided that the original work is not remixed, transformed, or built upon, and that appropriate credit to the original source is given. For a full description of the license, please visit https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode.


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Article | Open | Published:

# Modular assembly of proteins on nanoparticles

## Abstract

Generally, the high diversity of protein properties necessitates the development of unique nanoparticle bio-conjugation methods, optimized for each different protein. Here we describe a universal bio-conjugation approach which makes use of a new recombinant fusion protein combining two distinct domains. The N-terminal part is Glutathione S-Transferase (GST) from Schistosoma japonicum, for which we identify and characterize the remarkable ability to bind gold nanoparticles (GNPs) by forming gold–sulfur bonds (Au–S). The C-terminal part of this multi-domain construct is the SpyCatcher from Streptococcus pyogenes, which provides the ability to capture recombinant proteins encoding a SpyTag. Here we show that SpyCatcher can be immobilized covalently on GNPs through GST without the loss of its full functionality. We then show that GST-SpyCatcher activated particles are able to covalently bind a SpyTag modified protein by simple mixing, through the spontaneous formation of an unusual isopeptide bond.

## Introduction

Proteins possess a broad range of functional properties, including catalysis, cellular signaling, molecular recognition, and ligand binding. They are involved in virtually all biological processes with an unmatched range of physical and chemical properties, exceeding that of other biopolymers. Combining proteins with nanoparticles yields potentially new functional materials with a vast range of properties and applications. However, proteins bound to nanoparticles are not necessarily in their native environment and it is possible that conjugation can somehow compromise their functionality. For this reason, protein-nanoparticle bio-conjugation increasingly focuses on optimizing the orientation, accessibility and bioactivity of the conjugated molecule1,2,3,4. This is especially important in nanomedicine, as nanoparticles intended for drug delivery often fail to fully exploit their clinical potential due to limitations linked to their targeting ability and subsequent bio-distribution issues5. The goal of making nano-therapeutics that better retain the biological activity of bound biomolecules stimulated extensive studies of the interaction between nanoparticles and body fluids and the discovery of biological barriers that determine the fate of a nanoparticle within a living organism6,7. In drug delivery, the first biological barrier that nano-therapeutics face is given by the sequestration by phagocytic cells, which happens as a consequence of opsonization. This involves the adsorption of plasma proteins onto the surface of nanoparticles, the so-called protein corona8. It is widely accepted that the protein corona undergoes a dynamic exchange of molecules bound to the surface that depends on the exact proteins present in the specific body fluid, cellular compartment or environment9,10,11. Eventually, a stable “hard” corona forms on nanoparticles and this affects their uptake12, cell association13,14,15 and toxicity16,17,18.

There exist a plethora of methods suitable for studying protein-nanoparticle interactions19,20,21,22. Expanding this knowledge could lead to the synthesis of designer recombinant proteins to facilitate the production of functionalized nanoparticles by forming a stable, artificial corona that modulates nanoparticle properties. This could be used to replace existing methods, for example based on pegylation, streptavidin-biotin interaction or tailored surface chemistry23,24, which require the chemical modification of either the protein, the particle or both. A biotechnological, rather than purely chemical approach to bio-conjugation and particle surface modification could be advantageous when handling biomolecules intended for nanomedicine, especially in the case of protein therapeutics produced recombinantly.

Gold nanoparticles (GNPs) are of great importance in nanomedicine and have been used in nanoparticle-based biosensors25,26. Their interaction with proteins has been previously characterized using a combination of biochemical27, biophysical28 and computational approaches29, therefore they represent an ideal model material for developing new decoration strategies. The ability of the engineered protein SpyCatcher to interact specifically with a SpyTag peptide has been used as a convenient protein–protein conjugation method30. The SpyCatcher/SpyTag pair has been shown to provide the ability to self-assemble and form a covalent isopeptide bond between the amino and carboxylic groups on the side chain of lysine and aspartate residues of the two distinct polypeptides. Interestingly, the formation of this unusual bond is self-catalyzed, making this one of the very few systems, together with SnoopCatcher/SnoopTag31 and inteins32 that allow protein–protein covalent conjugation without using chemical cross-linking. The ability to produce multi-protein mega-molecules from individual building blocks by using isopeptide bonds opened the way to applications well beyond protein biochemistry, for example in material science33,34,35.

Here we describe a GST-SpyCatcher fusion protein that binds to GNPs due to the gold-binding ability of GST and allows the hierarchical assembly of an extra protein layer through the SpyCatcher/SpyTag system. This modular approach to bio-conjugation of recombinant proteins to nanoparticles does not require optimization of every specific protein-particle pair and provides universal platform for immobilizing functional proteins on gold nanoparticles.

## Results

### Binding properties of GST to GNPs

We extensively characterized the interaction and adsorption of GST onto the surface of GNPs, as in our design this constitutes the primary interface between gold and subsequently attached proteins. GST binding was initially characterized by time-resolved dynamic light scattering (DLS), under the assumption that the increase of average particle diameter (Δd) was proportional to the amount of protein that binds to the particles28 (see Supplementary Note 1 for a detailed explanation of the binding model we used). We measured the time dependent increase of Δd as a result of the formation of a protein corona (Fig. 1a). Incubation with different concentrations of GST determined a trend that was consistent with pseudo-first order association kinetics (see Eq. 1 in Methods section), and the observed rate (kOBS) increased linearly with the concentration of GST (see the inset of Fig. 1a). Linear regression analysis of kOBS changes vs. GST concentration, revealed the on-rate (kON) and off-rate (kOFF) which were 3.7 × 104 M−1s−1 and 0.001789 s−1, respectively. Even at concentrations as low as 20 nM, the system reached an equilibrium within about 15 min, suggesting fast binding of GST to GNPs. For concentrations larger than 100 nM the equilibrium was too fast to determine a reliable association rate, as the equilibrium was reached within the very first data points.

