Search

The biophysical interactions between the T cell receptor (TCR) and its ligands determine the specificity of the cellular immune response. However, the immense diversity of receptors and ligands has made it challenging to discover generalizable rules across the distinct binding affinity landscapes created by different ligands. Here, we present an optimization framework for discovering biophysical rules that predict whether TCRs share specificity to a ligand. Applying this framework to TCRs associated with a collection of SARS-CoV-2 peptides we establish how co-specificity depends on the type and position of amino-acid differences between receptors. We also demonstrate that the inferred rules generalize to ligands not seen during training. Our analysis reveals that matching of steric properties between substituted amino acids is important for receptor co-specificity, in contrast with the hydrophobic properties that more prominently determine evolutionary substitutability. We furthermore find that positions not in direct contact with the peptide still significantly impact specificity. These findings highlight the potential for data-driven approaches to uncover the molecular mechanisms underpinning the specificity of adaptive immune responses., Comment: 15 pages, 10 figures

Colonies of the social bacterium Myxococcus xanthus go through a morphological transition from a thin colony of cells to three-dimensional droplet-like fruiting bodies as a strategy to survive starvation. The biological pathways that control the decision to form a fruiting body have been studied extensively. However, the mechanical events that trigger the creation of multiple cell layers and give rise to droplet formation remain poorly understood. By measuring cell orientation, velocity, polarity, and force with cell-scale resolution, we reveal a stochastic local polar order in addition to the more obvious nematic order. Average cell velocity and active force at topological defects agree with predictions from active nematic theory, but their fluctuations are anomalously large due to polar active forces generated by the self-propelled rod-shaped cells. We find that M. xanthus cells adjust their reversal frequency to tune the magnitude of this local polar order, which in turn controls the mechanical stresses and triggers layer formation in the colonies., Comment: 35 page, 26 figures

Microbial communities are ubiquitous in nature and come in a multitude of forms, ranging from communities dominated by a handful of species to communities containing a wide variety of metabolically distinct organisms. This huge range in diversity is not a curiosity - microbial diversity has been linked to outcomes of substantial ecological and medical importance. However, the mechanisms underlying microbial diversity are still under debate, as simple mathematical models only permit as many species to coexist as there are resources. A plethora of mechanisms have been proposed to explain the origins of microbial diversity, but many of these analyses omit a key property of real microbial ecosystems: the propensity of the microbes themselves to change their growth properties within and across generations. In order to explore the impact of this key property on microbial diversity, we expand upon a recently developed model of microbial diversity in fluctuating environments. We implement changes in growth strategy in two distinct ways. First, we consider the regulation of a cell's enzyme levels within short, ecological times, and second we consider evolutionary changes driven by mutations across generations. Interestingly, we find that these two types of microbial responses to the environment can have drastically different outcomes. Enzyme regulation may collapse diversity over long enough times while, conversely, strategy-randomizing mutations can produce a "rich-get-poorer" effect that promotes diversity. This work makes explicit, using a simple serial-dilutions framework, the conflicting ways that microbial adaptation and evolution can affect community diversity., Comment: This work extends the modeling framework from "Nutrient levels and trade-offs control diversity in a serial dilution ecosystem" at https://elifesciences.org/articles/57790 ; Main text: 8 pages, 3 figures. Appendix: 4 pages, 5 figures

Despite the absence of a membrane-enclosed nucleus, the bacterial DNA is typically condensed into a compact body - the nucleoid. This compaction influences the localization and dynamics of many cellular processes including transcription, translation, and cell division. Here, we develop a model that takes into account steric interactions among the components of the Escherichia coli transcriptional-translational machinery (TTM) and out-of-equilibrium effects of mRNA transcription, translation, and degradation, in order to explain many observed features of the nucleoid. We show that steric effects, due to the different molecular shapes of the TTM components, are sufficient to drive equilibrium phase separation of the DNA, explaining the formation and size of the nucleoid. In addition, we show that the observed positioning of the nucleoid at midcell is due to the out-of-equilibrium process of messenger RNA (mRNA) synthesis and degradation: mRNAs apply a pressure on both sides of the nucleoid, localizing it to midcell. We demonstrate that, as the cell grows, the production of these mRNAs is responsible for the nucleoid splitting into two lobes, and for their well-known positioning to 1/4 and 3/4 positions on the long cell axis. Finally, our model quantitatively accounts for the observed expansion of the nucleoid when the pool of cytoplasmic mRNAs is depleted. Overall, our study suggests that steric interactions and out-of-equilibrium effects of the TTM are key drivers of the internal spatial organization of bacterial cells., Comment: 21 pages, 11 figures

