We present a novel approach for embedding experimental contact information in the protein structure prediction tool AlphaFold2 that harnesses the principles of protein sequence coevolution to enforce disulfide connectivity patterns in the prediction of disulfide-rich peptide (DRP) structures. While AlphaFold2 generates accurate DRP structure prediction in most cases, it sometimes fails at predicting the specific connectivity pattern of the multiple disulfide bonds. Here, we take advantage of the principles of sequence coevolution to engineer the multiple sequence alignment (MSA) input with specific connectivity patterns by mutating highly conserved cysteines in subsets of the MSA—which we term “simulated coevolution.” Engineering the MSA prompt with simulated coevolution provides sufficient context in most cases for AlphaFold2 to obey the provided connectivity. Our approach—KnotFold—can be used to incorporate experimental disulfide connectivity patterns from mass spectrometry into DRP structure prediction. Lastly, we find that peptide properties and AF2Rank Composite Confidence scores can be used to differentiate native from non-native connectivity patterns in some cases, improving the ability to determine native connectivity of DRPs from sequence alone.

The mitotic spindle, a micromachine composed of microtubules and associated proteins, plays a pivotal role in ensuring the accurate segregation of chromosomes. During spindle assembly, initially randomly distributed chromosomes are transported toward the equatorial plate and experiments suggest that several competing mechanisms can contribute to this process of chromosome congression. However, a systematic theoretical study of forces relevant to chromosome congression is still lacking. Here we show, by introducing a physical model, that length-dependent forces generated by motor proteins transport chromosomes toward the spindle equator. Passive cross-linkers, on the other hand, can generate off-centering forces that impair chromosome congression. Our mean-field approach also reveals that stable points can exist in the vicinity of spindle poles, in addition to the one in the center, and thus provides an explanation for erroneous spindles with polar chromosomes. Taking all these processes into account, our study provides a comprehensive approach to understanding how different spindle components interact with each other and generate forces that drive chromosome congression.

The integration of neural representations in the two brain hemispheres has been studied extensively in vision, audition, and somatosensation, but less so in olfaction. Recent experiments have revealed that odor responses in cortical neurons driven by separate stimulation of the two nostrils are highly correlated. This bilateral alignment points to structured, nonrandom interhemispheric connections, but how this structure leads to alignment is unclear. Here, we hypothesized that continuous exposure to environmental odors shapes these projections and modeled it as online learning with a local Hebbian rule. We found that Hebbian learning with sparse connections achieves bilateral alignment, exhibiting a linear tradeoff between speed and accuracy (lower learning rate leads to higher alignment level but slower convergence). Furthermore, we identified an inverse scaling relationship between the number of cortical neurons and the interhemispheric projection density required for desired alignment accuracy. Thus, more cortical neurons allow sparser interhemispheric projections, which was explained analytically. We next compared the alignment performance of local Hebbian rule and the global stochastic gradient descent (SGD) learning rule used in artificial neural networks. We found that although SGD leads to the same alignment accuracy with a slightly reduced sparsity, the same inverse scaling relation holds. Our analysis showed that their similar performance originates from the fact that the update vectors of the two learning rules align with each other throughout the entire learning process. Our work suggests that a biologically plausible mechanism with sparse connections suffices for correlated bilateral responses. The quantitative comparison between the local Hebbian rule and the global SGD rule may inspire efficient sparse local learning algorithms for more complex problems.