To better determine the affinity of GST to GNPs across a broader range of concentrations, we measured Δd at equilibrium and fitted the data to a saturation one-site binding model (see Eq. 2 in Methods section). The dissociation constant (KD) and the plateau value for ΔddMAX) obtained were 54 nM and 7.9 nm, respectively (Fig. 1b). Interestingly, the binding affinity of GST to gold was an order of magnitude higher than a previously reported value for human serum albumin (HSA), with an estimated KD of 833 nM36. Since HSA is the most abundant protein in serum, it is generally accepted that nanoparticles injected into the blood would be quickly covered by a protein corona, dominated by albumin and fibrinogen37. The remarkable affinity that GST has for gold suggests that it would be a good candidate to protect GNPs from rapid binding of serum proteins and subsequent opsonization. To test this, we incubated “naked” and GST-coated GNPs in human serum for 3 h and compared the pattern of bound protein by SDS-PAGE (Fig. 1c). Whereas unprotected GNPs show extensive binding of proteins, resembling the same pattern of human serum with prominent amount of HSA (Supplementary Figure 2), the particles previously protected with GST did not bind further proteins, providing evidence that GST can strongly influence the formation of a protein corona in serum.

We have assessed whether GST-coated GNPs were responsive to pH changes by measuring their zeta potential at different pHs (Fig. 1d). We found that naked GNPs had a highly negative potential due to citrate capping and thus were essentially not responsive to pH change. On the contrary, GST-coated GNPs showed a marked increase of potential at lower pH, similar to what was previously observed for GNPs exposed to plasma proteins38. This trend was also consistent with the predicted net charge of GST at different pHs, estimated using an Adaptive Poisson-Boltzmann Solver (APBS) algorithm39, which gave a theoretical isoelectric point (pI) of 6.65 (inset of Fig. 1d). Positively charged GST at pH 6 and 6.5 compensated the highly negative potential of GNPs; whereas, the potential at pH above the GST pI was nearly unaffected by the presence of GST. To further assess how pH affects GST binding properties, we repeated the equilibrium binding measurement of Fig. 1b, which was taken at pH 7.3, for the same pH values for which we measured the zeta potential. We fitted the data using Eq. 2 (Methods section) and the results are reported in Fig. 1e.

KD values at different pH were found to be not significantly different, whereas ΔdMAX values were found to belong to two significantly different groups, with the two values obtained at pH below pI being significantly higher than those above pI. According to the binding model used, higher values of ΔdMAX indicate a larger average number of molecules bound per particle. The higher protein load at lower pH could be explained by a more dense protein packing on the GNP surface, likely facilitated by the net positive charge of GST at lower pH, which can partially compensate the negative charges due to citrate capping on the gold surface. As maximizing the protein load was not the scope of our design, we used pH 7.3 for all the subsequent experiments, as this is the pH at which the proteins we used were stably stored and it is also more representative of physiological conditions compared to pH 6.0 or 6.5.

### Binding mechanism of GST to GNPs

Our initial findings indicated a stable interaction at the GST-GNP interface. We therefore assessed whether GST binds to GNPs by physisorption or chemisorption, with the latter known to provide more stable GNP bioconjugates. We studied the mechanism of binding with a specific focus on the thiol groups at the 4 cysteine residues of GST, as these have been reported to form covalent Au–S bonds in other proteins40. First, we compared the binding properties of GST and N-ethylmaleimide (NEM)-modified GST (NEM-GST). NEM was used to convert the sulfhydryl at cysteine residues into thioester groups, so the potential formation of Au–S bonds and their involvement in the binding mechanism to gold could be investigated. We found that KD and ΔdMAX of NEM-GST were 73 nM and 8.3 nm, respectively. Interestingly, these are not significantly different compared to the values obtained for GST, suggesting that thiols are not essential for the initial adsorption of GST onto GNPs (Fig. 2a and Supplementary Figure 3).

We evaluated the stability of the colloids by measuring the absorbance near the surface plasmon resonance (SPR) peak at 525 nm. As expected, addition of either GST or NEM-GST did not destabilize the colloid, as evidenced by a clear SPR peak near 525 nm in all the preparations tested (Fig. 2b). However, the addition of 2-mercaptethanol (2-ME) resulted in a pronounced reduction of the SPR of naked GNPs and of those bound to NEM-GST; whereas, GST-coated GNPs were unaffected (Fig. 2c). This suggests that 2-ME can destabilize the colloid by binding to the gold surface and displacing NEM-GST. However, 2-ME could not displace GST with active thiol groups, most likely because they form a covalent bond with the gold surface. We defined an Au–S index by measuring the ratio between the absorbance near the SPR peak (525 nm) and the absorbance at a wavelength far from the peak (600 nm). Instability of the colloid in 2-ME would result in aggregation and decreased absorbance at the SPR peak, resulting in an Au–S index of ~1, as an aqueous buffer without a colloid suspended would have similar absorbance at 525 nm and 600 nm. Values larger than 1, instead, indicate presence of colloid highly stable in 2-ME, as observed in the case of GST. Here, the SPR peak was twice higher than the absorbance at 600 nm (Fig. 2c), giving an Au–S index of ~2. The assay wavelength was chosen to be sufficiently far away from typical SPR wavelengths of gold and silver nanoparticles and yet be compatible with a broad range of absorbance spectrometers including instruments used for turbidity assays.