Multivalent associative proteins with strong complementary interactions play a crucial role in phase separation of intracellular liquid condensates. We study the internal dynamics of such "bond-network" condensates comprised of two complementary proteins via scaling analysis and molecular dynamics. We find that when stoichiometry is balanced, relaxation slows down dramatically due to a scarcity of alternative partners following a bond break. This microscopic slow-down strongly affects the bulk diffusivity, viscosity and mixing, which provides a means to experimentally test our predictions.

Studies of active matter, from molecular assemblies to animal groups, have revealed two broad classes of behavior: a tendency to align yields orientational order and collective motion, whereas particle repulsion leads to self-trapping and motility-induced phase separation. Here, we report a third class of behavior: orientational interactions that produce active phase separation. Combining theory and experiments on self-propelled Janus colloids, we show that stronger repulsion on the rear than on the front of these particles produces non-reciprocal torques that reorient particle motion toward high-density regions. Particles thus self-propel toward crowded areas, which leads to phase separation. Clusters remain fluid and exhibit fast particle turnover, in contrast to the jammed clusters that typically arise from self-trapping, and interfaces are sufficiently wide that they span entire clusters. Overall, our work identifies a torque-based mechanism for phase separation in active fluids, and our theory predicts that these orientational interactions yield coexisting phases that lack internal orientational order.

The soil bacterium Myxococcus xanthus lives in densely packed groups that form dynamic three-dimensional patterns in response to environmental changes, such as droplet-like fruiting bodies during starvation. The development of these multicellular structures begins with the sequential formation of cell layers in a process that is poorly understood. Using confocal three-dimensional imaging, we find that motile rod-shaped M. xanthus cells are densely packed and aligned in each layer, forming an active nematic liquid crystal. Cell alignment is nearly perfect throughout the population except at point defects that carry half-integer topological charge. We observe that new cell layers preferentially form at the position of +1/2 defects, whereas holes preferentially open at -1/2 defects. To explain these findings, we model the bacterial colony as an extensile active nematic fluid with anisotropic friction. In agreement with our experimental measurements, this model predicts an influx of cells toward +1/2 defects, and an outflux of cells from -1/2 defects. Our results suggest that cell motility and mechanical cell-cell interactions are sufficient to promote the formation of cell layers at topological defects, thereby seeding fruiting bodies in colonies of M. xanthus., Comment: Final version

During development, organisms acquire three-dimensional shapes with important physiological consequences. While the basic mechanisms underlying morphogenesis are known in eukaryotes, it is often difficult to manipulate them in vivo. To circumvent this issue, here we present a study of developing Vibrio cholerae biofilms grown on agar substrates in which the spatiotemporal morphological patterns were altered by varying the agar concentration. Expanding biofilms are initially flat, but later experience a mechanical instability and become wrinkled. Whereas the peripheral region develops ordered radial stripes, the central region acquires a zigzag herringbone-like wrinkle pattern. Depending on the agar concentration, the wrinkles initially appear either in the peripheral region and propagate inward (low agar concentration) or in the central region and propagate outward (high agar concentration). To understand these experimental observations, we developed a model that considers diffusion of nutrients and their uptake by bacteria, bacterial growth/biofilm matrix production, mechanical deformation of both the biofilm and the agar, and the friction between them. Our model demonstrates that depletion of nutrients beneath the central region of the biofilm results in radially-dependent growth profiles, which in turn, produce anisotropic stresses that dictate the morphology of wrinkles. Furthermore, we predict that increasing surface friction (agar concentration) reduces stress anisotropy and shifts the location of the maximum compressive stress, where the wrinkling instability first occurs, toward the center of the biofilm, in agreement with our experimental observations. Our results are broadly applicable to bacterial biofilms with similar morphologies and also provide insight into how other bacterial biofilms form distinct wrinkle patterns., Comment: 16 pages, 4 figures + supplementary information (36 pages, 14 figures)