Maintaining intracellular homeostases is a hallmark of life, and Escherichia coli works to maintain multiple interconnected electrophysiological variables, such as a near-neutral pH and a sufficient electrochemical gradient of protons, the so-called proton motive force (PMF). To generate the latter, E. coli relies on central metabolism to move protons out of the cell, where in its preferred near-neutral extracellular environments this is not enough to achieve reported physiological PMF values. Using mathematical modeling, we predict that E. coli also uses proton-ion antiporters for this purpose. Their principal function, powered by the central-metabolism-enabled proton efflux, is to generate the PMF by moving other ions. Consistently, our model predicts that the strength of the PMF sets the maximal rate at which the antiporters work, and so determines the extracellular pH range for which the two homeostases hold. We further predict that artificially collapsing the PMF destroys the membrane potential. In support and by concurrently measuring the PMF and pH in individual cells of E. coli, we show that decreasing the PMF's strength impairs the cells' ability to maintain pH and that they have negligible membrane potential when there is no PMF. Finally, we use our model to predict the previously reported ranges of extracellular pH for which E. coli expresses three antiporters, by defining their cost through the rate at which they divert protons from generating ATP. Taken together our results suggest a new perspective on bacterial electrophysiology, where cells use antiporters to generate the plasma membrane potential and thus their PMF.

Synaptic plasticity dynamically shapes the connectivity of neural systems and is key to learning processes in the brain. To what extent the mechanisms of plasticity can be exploited to drive a neural network and make it perform some kind of computational task remains unclear. This question, relevant in a bioengineering context, can be formulated as a control problem on a high-dimensional system with strongly constrained and nonlinear dynamics. We present a self-contained procedure which, through appropriate spatiotemporal stimulations of the neurons, is able to drive rate-based neural networks with arbitrary initial connectivity towards a desired functional state. We illustrate our approach on two different computational tasks: a nonlinear association between multiple input stimulations and activity patterns (representing digit images), and the construction of a continuous attractor encoding a collective variable in a neural population. Our work thus provides a proof of principle for emerging paradigms of in vitro computation based on real neurons.

The relationships between protein sequences, structures, and functions are determined by complex codes that scientists aim to decipher. While structures contain key information about proteins' biochemical functions, they are often experimentally difficult to obtain. In contrast, protein sequences are abundant but are a step removed from function. In this paper, we propose residue level alignment (RLA)—a self-supervised objective for aligning sequence and structure embedding spaces. By situating sequence and structure encoders within the same latent space, RLA enriches the sequence encoder with spatial information. Moreover, our framework enables us to measure the similarity between a sequence and structure by comparing their RLA embeddings. We show how RLA similarity scores can be used for binder design by selecting true binders from sets of designed binders. RLA scores are informative even when they are calculated given only the backbone structure of the binder and no binder sequence information, which simulates the information available in many early-stage binder design libraries. RLA performs similarly to benchmark methods and is orders of magnitude faster, making it a valuable new screening tool for binder design pipelines.

The protein design problem involves finding polypeptide sequences folding into a given three-dimensional structure. Its rigorous algorithmic solution is computationally demanding, involving a nested search in sequence and structure spaces. Structure searches can now be bypassed thanks to recent machine-learning breakthroughs, which have enabled accurate and rapid structure predictions. Similarly, sequence searches might be entirely transformed by the advent of quantum annealing machines and by the required new encodings of the search problem, which could be performative even on classical machines. In this work, we introduce a general protein design scheme where algorithmic and technological advancements in machine learning and quantum-inspired algorithms can be integrated, and an optimal physics-based scoring function is iteratively learned. In this first proof-of-concept application, we apply the iterative method to a lattice protein model amenable to exhaustive benchmarks, finding that it can rapidly learn a physics-based scoring function and achieve promising design performances. Strikingly, our quantum-inspired reformulation outperforms conventional sequence optimization even when adopted on classical machines. The scheme is general and can be extended, e.g., to encompass off-lattice models, and it can integrate progress on various computational platforms, thus representing a new paradigm approach for protein design.