We further evaluated the kinetics of GNPs stabilization using the 2-ME assay. GNPs were incubated with either GST or NEM-GST for increasing defined times prior to 2-ME treatment and the stability index was calculated for each time point (Fig. 2d). Whereas NEM-GST was unable to stabilize the colloid irrespective of the incubation time, GST was able to fully protect GNPs from aggregation, but only following an incubation time of ~10 min, as evidenced by the increase of the Au–S index from 1 to 2. This is a strong indication that, although the 4 thiols on GST do not contribute to the initial rapid adsorption on gold (physisorption), they bind and stabilize the GNPs in the longer term, presumably by formation of covalent bonds (chemisorption). We fitted the Au–S index time course data with a sigmoid model (see Eq. 3 in Methods section) and obtained a half-time of 5.3 min, which represents the time required for the Au–S stability index to reach half of the plateau value. This time is much longer than the half-time of 12 s calculated from the on-rate estimation of Fig. 1a, suggesting a multi-step process of binding of GST to GNPs, which relies on multiple mechanisms having very different kinetics. This observation is consistent with a three-steps model of adsorption previously described only qualitatively41, which involves an initial reversible association step (presented in Fig. 1), a rearrangement/reorientation step on the gold surface, and a final cysteine-dependent “hardening” step, after which binding becomes irreversible. We then used surface enhanced Raman scattering (SERS) on silver colloid-adsorbed protein to provide extra evidence of cysteine involvement in the mechanism of binding of GST to metal nanoparticles. Comparison of the Raman spectra of GST and NEM-GST adsorbed on citrate-capped silver nanoparticles (SNPs) revealed a Raman peak at 233 cm−1 only in the GST sample (Fig. 2e). This peak was previously attributed to Ag–S stretching mode in the SERS of thiols on silver colloid42 and also in the case of proteins adsorbed on SNPs43,44. These data further support the idea that the different interaction that GST and NEM-GST have with metal surfaces is likely due to thiols availability to form a covalent bond.

To better understand the rearrangement/reorientation step, we used molecular dynamics (MD) to model likely orientations of GST on a citrate capped gold surface. The results indicated that all the conformations obtained within the time scale of the simulations (20 ns) relied on lysine residues forming salt-bridges with citrate molecules (Fig. 3a and Supplementary Figure 4). This is consistent with our previous observation that positive charges on GST surface play a role in adsorption (Fig. 1d–e) and Au–S bond formation is not the initial driving force for adsorption (Fig. 2d).

To establish the nature of the subsequent GST rearrangement and the degree of conformational changes necessary for Au–S formation, beyond the time scale of a MD simulation, we compared the secondary structure of GST in solution with that of GST-GNPs using synchrotron radiation circular dichroism (SRCD)45 (Fig. 3b). We found that, whereas the overall secondary structure was well preserved, there were some changes in the spectrum in the presence of GNPs, especially a marked reduction of the SRCD value around 190 nm. This is consistent with an increased contribution of disordered/irregular conformation, which would reduce the positive band at about 190 nm associated to the α-helical conformation of GST in solution. We concluded that the rearrangement of GST on GNPs leads to partial denaturation of the GST secondary structure. A similar change in the structure of GST bound to silver colloid was detected, suggesting a similar interaction (Supplementary Figure 5). It is still debated to what degree proteins on nanoparticles do denature and what the actual impact on their function is. For example, it has been reported that albumin-specific antibodies can bind albumin adsorbed on GNPs, suggesting that denaturation is not dramatic and does not affect all of the native epitopes10,45.

In our design, GST serves merely as the interface with gold and the preservation of its native transferase activity is not required. Therefore, we focused on the ability of GST to bind gold, which was observed before46 but not extensively characterized. We concluded that GST binds to GNPs with high affinity in a predictable, oriented manner. GST forms a covalently attached protein corona on GNPs and enables the attachment of the next hierarchical level of proteins.

### Hierarchical and controlled assembly of a protein corona

The nanoparticle-protein interface was further modified by adding SpyCatcher to the C-terminal of the GST. We set out to verify whether or not gold-immobilized SpyCatcher retains its spontaneous interaction with SpyTag and whether the fusion protein GST-SpyCatcher retains its ability to irreversibly bind GNPs. We therefore tagged a protein of interest, in this specific case NEM-GST, with a SpyTag peptide and probed the ability of NEM-GST-SpyTag to bind GST-SpyCatcher activated GNPs (Fig. 4a).

Initially, we measured KD and ΔdMAX of GST-SpyCatcher in an equilibrium binding experiment, to assess whether the protein binds effectively to GNPs (Fig. 4b). We found a KD of 438 nM and a ΔdMAX of 15.3 nm, both larger than GST alone. The higher dissociation constant might be attributed to the lower pI of GST-SpyCatcher (pI = 5.17) compared to GST (pI = 6.65), and therefore a lower propensity to bind negatively charged particles. The larger ΔdMAX is consistent with the larger size of the protein (GST-SpyCatcher is 38.5 kDa compared to 28.6 kDa of GST). We also measured KD and ΔdMAX of SpyCatcher not fused to GST and found values of 1.21 µM and 12.5 nm, respectively. Whereas ΔdMAX was slightly, but not significantly smaller than GST-SpyCatcher, KD was significantly higher (see confidence intervals in Supplementary Figure 6). This suggests that GST has a positive role in affecting the affinity of fusion proteins to GNPs. We verified whether GST can mediate the chemisorption of GST-SpyCatcher by measuring the SPR peak in the presence of destabilizing 2-ME (Fig. 4c). The results show that, whereas SpyCatcher alone was displaced by 2-ME, the GST-SpyCatcher fusion was stable, suggesting formation of Au–S bonds at cysteine residues on GST (SpyCatcher does not contribute any cysteine), making GST-SpyCatcher an ideal protein to form the first layer of the hierarchical protein corona.

To prove the ability of GST-SpyCatcher to assemble a second layer of protein on GNPs, SpyTag was fused to GST and its binding to GNP-GST-SpyCatcher was studied. Cysteines of GST-SpyTag were inactivated using NEM (NEM-GST-SpyTag) to rule out any possible chemisorption that would make the interpretation of binding data more difficult. We exposed two preparations of GNP-GST-SpyCatcher to excess of NEM-GST-SpyTag or untagged NEM-GST and measured the resulting Δd after 3 h incubation (Fig. 4d). Whereas NEM-GST did not significantly increase the overall size of the particles, NEM-GST-SpyTag did bind to the activated particles and increased the diameter by 3 nm. The proteins that were bound to the GNPs of Fig. 4d were loaded on SDS-PAGE to verify whether NEM-GST-SpyTag formed the expected isopeptide covalent bond with GST-SpyCatcher. A prominent band was found compatible with the expected molecular weight of a GST-SpyCatcher/NEM-GST-SpyTag complex which is 66.5 kDa (38,5 kDa from GST-SpyCatcher and 28 kDa from NEM-GST-SpyTag). We concluded that NEM-GST-SpyTag was able to bind to GST-SpyCatcher activated GNPs and form a second level of protein stably associated to GNPs.

