Diana Fusco

Crystallization of asymmetric patchy models for globular proteins in solution.

Asymmetric patchy particle models have recently been shown to describe the crystallization of small globular proteins with near-quantitative accuracy. Here, we investigate how asymmetry in patch geometry and bond energy generally impacts the phase diagram and nucleation dynamics of this family of soft matter models. We find the role of the geometry asymmetry to be weak, but the energy asymmetry to markedly interfere with the crystallization thermodynamics and kinetics. These results provide a rationale for the success and occasional failure of the proposal of George and Wilson for protein crystallization conditions as well as physical guidance for developing more effective protein crystallization strategies.

Characterizing protein crystal contacts and their role in crystallization: rubredoxin as a case study

The fields of structural biology and soft matter have independently sought out fundamental principles to rationalize protein crystallization. Yet the conceptual differences and the limited overlap between the two disciplines have thus far prevented a comprehensive understanding of the phenomenon to emerge. We conduct a computational study of proteins from the rubredoxin family that bridges the two fields. Using atomistic simulations, we characterize the protein crystal contacts, and accordingly parameterize patchy particle models. Comparing the phase diagrams of these schematic models with experimental results enables us to critically examine the assumptions behind the two approaches. The study also reveals features of protein–protein interactions that can be leveraged to crystallize proteins more generally.

Soft matter perspective on protein crystal assembly

Crystallography may be the gold standard of protein structure determination, but obtaining the necessary high-quality crystals is also in some ways akin to prospecting for the precious metal. The tools and models developed in soft matter physics to understand colloidal assembly offer some insights into the problem of crystallizing proteins. This topical review describes the various analogies that have been made between proteins and colloids in that context. We highlight the explanatory power of patchy particle models, but also the challenges of providing guidance for crystallizing specific proteins. We conclude with a presentation of possible future research directions. This review is intended for soft matter scientists interested in protein crystallization as a self-assembly problem, and as an introduction to the pertinent physics literature for protein scientists more generally.

Statistical Analysis of Crystallization Database Links Protein Physico-Chemical Features with Crystallization Mechanisms

X-ray crystallography is the predominant method for obtaining atomic-scale information about biological macromolecules. Despite the success of the technique, obtaining well diffracting crystals still critically limits going from protein to structure. In practice, the crystallization process proceeds through knowledge-informed empiricism. Better physico-chemical understanding remains elusive because of the large number of variables involved, hence little guidance is available to systematically identify solution conditions that promote crystallization. To help determine relationships between macromolecular properties and their crystallization propensity, we have trained statistical models on samples for 182 proteins supplied by the Northeast Structural Genomics consortium. Gaussian processes, which capture trends beyond the reach of linear statistical models, distinguish between two main physico-chemical mechanisms driving crystallization. One is characterized by low levels of side chain entropy and has been extensively reported in the literature. The other identifies specific electrostatic interactions not previously described in the crystallization context. Because evidence for two distinct mechanisms can be gleaned both from crystal contacts and from solution conditions leading to successful crystallization, the model offers future avenues for optimizing crystallization screens based on partial structural information. The availability of crystallization data coupled with structural outcomes analyzed through state-of-the-art statistical models may thus guide macromolecular crystallization toward a more rational basis.

Competition between monomeric and dimeric crystals in schematic models for globular proteins.

Advances in experimental techniques and in theoretical models have improved our understanding of protein crystallization. However, they have also left open questions regarding the protein phase behavior and self-assembly kinetics, such as why (nearly) identical crystallization conditions can sometimes result in the formation of different crystal forms. Here, we develop a patchy particle model with competing sets of patches that provides a microscopic explanation of this phenomenon. We identify different regimes in which one or two crystal forms can coexist with a low-density fluid. Using analytical approximations, we extend our findings to different crystal phases, providing a general framework for treating protein crystallization when multiple crystal forms compete. Our results also suggest different experimental routes for targeting a specific crystal form, and for reducing the dynamical competition between the two forms, thus facilitating protein crystal assembly.

Excess of mutational jackpot events in expanding populations revealed by spatial Luria–Delbrück experiments

The genetic diversity of growing cellular populations, such as biofilms, solid tumours or developing embryos, is thought to be dominated by rare, exceptionally large mutant clones. Yet, the emergence of these mutational jackpot events is only understood in well-mixed populations, where they stem from mutations that arise during the first few cell divisions. To study jackpot events in spatially structured populations, we track mutant clones in microbial populations using fluorescence microscopy and population sequencing. High-frequency mutations are found to be massively enriched in microbial colonies compared with well-shaken liquid cultures, as a result of late-occurring mutations surfing at the edge of range expansions. Thus, jackpot events can be generated not only when mutations arise early but also when they occur at favourable locations, which exacerbates their role in adaptation and disease. In particular, because spatial competition with the wild type keeps most mutant clones in a quiescent state, strong selection pressures that kill the wild type promote drug resistance.