Living systems continually respond to signals from the surrounding environment. Survival requires that their responses adapt quickly and robustly to the changes in the environment. One particularly challenging example is olfactory navigation in turbulent plumes, where animals experience highly intermittent odor signals while odor concentration varies over many length- and timescales. Here, we show theoretically that Drosophila olfactory receptor neurons (ORNs) can exploit proximity to a bifurcation point of their firing dynamics to reliably extract information about the timing and intensity of fluctuations in the odor signal, which have been shown to be critical for odor-guided navigation. Close to the bifurcation, the system is intrinsically invariant to signal variance, and information about the timing, duration, and intensity of odor fluctuations is transferred efficiently. Importantly, we find that proximity to the bifurcation is maintained by mean adaptation alone and therefore does not require any additional feedback mechanism or fine-tuning. Using a biophysical model with calcium-based feedback, we demonstrate that this mechanism can explain the measured adaptation characteristics of Drosophila ORNs.

Multicellular self-assembly into functional structures is a dynamic process that is critical in the development of biological structures and diseases, including embryo development, organ formation, tumor invasion, and other processes. Being able to infer collective cell migratory dynamics from their static configuration is valuable for both understanding and predicting these complex behaviors. However, the identification of structural features that can indicate multicellular motion has been difficult, and existing metrics largely rely on physical instincts. Here we show that, through the use of a graph neural network, the motion of multicellular collectives can be inferred from a static snapshot of cell positions, in both experimental and synthetic datasets.

Phenotype transitions occur in many biological processes such as differentiation and reprogramming. A fundamental question is how cells coordinate switching of gene expression clusters. By analyzing single-cell RNA sequencing data within the framework of transition path theory, we studied the genome-wide expression program switching in five different cell transition processes. For each process we reconstructed a reaction coordinate describing the transition progression, and we inferred the gene regulatory network along this reaction coordinate. In all processes we observed a common pattern: the overall effective number and strength of regulation between different communities increase first and then decrease. This change is accompanied by similar changes in gene regulatory network frustration—defined as the overall conflict between the regulation received by genes and their expression states. Complementing previous studies suggesting that biological networks are modularized to contain perturbation effects locally, our analyses on the five cell transition processes likely reveal a general principle: during a cell phenotypic transition, intercommunity interactions increase to concertedly coordinate global gene expression reprogramming and canalize to specific cell phenotype, as Waddington visioned.

Entrainment experiments on the vertebrate segmentation clock have revealed that embryonic oscillators actively change their internal frequency to adapt to the driving signal. This is not consistent with either a one-dimensional clock model or a limit-cycle model, but rather it suggests a new “unclocklike” behavior. In this work, we propose simple, biologically realistic descriptions of such internal frequency adaptation, where a phase oscillator activates a memory variable controlling the oscillator's frequency. We study two opposite limits for the control of the memory variable, one with a smooth phase-averaging memory field, and the other with a pulsatile, phase-dependent activation. Both models recapitulate intriguing properties of the entrained segmentation clock, such as very broad Arnold tongues and an entrainment phase plateauing with detuning. We compute analytically multiple properties of such systems, such as entrainment phases and cycle shapes. We further describe new phenomena, including hysteresis in entrainment, bistability in the frequency of the entrained oscillator, and probabilistic entrainment. Our work shows that oscillators with frequency memory can exhibit new classes of unclocklike properties that can be tested through experimental entrainment.

The establishment of the body plan is a major step in animal morphogenesis. The role of mechanical forces and feedback in patterning the body plan remains unclear. Here we explore this question by studying regenerating Hydra tissues confined in narrow cylindrical channels, which constrain their morphology. We find that frustration between the orientation of the channel and the inherited axis in the regenerating tissues can lead to the formation of a multiaxial body plan. The morphological outcome is directly related to the pattern of nematic topological defects that emerges in the organization of the supracellular actomyosin fibers. When the inherited axis, which can be read out from the initial alignment of the supracellular fibers in the confined spheroid, is parallel to the channel's axis, the tissue regenerates normally into animals with a single body axis aligned with the channel. However, regenerating spheroids that are confined in a frustrated perpendicular configuration often develop excess defects (including negatively charged −1/2 defects) and regenerate into multiaxial morphologies. The influence of mechanical constraints on the regenerated body plan argues against an axial patterning mechanism that is based solely on inherited gradients of biochemical morphogens. We further show that the dependence of the regeneration outcomes on the initial tissue orientation can be recapitulated by a biophysical model, which considers the coupled dynamics of the nematic organization of the actomyosin fibers and a morphogen concentration field, incorporating a mechanochemical feedback loop involving strain-dependent morphogen production at defect sites.