This step-wise self-assembly method could be applied in principle to other gold nanomaterials (for example nanorods or gold nanoelectrodes) or even materials other than gold. For example we replicated the DLS experiment and SDS-PAGE of Fig. 4 (d and e, respectively) using citrate-capped silver nanoparticles (SNPs) in place of GNPs and we obtained very similar results, which are reported in Supplementary Figure 7. Activation of surfaces other than gold and silver could be potentially explored by fusion of SpyCatcher to established protein-material interfaces other than GST. For example peptides that are able to selectively bind to carbon nanotubes, polystyrene, silica and many other materials have been previously reported23,47.

## Discussion

In summary, we have achieved covalent immobilization of proteins onto GNPs using a two-steps approach. The first step relies on GNPs modification mediated by GST through Au–S cross-linking. The second step relies on spontaneous covalent formation of a unique isopeptide bond between SpyCatcher and the SpyTag peptide. The latter can be easily added to any recombinant protein. The GNP-GST-SpyCatcher complex is stable and thus provides a universal platform for decorating GNPs, using a simple and easily reproducible protocol. We designed this robust conjugation strategy primarily for the bio-conjugation of recombinant proteins to nanoparticles or other surfaces, with applications in nanomedicine and biosensors in mind and a particular emphasis on preserving protein structure and function throughout the process. Several other protein-particle conjugation approaches have been extensively reviewed recently3,23. The most common covalent method applied to gold and silver nanoparticles makes use of Au–S or Ag–S bonds from cysteine residues, either native or deliberately introduced within a recombinant protein. Although this method benefits from the high stability and spontaneous nature of the interaction, the protein structure is often affected by mutagenesis and by strong interaction of the cysteines with the metal nanoparticle3. The close proximity and extensive physical contact of the recombinant protein with the nanoparticles often has detrimental effect on the structure and function of the immobilized protein48. Our approach takes advantage of the unique gold-binding properties of GST whilst also limiting the risk of structural interference with the protein of interest through oriented immobilization and by acting as a spacer to distance the protein from the gold surface. A common alternative to covalent protein-nanoparticle conjugation is represented by the biotin–avidin chemistry and the several derivatives and homologs, due to the unusually high affinity between the two components3,23. These systems are often the first choice when prototyping bioconjugates, as many commercial products are already available. Biotin–avidin interaction is almost ubiquitous in molecular diagnostics and research; however, the simplicity of this strategy comes with limitations when using bioconjugates in nanomedicine, such as (i) heterogeneity of labeling due to the tetravalent nature of avidin, (ii) poor control on binding site of biotin during chemical cross-linking3 and (iii) interference of endogenous biotin with conjugates in vivo, as the concentration of biotin (also known as vitamin H) is not negligible in serum and tissues49. Site-specific recombinant inclusion of a designer conjugation tag, such as SpyTag is an increasingly common choice for protein bioconjugation35 and proved to successfully preserve structure and/or function of target proteins in several contexts, such as embedding enzymes in nanovesicles50, displaying target antigens on virus-like particles51, enclosure of cargo proteins in phage capsids52, conjugation of affibodies to fluorescent proteins53, protein labeling for super-resolution imaging54, supramolecular assembly of multi-enzyme metabolic pathways55, conjugation of a DNA polymerase to a nanopore56, and protein hydrogels33,34. SpyCatcher protein has been successfully used in combination with quantum dots to make protein-nanomaterials conjugates57,58. In the latter works, SpyCatcher was modified by introducing two cysteine residues at the N-terminal specifically for conjugation purpose. We opted for a GST-fusion of the unmodified SpyCatcher polypeptide instead. This brought about a substantially increased gold-binding affinity of the fusion protein due to the presence of GST tag, as clearly indicated by equilibrium binding curves obtained for SpyCatcher and GST-SpyCatcher (Fig. 4b).

The ability of GST to adsorb effectively onto gold nanoparticles and to provide a stable anchor for SpyCatcher, makes development of complicated surface chemistries unnecessary. Citrate capped metal nanoparticles can easily be synthesized in the lab or manufactured at large scales. All conjugation experiments could be conducted in aqueous buffers at neutral pH. Expression and purification of GST-SpyCatcher in bacteria is standard and scalable procedure, suggesting that the overall strategy can be potentially used industrially. Importantly, as nanomaterials are likely to receive closer attention from pharmaceutical regulatory bodies59, the use of metal nanoparticles that are already well-established in nanomedicine60,61,62 and do not carry extra chemical modifications at the surface, makes this bio-conjugation method suitable for consideration in nanopharmaceutical projects.

## Methods

### Preparation of nanoparticles

Citrate capped 40 nm GNPs were purchased from BBI Solutions at a concentration of 5 OD in water (corresponding to 4.5 × 1011 particles ml−1 according to the provider). For the SRCD experiment we used citrate capped 20 nm GNPs purchased from Sigma-Aldrich at a stock concentration of 1 OD in 0.1 mM PBS (corresponding to 6.5 × 1011 particles ml−1 according to the provider). Citrate capped 40 nm silver nanoparticles were purchased from Sigma-Aldrich at a concentration of 0.02 mg ml−1 in aqueous buffer. For protein adsorption experiments, nanoparticles were washed by centrifugation, re-suspended in 10 mM HEPES, pH 7.3, 10 mM NaCl and their concentration measured and normalized at the desired OD using NanoDrop 2000 (Thermo Fisher Scientific). For the initial characterization of GST adsorption at different pH, phosphate buffers at the indicated pH were used in place of HEPES. Human serum used in nanoparticle binding experiments was from Sigma-Aldrich.