Microbial communities feature an immense diversity of species and this diversity is linked with outcomes ranging from ecosystem stability to medical prognoses. Yet the mechanisms underlying microbial diversity are under debate. While simple resource-competition models don't allow for coexistence of a large number of species, it was recently shown that metabolic trade-offs can allow unlimited diversity. Does this diversity persist with more realistic, intermittent nutrient supply? Here, we demonstrate theoretically that in serial dilution culture, metabolic trade-offs allow for high diversity. When a small amount of nutrient is supplied to each batch, the serial dilution dynamics mimic a chemostat-like steady state. If more nutrient is supplied, diversity depends on the amount of nutrient supplied due to an "early-bird" effect. The interplay of this effect with different environmental factors and diversity-supporting mechanisms leads to a variety of relationships between nutrient supply and diversity, suggesting that real ecosystems may not obey a universal nutrient-diversity relationship., Comment: Appendix follows main text

Cells possess non-membrane-bound bodies, many of which are now understood as phase-separated condensates. One class of such condensates is composed of two polymer species, where each consists of repeated binding sites that interact in a one-to-one fashion with the binding sites of the other polymer. Previous biologically-motivated modeling of such a two-component system surprisingly revealed that phase separation is suppressed for certain combinations of numbers of binding sites. This phenomenon, dubbed the "magic-number effect", occurs if the two polymers can form fully-bonded small oligomers by virtue of the number of binding sites in one polymer being an integer multiple of the number of binding sites of the other. Here we use lattice-model simulations and analytical calculations to show that this magic-number effect can be greatly enhanced if one of the polymer species has a rigid shape that allows for multiple distinct bonding conformations. Moreover, if one species is rigid, the effect is robust over a much greater range of relative concentrations of the two species. Our findings advance our understanding of the fundamental physics of two-component polymer-based phase-separation and suggest implications for biological and synthetic systems., Comment: 8 pages + 15 pages SI

Statistical analysis of alignments of large numbers of protein sequences has revealed "sectors" of collectively coevolving amino acids in several protein families. Here, we show that selection acting on any functional property of a protein, represented by an additive trait, can give rise to such a sector. As an illustration of a selected trait, we consider the elastic energy of an important conformational change within an elastic network model, and we show that selection acting on this energy leads to correlations among residues. For this concrete example and more generally, we demonstrate that the main signature of functional sectors lies in the small-eigenvalue modes of the covariance matrix of the selected sequences. However, secondary signatures of these functional sectors also exist in the extensively-studied large-eigenvalue modes. Our simple, general model leads us to propose a principled method to identify functional sectors, along with the magnitudes of mutational effects, from sequence data. We further demonstrate the robustness of these functional sectors to various forms of selection, and the robustness of our approach to the identification of multiple selected traits., Comment: 37 pages, 28 figures

An essential feature of the adaptive immune system is the proliferation of antigen-specific lymphocytes during an immune reaction to form a large pool of effector cells. This proliferation must be regulated to ensure an effective response to infection while avoiding immunopathology. Recent experiments in mice have demonstrated that the expansion of a specific clone of T cells in response to cognate antigen obeys a striking inverse power law with respect to the initial number of T cells. Here, we show that such a relationship arises naturally from a model in which T cell expansion is limited by decaying levels of presented antigen. The same model also accounts for the observed dependence of T cell expansion on affinity for antigen and on the kinetics of antigen administration. Extending the model to address expansion of multiple T cell clones competing for antigen, we find that higher affinity clones can suppress the proliferation of lower affinity clones, thereby promoting the specificity of the response. Employing the model to derive optimal vaccination protocols, we find that exponentially increasing antigen doses can achieve a nearly optimized response. We thus conclude that the dynamics of presented antigen is a key regulator of both the size and specificity of the adaptive immune response.

Are "turn-on" and "turn-off" functions in protein-protein interaction networks exact opposites of each other? To answer this question, we implement a minimal model for the evolution of functional protein-interaction networks using a sequence-based mutational algorithm, and apply the model to study neutral drift in networks that yield oscillatory dynamics. We study the roles of activators and deactivators, two core components of oscillatory protein interaction networks, and find a striking asymmetry in the roles of activating and deactivating proteins, where activating proteins tend to be synergistic and deactivating proteins tend to be competitive., Comment: 7 Pages, 5 Figures