Effects of polymorphism for locally adapted genes on rates of neutral introgression in structured populations.

Adaptation to local conditions within demes balanced by migration can maintain polymorphisms for variants that reduce fitness in certain ecological contexts. Here, we address the effects of such polymorphisms on the rate of introgression of neutral marker genes, possibly genetically linked to targets of selection. Barriers to neutral gene flow are expected to increase with linkage to targets of local selection and with differences between demes in the frequencies of locally adapted alleles. This expectation is borne out under purifying and disruptive selection, regimes that promote monomorphism within demes. In contrast, overdominance within demes induces minimal barriers to neutral introgression even in the face of very large differences between demes in the frequencies of locally adapted alleles. Further, segregation distortion, a phenomenon observed in a number of interspecific hybrids, can in fact promote transmission by migrants to future generations at rates exceeding those of residents.

Collective motion conceals fitness differences in crowded cellular populations

Many cellular populations are tightly-packed, for example microbial colonies and biofilms [39, 10, 41], or tissues and tumors in multi-cellular organisms [11, 29]. Movement of one cell inside such crowded assemblages requires movement of others, so that cell displacements are correlated over many cell diameters [28, 6, 31]. Whenever movement is important for survival or growth [15, 34, 38, 9], such correlated rearrangements could couple the evolutionary fate of different lineages. Yet, little is known about the interplay between mechanical stresses and evolution in dense cellular populations. Here, by tracking deleterious mutations at the expanding edge of yeast colonies, we show that crowding-induced collective motion prevents costly mutations from being weeded out rapidly. Joint pushing by neighboring cells generates correlated movements that suppress the differential displacements required for selection to act. Such mechanical screening of fitness differences allows the mutants to leave more descendants than expected under non-mechanical models, thereby increasing their chance for evolutionary rescue [2, 5]. Our work suggests that mechanical interactions generally influence evolutionary outcomes in crowded cellular populations, which has to be considered when modeling drug resistance or cancer evolution [1, 22, 34, 30, 36, 42].

Learning about Biomolecular Solvation from Water in Protein Crystals

Water occupies typically 50% of a protein crystal and thus significantly contributes to the diffraction signal in crystallography experiments. Separating its contribution from that of the protein is, however, challenging because most water molecules are not localized and are thus difficult to assign to specific density peaks. The intricateness of the protein-water interface compounds this difficulty. This information has, therefore, not often been used to study biomolecular solvation. Here, we develop a methodology to surmount in part this difficulty. More specifically, we compare the solvent structure obtained from diffraction data for which experimental phasing is available to that obtained from constrained molecular dynamics (MD) simulations. The resulting spatial density maps show that commonly used MD water models are only partially successful at reproducing the structural features of biomolecular solvation. The radial distribution of water is captured with only slightly higher accuracy than its angular distribution, and only a fraction of the water molecules assigned with high reliability to the crystal structure is recovered. These differences are likely due to shortcomings of both the water models and the protein force fields. Despite these limitations, we manage to infer protonation states of some of the side chains utilizing MD-derived densities.

Convection shapes the trade-off between antibiotic efficacy and the selection for resistance in spatial gradients

Since penicillin was discovered about 90 years ago, we have become used to using drugs to eradicate unwanted pathogenic cells. However, using drugs to kill bacteria, viruses or cancer cells has the serious side effect of selecting for mutant types that survive the drug attack. A crucial question therefore is how one could eradicate as many cells as possible for a given acceptable risk of drug resistance evolution. We address this general question in a model of drug resistance evolution in spatial drug gradients, which recent experiments and theories have suggested as key drivers of drug resistance. Importantly, our model takes into account the influence of convection, resulting for instance from blood flow. Using stochastic simulations, we study the fates of individual resistance mutations and quantify the trade-off between the killing of wild-type cells and the rise of resistance mutations: shallow gradients and convection into the antibiotic region promote wild-type death, at the cost of increasing the establishment probability of resistance mutations. We can explain these observed trends by modeling the adaptation process as a branching random walk. Our analysis reveals that the trade-off between death and adaptation depends on the relative length scales of the spatial drug gradient and random dispersal, and the strength of convection. Our results show that convection can have a momentous effect on the rate of establishment of new mutations, and may heavily impact the efficiency of antibiotic treatment.