### Synthesis of proteins

All proteins were synthesized recombinantly using pGEX-KG GST gene fusion system (Addgene) expressed in BL21(DE3)pLysS E.coli strain (Thermo Fisher Scientific). The resulting amino acid sequences of all the proteins used in this paper are reported in Supplementary Table 1 along with the relevant European Nucleotide Archive (ENA) accession numbers of each coding DNA sequence used. All recombinant proteins were purified from bacterial lysates by affinity chromatography using Glutathione Sepharose 4B resins (GE Healthcare). SpyCatcher was obtained by thrombin cleavage at a proteolytic site between GST and SpyCatcher and elution from the affinity resin. All proteins were further purified by size exclusion chromatography using Superdex 75 10/300 GL columns on an ÄKTA Pure chromatography system (GE Healthcare). Protein concentration was determined with BCA assay (Thermo Fisher Scientific). Inactivation of thiols of GST and GST-SpyTag was achieved by treating 30 µM protein with 1.2 mM NEM for 2 h at room temperature. Excess of NEM was removed by using Zeba spin desalting columns with a molecular weight cutoff of 7 kDa (Thermo Fisher Scientific). The inactivation was verified by Ellman’s reaction using 4 mg of 5,5′-Dithiobis(2-nitrobenzoic acid) (Sigma-Aldrich) dissolved in 1 mL of 0.1 M sodium phosphate buffer pH 8.0 and 1 mM EDTA. Ellman’s reagent was mixed with protein in a 3:1 ratio for 10 min at room temperature, the absorbance was measured at 412 nm and compared with the values obtained from a standard curve made using l-cysteine. The inactivation was considered successful if the absorbance was suggesting negligible presence of active thiols.

### Dynamic light scattering and zeta potential measurements

All measurements were performed at 20 °C using Zetasizer Nano ZS (Malvern), using disposable micro-cuvettes or folded capillary cells (zeta potential) and automatic optimization of parameters. In DLS measurements, the diameter (d) was defined by the Z-average particle size and the increment of diameter (Δd) was calculated by subtracting the Z-average of the naked nanoparticles to each measurement. Increments were measured in the same cuvette by increasing the protein concentration every 30 min of incubation (equilibrium data) or, for kinetic data, particle size was recorded continuously and immediately after adding the protein, except for the value at time 0, which was recorded before addition of protein.

### Surface plasmon resonance

Absorption spectra were recorded using an Infinite M200 PRO plate reader (TECAN) from 200 µL suspensions of GNPs at a final concentration of 0.4 OD, incubated for a determined duration with the relevant protein, before and after addition of 2-ME at a final concentration of 0.2 mM.

### Surface enhanced Raman scattering

Protein was adsorbed on citrate capped SNPs, concentrated and washed as described above. To improve SERS signal, protein-SNPs were mixed with hydroxylamine phosphate silver nanoparticles in aqueous buffer, prepared as previously described63 in a volume of 500 µl in a glass cuvette (0.5 cm path length). Raman spectra were recorded using a LABRAM 300 (Horiba Jobin Yvon) with an excitation line of 532 nm, equipped with an Olympus microscope BX41. The laser output power used was 50 mW for 10 s of exposure time (2 accumulations).

### Molecular dynamics

The structure of GST was obtained from the Protein Data Bank (PDB ID: 1UA5 [https://doi.org/10.2210/pdb1UA5/pdb]). The ligand glutathione and sulfate ions were removed while the crystallization water was kept. The crystal structure does not contain the C-terminal sequence which is part of the pGEX-KG expression vector (see Supplementary Table 1), therefore this part was initially modeled from the amino acid sequence using Modeller64 which yielded a random coil. All the molecular dynamics simulations were performed using GROMACS (version 5)65,66, VMD67 was used for visualization. MD simulation conditions are detailed in Supplementary Methods. The initial structure was equilibrated in absence of gold surfaces for 100 ns and its conformation, inclusive of the extra amino acids from the expression vector, is reported in Supplementary Figure 4A. The surface of the nanoparticle was approximated to two opposite planar slabs of gold atoms each consisting of four 10 × 10 nm layers of gold atoms. Since the average diameter of the nanoparticles used in the experiment was ~40 nm the effect of their curvature is negligible for a protein of ~2.4 nm in size. The two parallel gold slabs formed the opposite faces on the longest side of a rectangular box of size 10 × 10 × 12 nm. The citrate coating of the surfaces was obtained using 384 citrate molecules initially located in the middle of the simulation box. The box was then filled with water and sodium counter-ions to neutralize the total charge of the system and 20 ns MD simulation allowed the two Au surface to be coated with ~100 citrate molecules. Water, citrate molecules and sodium ions were removed from the central region of the box. The protein conformation obtained after 100 ns of simulation in solution, comprising a 0.6 nm thick solvation shell, was placed in the center of the box and oriented with the longest principal axes parallel to the Au surface as shown in Supplementary Figure 4. The remaining empty space was refilled with water molecules and the total charge of the box was adjusted to neutrality and, finally, binding of GST to GNPs was simulated for 20 ns in three distinct simulations with different starting velocity. The compositions of all simulated systems are reported in Supplementary Table 2.

### Synchrotron radiation circular dichroism (SRCD)

SRCD spectra were measured at B23 beamline for SRCD of Diamond Light Source (UK)68 and processed using CDApps69. A cuvette cell (Starna) of 2 mm path-length was filled with high-OD nanoparticles re-suspended in 0.1 mM HEPES. The beamline’s Zetasizer ZSP (Malvern) was used before SRCD measurements to verify presence of the expected protein corona after extensive washes. Spectra were averaged over three measurements with a 1 s integration time.

### Gel electrophoresis

Nanoparticles at OD 5 were incubated with the relevant proteins, washed twice in 10 mM HEPES, pH 7.3, 10 mM, NaCl by centrifugation at 5000×g for 5 min and re-suspended in 15 µl buffer. Washed nanoparticles were mixed with 5 µl of 4× SDS-PAGE loading buffer (0.06 M Tris, pH 6.8, 10% glycerol, 2% SDS, 0.005% bromophenol blue, 5% 2-ME), heated at 95 °C for 5 min and left at 42 °C for 10 h. Proteins that were originally bound to the particles were fully recovered after removal of GNPs by centrifugation at 5000×g for 5 min and loaded on a 12% pre-cast SDS-PAGE gel (Expedeon) along with a protein ladder (Precision Plus Protein Dual Color Standard, BioRad). The gel was stained for 6 h by InstantBlue (Expedeon) and destained in water for 10 h before imaging.