Biofilms are communities of bacteria adhered to surfaces. Recently, biofilms of rod-shaped bacteria were observed at single-cell resolution and shown to develop from a disordered, two-dimensional layer of founder cells into a three-dimensional structure with a vertically-aligned core. Here, we elucidate the physical mechanism underpinning this transition using a combination of agent-based and continuum modeling. We find that verticalization proceeds through a series of localized mechanical instabilities on the cellular scale. For short cells, these instabilities are primarily triggered by cell division, whereas long cells are more likely to be peeled off the surface by nearby vertical cells, creating an "inverse domino effect". The interplay between cell growth and cell verticalization gives rise to an exotic mechanical state in which the effective surface pressure becomes constant throughout the growing core of the biofilm surface layer. This dynamical isobaricity determines the expansion speed of a biofilm cluster and thereby governs how cells access the third dimension. In particular, theory predicts that a longer average cell length yields more rapidly expanding, flatter biofilms. We experimentally show that such changes in biofilm development occur by exploiting chemicals that modulate cell length., Comment: Main text 10 pages, 4 figures; Supplementary Information 35 pages, 15 figures

Signal transduction networks can form highly interconnected systems within cells due to network crosstalk, the sharing of input signals between multiple downstream responses. To better understand the evolutionary design principles underlying such networks, we study the evolution of crosstalk and the emergence of specificity for two parallel signaling pathways that arise via gene duplication and are subsequently allowed to diverge. We focus on a sequence based evolutionary algorithm and evolve the network based on two physically motivated fitness functions related to information transmission. Surprisingly, we find that the two fitness functions lead to very different evolutionary outcomes, one with a high degree of crosstalk and the other without., Comment: 18 Pages, 16 Figures

The bacterial genome is organized in a structure called the nucleoid by a variety of associated proteins. These proteins can form complexes on DNA that play a central role in various biological processes, including chromosome segregation. A prominent example is the large ParB-DNA complex, which forms an essential component of the segregation machinery in many bacteria. ChIP-Seq experiments show that ParB proteins localize around centromere-like parS sites on the DNA to which ParB binds specifically, and spreads from there over large sections of the chromosome. Recent theoretical and experimental studies suggest that DNA-bound ParB proteins can interact with each other to condense into a coherent 3D complex on the DNA. However, the structural organization of this protein-DNA complex remains unclear, and a predictive quantitative theory for the distribution of ParB proteins on DNA is lacking. Here, we propose the Looping and Clustering (LC) model, which employs a statistical physics approach to describe protein-DNA complexes. The LC model accounts for the extrusion of DNA loops from a cluster of interacting DNA-bound proteins. Conceptually, the structure of the protein-DNA complex is determined by a competition between attractive protein interactions and the configurational and loop entropy of this protein-DNA cluster. Indeed, we show that the protein interaction strength determines the "tightness" of the loopy protein-DNA complex. With this approach we consider the genomic organization of such a protein-DNA cluster around a single high-affinity binding site. Thus, our model provides a theoretical framework to quantitatively compute the binding profiles of ParB-like proteins around a cognate (parS) binding site., Comment: 13 pages, 7 figures, SI, resubmitted

We introduce a minimal model for the evolution of functional protein-interaction networks using a sequence-based mutational algorithm, and apply the model to study neutral drift in networks that yield oscillatory dynamics. Starting with a functional core module, random evolutionary drift increases network complexity even in the absence of specific selective pressures. Surprisingly, we uncover a hidden order in sequence space that gives rise to long-term evolutionary memory, implying strong constraints on network evolution due to the topology of accessible sequence space., Comment: 20 Pages, 14 Figures

Cells actively probe and respond to the stiffness of their surroundings. Since mechanosensory cells in connective tissue are surrounded by a disordered network of biopolymers, their in vivo mechanical environment can be extremely heterogeneous. Here, we investigate how this heterogeneity impacts mechanosensing by modeling the cell as an idealized local stiffness sensor inside a disordered fiber network. For all types of networks we study, including experimentally-imaged collagen and fibrin architectures, we find that measurements applied at different points throughout a given network yield a strikingly broad range of local stiffnesses, spanning roughly two decades. We verify via simulations and scaling arguments that this broad range of local stiffnesses is a generic property of disordered fiber networks, and show that the range can be further increased by tuning specific network features, including the presence of long fibers and the proximity to elastic transitions. These features additionally allow for a highly tunable dependence of stiffness on probe length. Finally, we show that to obtain optimal, reliable estimates of global tissue stiffness, a cell must adjust its size, shape, and position to integrate multiple stiffness measurements over extended regions of space., Comment: 30 pages, 14 figures