While two-body fighting behavior occurs throughout the animal kingdom to settle dominance disputes, important questions such as how the dynamics ultimately lead to a winner and loser are unresolved. Here we examine fighting behavior at high resolution in male zebrafish. We combine multiple cameras, a large volume containing a transparent interior cage to avoid reflection artifacts, with computer vision to track multiple body points across multiple organisms while maintaining individual identity in three dimensions. In the body point trajectories we find a spectrum of timescales which we use to build informative joint coordinates consisting of relative orientation and distance. We use the distribution of these coordinates to automatically identify fight epochs, and we demonstrate the postfight emergence of an abrupt asymmetry in relative orientations—a clear and quantitative signal of hierarchy formation. We identify short-time, multi-animal behaviors as clustered transitions between joint configurations, and show that fight epochs are spanned by a subset of these clusters, which we denote as maneuvers. The resulting space of maneuvers is rich but interpretable, including motifs such as “attacks” and “circling.” In the longer-time dynamics of maneuver frequencies we find differential and changing strategies, including that the eventual loser attacks more often towards the end of the contest. Our results suggest a reevaluation of relevant assessment models in zebrafish, while our approach is generally applicable to other animal systems.

Mitochondrial network structure is controlled by the dynamical processes of fusion and fission, which merge and split mitochondrial tubes into structures including branches and loops. To investigate the impact of mitochondrial network dynamics and structure on the spread of proteins and other molecules through mitochondrial networks, we used stochastic simulations of two distinct quantitative models that each included mitochondrial fusion and fission, and particle diffusion via the network. Better-connected mitochondrial networks and networks with faster dynamics exhibit more rapid particle spread on the network, with little further improvement once a network has become well connected. As fragmented networks gradually become better connected, particle spread either steadily improves until the networks become well connected for slow-diffusing particles or plateaus for fast-diffusing particles. We compared model mitochondrial networks with both end-to-end and end-to-side fusion, which form branches, to nonbranching model networks that lack end-to-side fusion. To achieve the optimum (most rapid) spread that occurs on well-connected branching networks, nonbranching networks require much faster fusion and fission dynamics. Thus, the process of end-to-side fusion, which creates branches in mitochondrial networks, enables rapid spread of particles on the network with relatively slow fusion and fission dynamics. This modeling of protein spread on mitochondrial networks builds toward mechanistic understanding of how mitochondrial structure and dynamics regulate mitochondrial function.

Epithelial cells generate functional tissues in developing embryos through collective movements and shape changes. In some morphogenetic events, a tissue dramatically reorganizes its internal structure—often generating high degrees of structural disorder—to accomplish changes in tissue shape. However, the origins of structural disorder in epithelia and what roles it might play in morphogenesis are poorly understood. We study this question in the Drosophila germband epithelium, which undergoes dramatic changes in internal structure as cell rearrangements drive elongation of the embryo body axis. Using two order parameters that quantify volumetric and shear disorder, we show that structural disorder increases during body axis elongation and is strongly linked with specific developmental processes. Both disorder metrics begin to increase around the onset of axis elongation, but then plateau at values that are maintained throughout the process. Notably, the disorder plateau values for volumetric disorder are similar to those for random cell packings, suggesting this may reflect a limit on tissue behavior. In mutant embryos with disrupted external stresses from the ventral furrow, both disorder metrics reach wild-type maximum disorder values with a delay, correlating with delays in cell rearrangements. In contrast, in mutants with disrupted internal stresses and cell rearrangements, volumetric disorder is reduced compared to wild type, and shear disorder depends on specific external stress patterns. Together, these findings demonstrate that internal and external stresses both contribute to epithelial tissue disorder and suggest that the maximum values of disorder in a developing tissue reflect physical or biological limits on morphogenesis.