### Curve fitting and statistics

All kinetics and equilibrium binding curves were fitted using a previously described nonlinear least-squares method70. The same method was also used to estimate the confidence interval of each parameter and the statistical significance of the differences between them. Kinetics Δd data acquired at different times (t) were fitted to equation 1 to retrieve observed rate at a determined concentration (kOBS) and maximum size increment observed at the same concentration (ΔdOBS).

$$\Delta d = \Delta d_{{\rm OBS}}(1 - e^{ - k_{{\rm OBS}}t}).$$
(1)

Equilibrium binding data were fitted to equation 2 to estimate ΔdMAX and KD from Δd data obtained at different protein concentrations [P].

$$\Delta d = \Delta d_{{\rm MAX}}\frac{{[P]}}{{K_{\rm D} + [P]}}.$$
(2)

The 4-parameters sigmoid of equation 3 was used for the estimation of the half-time (c) of Au–S bond formation from Au–S index data measured at different times (t).

$${\rm Au - S}\,{\rm index} = a + \frac{{b - a}}{{1 + \left( {\frac{c}{t}} \right)^d}}.$$
(3)

### Data availability

The authors declare that the main data supporting the findings of this study are available within the article and its Supplementary Information files. All the coding DNA sequences of the proteins used in this study have been deposited in the European Nucleotide Archive (ENA), accession numbers LT986714, LT986711, and LT986708. Extra data are available from the corresponding author upon reasonable request.

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## References

1. 1.

Reed, A. M. W. & Metallo, S. J. Oriented protein adsorption to gold nanoparticles through a genetically encodable binding motif. Langmuir 26, 18945–18950 (2010).

2. 2.

Lin, W. et al. Control of protein orientation on gold nanoparticles. J. Phys. Chem. C 119, 21035–21043 (2015).

3. 3.

Avvakumova, S., Colombo, M., Tortora, P. & Prosperi, D. Biotechnological approaches toward nanoparticle biofunctionalization. Trends Biotechnol. 32, 11–20 (2014).

4. 4.

Johnson, B. N. & Mutharasan, R. pH effect on protein G orientation on gold surfaces and characterization of adsorption thermodynamics. Langmuir 28, 6928–6934 (2012).

5. 5.

Salvati, A. et al. Transferrin-functionalized nanoparticles lose their targeting capabilities when a biomolecule corona adsorbs on the surface. Nat. Nanotechnol. 8, 137–143 (2013).

6. 6.

Blanco, E., Shen, H. & Ferrari, M. Principles of nanoparticle design for overcoming biological barriers to drug delivery. Nat. Biotechnol. 33, 941–951 (2015).

7. 7.

Canton, I. & Battaglia, G. Endocytosis at the nanoscale. Chem. Soc. Rev. 41, 2718–2739 (2012).

8. 8.

Tenzer, S. et al. Rapid formation of plasma protein corona critically affects nanoparticle pathophysiology. Nat. Nanotechnol. 8, 772–781 (2013).

9. 9.

Maiorano, G. et al. Effects of cell culture media on the dynamic formation of protein–nanoparticle complexes and influence on the cellular response. ACS Nano 4, 7481–7491 (2010).

10. 10.

Casals, E., Pfaller, T., Duschl, A., Oostingh, G. J. & Puntes, V. Time evolution of the nanoparticle protein corona. ACS Nano 4, 3623–3632 (2010).

11. 11.

Milani, S., Baldelli Bombelli, F., Pitek, A. S., Dawson, K. A. & Rädler, J. Reversible versus irreversible binding of transferrin to polystyrene nanoparticles: soft and hard corona. ACS Nano 6, 2532–2541 (2012).

12. 12.

Monteiro-Riviere, N. A., Samberg, M. E., Oldenburg, S. J. & Riviere, J. E. Protein binding modulates the cellular uptake of silver nanoparticles into human cells: implications for in vitro to in vivo extrapolations? Toxicol. Lett. 220, 286–293 (2013).

13. 13.

Walkey, C. D. et al. Protein corona fingerprinting predicts the cellular interaction of gold and silver nanoparticles. ACS Nano 8, 2439–2455 (2014).

14. 14.

Treuel, L. et al. Impact of protein modification on the protein corona on nanoparticles and nanoparticle-cell interactions. ACS Nano 8, 503–513 (2014).

15. 15.

Moore, T. L. et al. Nanoparticle colloidal stability in cell culture media and impact on cellular interactions. Chem. Soc. Rev. 44, 6287–6305 (2015).

16. 16.

Ge, C. et al. Binding of blood proteins to carbon nanotubes reduces cytotoxicity. Proc. Natl Acad. Sci. USA 108, 16968–16973 (2011).

17. 17.

Dutta, D. et al. Adsorbed proteins influence the biological activity and molecular targeting of nanomaterials. Toxicol. Sci. 100, 303–315 (2007).

18. 18.

Wigginton, N. S. et al. Binding of silver nanoparticles to bacterial proteins depends on surface modifications and inhibits enzymatic activity. Environ. Sci. Technol. 44, 2163–2168 (2010).

19. 19.

Mahmoudi, M. et al. Protein–nanoparticle interactions: opportunities and challenges. Chem. Rev. 111, 5610–5637 (2011).

20. 20.

Rabe, M., Verdes, D. & Seeger, S. Understanding protein adsorption phenomena at solid surfaces. Adv. Colloid Interface Sci. 162, 87–106 (2011).

21. 21.

Jiang, X. et al. Quantitative analysis of the protein corona on FePt nanoparticles formed by transferrin binding. J. R. Soc. Interface 7, S5–S13 (2010).