Specific protein-protein interactions are crucial in the cell, both to ensure the formation and stability of multi-protein complexes, and to enable signal transduction in various pathways. Functional interactions between proteins result in coevolution between the interaction partners, causing their sequences to be correlated. Here we exploit these correlations to accurately identify which proteins are specific interaction partners from sequence data alone. Our general approach, which employs a pairwise maximum entropy model to infer couplings between residues, has been successfully used to predict the three-dimensional structures of proteins from sequences. Thus inspired, we introduce an iterative algorithm to predict specific interaction partners from two protein families whose members are known to interact. We first assess the algorithm's performance on histidine kinases and response regulators from bacterial two-component signaling systems. We obtain a striking 0.93 true positive fraction on our complete dataset without any a priori knowledge of interaction partners, and we uncover the origin of this success. We then apply the algorithm to proteins from ATP-binding cassette (ABC) transporter complexes, and obtain accurate predictions in these systems as well. Finally, we present two metrics that accurately distinguish interacting protein families from non-interacting ones, using only sequence data., Comment: 25 pages, 19 figures, published version

Metagenomics has revealed hundreds of bacterial species in almost all microbiota. In a few well-studied cases, bacterial communities have been observed to coordinate their metabolic fluxes. In principle, bacteria can divide tasks to reap the benefits of specialization, as in human economies. However, the benefits and stability of an economy of bacterial specialists are far from obvious. Here, we physically model the population dynamics of bacteria that compete for steadily supplied resources. Importantly, we explicitly model the metabolic fluxes yielding cellular biomass production under the constraint of a limited enzyme budget. In our framework, we find that population dynamics generally leads to the coexistence of different metabolic types, which satisfy an extended competitive exclusion principle (even allowing for adaptive mutation). We establish that these consortia act as cartels, whereby population dynamics pins down resource concentrations at values for which no other strategy can invade. Finally, we propose that at steady supply, cartels of competing strategies automatically yield maximum biomass, thereby achieving a collective optimum.

How cells reliably infer information about their environment is a fundamentally important question. While sensing and signaling generally start with cell-surface receptors, the degree of accuracy with which a cell can measure external ligand concentration with even the simplest device - a single receptor - is surprisingly hard to pin down. Recent studies provide conflicting results for the fundamental physical limits. Comparison is made difficult as different studies either suggest different readout mechanisms of the ligand-receptor occupancy, or differ on how ligand diffusion is implemented. Here we critically analyse these studies and present a unifying perspective on the limits of sensing, with wide-ranging biological implications., Comment: 25 pages, 4 figures

In bacteria such as $\textit{Escherichia coli}$, DNA is compacted into a nucleoid near the cell center, while ribosomes$-$molecular complexes that translate messenger RNAs (mRNAs) into proteins$-$are mainly localized at the poles. We study the impact of this spatial organization using a minimal reaction-diffusion model for the cellular transcriptional-translational machinery. Our model predicts that $\sim 90\%$ of mRNAs are segregated to the poles and reveals a "circulation" of ribosomes driven by the flux of mRNAs, from synthesis in the nucleoid to degradation at the poles. To address the existence of non-specific, transient interactions between ribosomes and mRNAs, we developed a novel method to efficiently incorporate such transient interactions into reaction-diffusion equations, which allowed us to quantify the biological implications of such non-specific interactions, e.g. for ribosome efficiency.

Flagellated bacteria, such as Escherichia coli, perform directed motion in gradients of concentration of attractants and repellents in a process called chemotaxis. The E. coli chemotaxis signaling pathway is a model for signal transduction, but it has unique features. We demonstrate that the need for fast signaling necessitates high abundances of the proteins involved in this pathway. We show that further constraints on the abundances of chemotaxis proteins arise from the requirements of self-assembly, both of flagellar motors and of chemoreceptor arrays. All these constraints are specific to chemotaxis, and published data confirm that chemotaxis proteins tend to be more highly expressed than their homologs in other pathways. Employing a chemotaxis pathway model, we show that the gain of the pathway at the level of the response regulator CheY increases with overall chemotaxis protein abundances. This may explain why, at least in one E. coli strain, the abundance of all chemotaxis proteins is higher in media with lower nutrient content. We also demonstrate that the E. coli chemotaxis pathway is particularly robust to abundance variations of the motor protein FliM., Comment: 39 pages, 8 figures