Cytoplasmic streaming, the persistent flow of fluid inside a cell, induces intracellular transport, which plays a key role in fundamental biological processes. In meiosis II mouse oocytes (developing egg cells) awaiting fertilization, the spindle, which is the protein structure responsible for dividing genetic material in a cell, must maintain its position near the cell cortex (the thin actin network bound to the cell membrane) for many hours. However, the cytoplasmic streaming that accompanies this stable positioning would intuitively appear to destabilize the spindle position. Here, through a combination of numerical and analytical modeling, we reveal a hydrodynamic mechanism for stable spindle positioning beneath the cortical cap. We show that this stability depends critically on the spindle size and the active driving from the cortex and demonstrate that stable spindle positioning can result purely from a hydrodynamic suction force exerted on the spindle by the cytoplasmic flow. Our findings show that local fluid dynamic forces can be sufficient to stabilize the spindle, explaining robustness against perturbations not only perpendicular but also parallel to the cortex. Our results shed light on the importance of cytoplasmic streaming in mammalian meiosis.

In many cell types, mitochondria undergo extensive fusion and fission to form dynamic, responsive network structures that contribute to a number of homeostatic, metabolic, and signaling functions. The relationship between the dynamic interactions of individual mitochondrial units and the cell-scale network architecture remains an open area of study. In this work, we use coarse-grained simulations and approximate analytic models to establish how the network morphology is governed by local mechanical and kinetic parameters. The transition between fragmented structures and extensive networks is controlled by local fusion-to-fission ratios, network density, and geometric constraints. Similar fusion rate constants are found to account for the very different structures formed by mammalian networks (poised at the percolation transition) and well-connected budding yeast networks. Over a broad parameter range, the simulated network structures can be described by effective mean-field association constants that exhibit a nonlinear dependence on the microscopic nonequilibrium fusion, fission, and transport rates. Intermediate fusion rate constants are shown to result in the highest rates of network remodeling, with mammalian mitochondrial networks situated in a regime of high turnover. This spatially resolved modeling and simulation framework helps elucidate the emergence of cellular scale network structures, and allows for the quantitative extraction of microscopic kinetic parameters from past and future experimental data.

Deep-learning-based protein structure prediction has facilitated major breakthroughs in biological sciences. However, current methods struggle with alternative conformation prediction and offer limited integration of expert knowledge on protein dynamics. We introduce AFEXplorer, a generic approach that tailors AlphaFold predictions to user-defined constraints in coarse coordinate spaces by optimizing embedding features. Its effectiveness in generating functional protein conformations in accordance with predefined conditions is demonstrated through comprehensive examples. AFEXplorer serves as a versatile platform for conditioned protein structure prediction, bridging the gap between automated models and domain-specific insights.

We propose a polymer model to investigate in silico the dynamics of chromatin replication in three dimensions (PolyRep). Our results indicate that replication complexes, the replisomes, may self-assemble during the process and replicate chromatin by extruding it (immobile replisome) or by moving along the template filament (tracking replisome), reconciling previous discordant experimental evidence in favour of either scenario. Importantly, the emergence of one of the two morphologies depends in a major way on the replication origin distribution as well as on the presence of nonspecific interactions between unreplicated chromatin and firing factors—polymerases and other components of the replisome. Nonspecific interactions also appear instrumental to creating clusters of factors and replication forks, structures akin to the replication foci observed in mammalian cells in vivo. PolyRep simulations predict different mechanisms for foci evolution, including unanticipated loop-mediated fusion dynamics. We suggest that cluster formation, which our model suggests to be a generic feature of chromatin replication, provides a hitherto underappreciated but robust pathway to avoid stalled or faulty forks, which would otherwise diminish the efficiency of the replication process.