22. 22.

Shemetov, A. A., Nabiev, I. & Sukhanova, A. Molecular Interaction of proteins and peptides with nanoparticles. ACS Nano 6, 4585–4602 (2012).

23. 23.

Sapsford, K. E. et al. Functionalizing nanoparticles with biological molecules: developing chemistries that facilitate nanotechnology. Chem. Rev. 113, 1904–2074 (2013).

24. 24.

Dreaden, E. C., Alkilany, A. M., Huang, X., Murphy, C. J. & El-Sayed, M. A. The golden age: gold nanoparticles for biomedicine. Chem. Soc. Rev. 41, 2740–2779 (2012).

25. 25.

Brewer, S. H., Glomm, W. R., Johnson, M. C., Knag, M. K. & Franzen, S. Probing BSA binding to citrate-coated gold nanoparticles and surfaces. Langmuir 21, 9303–9307 (2005).

26. 26.

Dominguez-Medina, S., McDonough, S., Swanglap, P., Landes, C. F. & Link, S. In situ measurement of bovine serum albumin interaction with gold nanospheres. Langmuir 28, 9131–9139 (2012).

27. 27.

De Roe, C., Courtoy, P. J. & Baudhuin, P. A model of protein-colloidal gold interactions. J. Histochem. Cytochem. 35, 1191–1198 (1987).

28. 28.

Jans, H., Liu, X., Austin, L., Maes, G. & Huo, Q. Dynamic light scattering as a powerful tool for gold nanoparticle bioconjugation and biomolecular binding studies. Anal. Chem. 81, 9425–9432 (2009).

29. 29.

Tavanti, F., Pedone, A. & Menziani, M. C. Competitive binding of proteins to gold nanoparticles disclosed by molecular dynamics simulations. J. Phys. Chem. C 119, 22172–22180 (2015).

30. 30.

Zakeri, B. et al. Peptide tag forming a rapid covalent bond to a protein, through engineering a bacterial adhesin. Proc. Natl Acad. Sci. USA 109, E690–E697 (2012).

31. 31.

Veggiani, G. et al. Programmable polyproteams built using twin peptide superglues. Proc. Natl Acad. Sci. USA 113, 1202–1207 (2016).

32. 32.

Muralidharan, V. & Muir, T. W. Protein ligation: an enabling technology for the biophysical analysis of proteins. Nat. Methods 3, 429–438 (2006).

33. 33.

Sun, F., Zhang, W.-B., Mahdavi, A., Arnold, F. H. & Tirrell, D. A. Synthesis of bioactive protein hydrogels by genetically encoded SpyTag-SpyCatcher chemistry. Proc. Natl Acad. Sci. USA 111, 11269–11274 (2014).

34. 34.

Gao, X., Fang, J., Xue, B., Fu, L. & Li, H. Engineering protein hydrogels using SpyCatcher-SpyTag chemistry. Biomacromolecules 17, 2812–2819 (2016).

35. 35.

Reddington, S. C. & Howarth, M. Secrets of a covalent interaction for biomaterials and biotechnology: SpyTag and SpyCatcher. Curr. Opin. Chem. Biol. 29, 94–99 (2015).

36. 36.

Dell’Orco, D., Lundqvist, M., Oslakovic, C., Cedervall, T. & Linse, S. Modeling the time evolution of the nanoparticle-protein corona in a body fluid. PLoS ONE 5, e10949 (2010).

37. 37.

Cedervall, T. et al. Understanding the nanoparticle–protein corona using methods to quantify exchange rates and affinities of proteins for nanoparticles. Proc. Natl Acad. Sci. USA 104, 2050–2055 (2007).

38. 38.

Dobrovolskaia, M. A. et al. Interaction of colloidal gold nanoparticles with human blood: effects on particle size and analysis of plasma protein binding profiles. Nanomed. Nanotechnol., Biol. Med. 5, 106–117 (2009).

39. 39.

Baker, N. A., Sept, D., Joseph, S., Holst, M. J. & McCammon, J. A. Electrostatics of nanosystems: application to microtubules and the ribosome. Proc. Natl Acad. Sci. USA 98, 10037–10041 (2001).

40. 40.

Siriwardana, K., Wang, A., Vangala, K., Fitzkee, N. & Zhang, D. Probing the effects of cysteine residues on protein adsorption onto gold nanoparticles using wild-type and mutated GB3 proteins. Langmuir 29, 10990–10996 (2013).

41. 41.

Wang, A., Vangala, K., Vo, T., Zhang, D. & Fitzkee, N. C. A three-step model for protein–gold nanoparticle adsorption. J. Phys. Chem. C 118, 8134–8142 (2014).

42. 42.

Chen, Y. et al. Experimental and density functional theory study of Raman and SERS spectra of 5-amino-2-mercaptobenzimidazole. Spectrochim. Acta Part A Mol. Biomol. Spectrosc. 153, 344–348 (2016).

43. 43.

Valenti, L. E. & Giacomelli, C. E. Unaffected features of BSA stabilized Ag nanoparticles after storage and reconstitution in biological relevant media. Colloids Surf. B Biointerfaces 132, 71–77 (2015).

44. 44.

Joshi, D. & Soni, R. K. Laser-induced synthesis of silver nanoparticles and their conjugation with protein. Appl. Phys. A 116, 635–641 (2014).

45. 45.

Laera, S. et al. Measuring protein structure and stability of protein-nanoparticle systems with synchrotron radiation circular dichroism. Nano Lett. 11, 4480–4484 (2011).

46. 46.

Ferrari, E. et al. Binary polypeptide system for permanent and oriented protein immobilization. J. Nanobiotechnol. 8, 9 (2010).

47. 47.

Aubin-Tam, M.-E. et al. Adhesion through single peptide aptamers. J. Phys. Chem. A 115, 3657–3664 (2011).

48. 48.

Bailes, J., Gazi, S., Ivanova, R. & Soloviev, M. in Nanoparticles in Biology and Medicine. Methods in Molecular Biology (Methods and Protocols), vol. 906 (ed. Soloviev, M.), 89–99 (Humana Press, New York, 2012).

49. 49.

Wang, H. & Pevsner, J. Detection of endogenous biotin in various tissues: novel functions in the hippocampus and implications for its use in avidin-biotin technology. Cell. Tissue Res. 296, 511–516 (1999).

50. 50.

Alves, N. J. et al. Bacterial nanobioreactors–directing enzyme packaging into bacterial outer membrane vesicles. ACS Appl. Mater. Interfaces 7, 24963–24972 (2015).

51. 51.

Brune, K. D. et al. Plug-and-Display: decoration of Virus-Like Particles via isopeptide bonds for modular immunization. Sci. Rep. 6, 19234 (2016).

52. 52.

Giessen, T. W. & Silver, P. A. A catalytic nanoreactor based on in vivo encapsulation of multiple enzymes in an engineered protein nanocompartment. Chembiochem 17, 1931–1935 (2016).

53. 53.

Moon, H., Bae, Y., Kim, H. & Kang, S. Plug-and-playable fluorescent cell imaging modular toolkits using the bacterial superglue, SpyTag/SpyCatcher. Chem. Commun. 52, 14051–14054 (2016).

54. 54.

Pessino, V., Citron, Y. R., Feng, S. & Huang, B. Covalent protein labeling by SpyTag-SpyCatcher in fixed cells for super-resolution microscopy. Chembiochem 18, 1492–1495 (2017).

55. 55.

Pröschel, M., Detsch, R., Boccaccini, A. R. & Sonnewald, U. Engineering of metabolic pathways by artificial enzyme channels. Front. Bioeng. Biotechnol. 3, 168 (2015).

56. 56.

Stranges, P. B. et al. Design and characterization of a nanopore-coupled polymerase for single-molecule DNA sequencing by synthesis on an electrode array. Proc. Natl Acad. Sci. USA 113, E6749–E6756 (2016).

57. 57.

Chen, A. Y. et al. Synthesis and patterning of tunable multiscale materials with engineered cells. Nat. Mater. 13, 515–523 (2014).

58. 58.

Ke, X. et al. SpyCatcher–SpyTag mediated in situ labelling of progeny baculovirus with quantum dots for tracking viral infection in living cells. Chem. Commun. 54, 1189–1192 (2018).

59. 59.

Jain, K. K. Nanomedicine: application of nanobiotechnology in medical practice. Med. Princ. Pract. 17, 89–101 (2008).

60. 60.

Wicki, A., Witzigmann, D., Balasubramanian, V. & Huwyler, J. Nanomedicine in cancer therapy: challenges, opportunities, and clinical applications. J. Control Release 200, 138–157 (2015).

61. 61.

Doane, T. L. & Burda, C. The unique role of nanoparticles in nanomedicine: imaging, drug delivery and therapy. Chem. Soc. Rev. 41, 2885–2911 (2012).

62. 62.

Kim, B. Y. S., Rutka, J. T. & Chan, W. C. W. Nanomedicine. N. Engl. J. Med. 363, 2434–2443 (2010).

63. 63.

White, P. & Hjortkjaer, J. Preparation and characterisation of a stable silver colloid for SER(R)S spectroscopy. J. Raman Spectrosc. 45, 32–40 (2014).

64. 64.

Sali, A. & Blundell, T. L. Comparative protein modelling by satisfaction of spatial restraints. J. Mol. Biol. 234, 779–815 (1993).

65. 65.

Berendsen, H. J. C., van der Spoel, D. & van Drunen, R. GROMACS: a message-passing parallel molecular dynamics implementation. Comput. Phys. Commun. 91, 43–56 (1995).

66. 66.

Lindahl, E., Hess, B. & van der Spoel, D. GROMACS 3.0: a package for molecular simulation and trajectory analysis. J. Mol. Model. 7, 306–317 (2001).

67. 67.

Humphrey, W., Dalke, A. & Schulten, K. VMD: Visual molecular dynamics. J. Mol. Graph. 14, 33–38 (1996).

68. 68.

Hussain, R., Jávorfi, T. & Siligardi, G. Circular dichroism beamline B23 at the diamond light source. J. Synchrotron Radiat. 19, 132–135 (2012).

69. 69.

Hussain, R. et al. CDApps: integrated software for experimental planning and data processing at beamline B23, diamond light source. Corrigendum. J. Synchrotron Radiat. 22, 862–862 (2015).

70. 70.

Kemmer, G. & Keller, S. Nonlinear least-squares data fitting in Excel spreadsheets. Nat. Protoc. 5, 267–281 (2010).

## Acknowledgements

We appreciate the technical support of Giuliano Siligardi, Rohanah Hussain, and Tamas Javorfi from the Diamond Light Source (Didcot, UK). We thank the Diamond Light Source for experimental beamtime on B23 and the use of the beamline’s Zetasizer ZSP (Malvern) for SM12555, SM15232, and SM16042 awarded beamtimes. This work used EPCC's Cirrus HPC Service (https://www.epcc.ed.ac.uk/cirrus). D.A.-M. and E.F. acknowledge support from the Tullow Group Scholarships Programme and Tom West Analytical Fellowship, respectively. The work was in part supported by the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 645684 “Immuno-NanoDecoder”).

## Author information

W.M. performed most of the experiments, analyzed most data and contributed to conceiving the study; A.S. cloned GST-SpyCatcher, purified some of the protein used and performed SRCD experiments; D.R. performed all MD simulations and contributed to manuscript writing; D.A.-M. performed GST binding experiments at different pH and analyzed the data; M.A. performed Raman experiments and data analysis; M.J. cloned GST-SpyTag; F.D.N. performed z-potential measurements; M.B. contributed to Raman data analysis and experimental design; M.S. performed SRCD experiments and contributed to manuscript writing; E.F. contributed to experiments and data analysis, performed SRCD experiments, conceived the study and wrote the manuscript.

### Competing interests

The authors declare no competing interests.

Correspondence to Enrico Ferrari.