Unraveling biochemical spatial patterns: Machine learning approaches to the inverse problem of stationary Turing patterns.

The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is challenging. To address this, we aim to solve the inverse problem in artificial and experimental Turing patterns. This task is challenging since patterns are often corrupted by noise and slight changes in initial conditions can lead to different patterns. We used both least squares to explore the problem and physics-informed neural networks to build a noise-robust method. We elucidate the functionality of our network in scenarios mimicking biological noise levels and showcase its application using an experimentally obtained chemical pattern. The findings reveal the significant promise of machine learning in steering the creation of synthetic patterns in bioengineering, thereby advancing our grasp of morphological intricacies within biological systems while acknowledging existing limitations.

Design principles for selective polarization of PAR proteins by cortical flows.

Clustering of membrane-associated molecules is thought to promote interactions with the actomyosin cortex, enabling size-dependent transport by actin flows. Consistent with this model, in the Caenorhabditis elegans zygote, efficient anterior segregation of the polarity protein PAR-3 requires oligomerization. However, through direct assessment of local coupling between motion of PAR proteins and the underlying cortex, we find no links between PAR-3 oligomer size and the degree of coupling. Indeed, both anterior and posterior PAR proteins experience similar advection velocities, at least over short distances. Consequently, differential cortex engagement cannot account for selectivity of PAR protein segregation by cortical flows. Combining experiment and theory, we demonstrate that a key determinant of differential segregation of PAR proteins by cortical flow is the stability of membrane association, which is enhanced by clustering and enables transport across cellular length scales. Thus, modulation of membrane binding dynamics allows cells to achieve selective transport by cortical flows despite widespread coupling between membrane-associated molecules and the cell cortex.

Effectiveness of Pseudomonas aeruginosa type VI secretion system relies on toxin potency and type IV pili-dependent interaction.

The type VI secretion system (T6SS) is an antibacterial weapon that is used by numerous Gram-negative bacteria to gain competitive advantage by injecting toxins into adjacent prey cells. Predicting the outcome of a T6SS-dependent competition is not only reliant on presence-absence of the system but instead involves a multiplicity of factors. Pseudomonas aeruginosa possesses 3 distinct T6SSs and a set of more than 20 toxic effectors with diverse functions including disruption of cell wall integrity, degradation of nucleic acids or metabolic impairment. We generated a comprehensive collection of mutants with various degrees of T6SS activity and/or sensitivity to each individual T6SS toxin. By imaging whole mixed bacterial macrocolonies, we then investigated how these P. aeruginosa strains gain a competitive edge in multiple attacker/prey combinations. We observed that the potency of single T6SS toxin varies significantly from one another as measured by monitoring the community structure, with some toxins acting better in synergy or requiring a higher payload. Remarkably the degree of intermixing between preys and attackers is also key to the competition outcome and is driven by the frequency of contact as well as the ability of the prey to move away from the attacker using type IV pili-dependent twitching motility. Finally, we implemented a computational model to better understand how changes in T6SS firing behaviours or cell-cell contacts lead to population level competitive advantages, thus providing conceptual insight applicable to all types of contact-based competition.

T cell morphodynamics reveal periodic shape oscillations in three-dimensional migration.

T cells use sophisticated shape dynamics (morphodynamics) to migrate towards and neutralize infected and cancerous cells. However, there is limited quantitative understanding of the migration process in three-dimensional extracellular matrices (ECMs) and across timescales. Here, we leveraged recent advances in lattice light-sheet microscopy to quantitatively explore the three-dimensional morphodynamics of migrating T cells at high spatio-temporal resolution. We first developed a new shape descriptor based on spherical harmonics, incorporating key polarization information of the uropod. We found that the shape space of T cells is low-dimensional. At the behavioural level, run-and-stop migration modes emerge at approximately 150 s, and we mapped the morphodynamic composition of each mode using multiscale wavelet analysis, finding 'stereotyped' motifs. Focusing on the run mode, we found morphodynamics oscillating periodically (every approx. 100 s) that can be broken down into a biphasic process: front-widening with retraction of the uropod, followed by a rearward surface motion and forward extension, where intercalation with the ECM in both of these steps likely facilitates forward motion. Further application of these methods may enable the comparison of T cell migration across different conditions (e.g. differentiation, activation, tissues and drug treatments) and improve the precision of immunotherapeutic development.

Thermodynamic constraints on the assembly and diversity of microbial ecosystems are different near to and far from equilibrium.

Non-equilibrium thermodynamics has long been an area of substantial interest to ecologists because most fundamental biological processes, such as protein synthesis and respiration, are inherently energy-consuming. However, most of this interest has focused on developing coarse ecosystem-level maximisation principles, providing little insight into underlying mechanisms that lead to such emergent constraints. Microbial communities are a natural system to decipher this mechanistic basis because their interactions in the form of substrate consumption, metabolite production, and cross-feeding can be described explicitly in thermodynamic terms. Previous work has considered how thermodynamic constraints impact competition between pairs of species, but restrained from analysing how this manifests in complex dynamical systems. To address this gap, we develop a thermodynamic microbial community model with fully reversible reaction kinetics, which allows direct consideration of free-energy dissipation. This also allows species to interact via products rather than just substrates, increasing the dynamical complexity, and allowing a more nuanced classification of interaction types to emerge. Using this model, we find that community diversity increases with substrate lability, because greater free-energy availability allows for faster generation of niches. Thus, more niches are generated in the time frame of community establishment, leading to higher final species diversity. We also find that allowing species to make use of near-to-equilibrium reactions increases diversity in a low free-energy regime. In such a regime, two new thermodynamic interaction types that we identify here reach comparable strengths to the conventional (competition and facilitation) types, emphasising the key role that thermodynamics plays in community dynamics. Our results suggest that accounting for realistic thermodynamic constraints is vital for understanding the dynamics of real-world microbial communities.

Physics-informed deep learning characterizes morphodynamics of Asian soybean rust disease.

Medicines and agricultural biocides are often discovered using large phenotypic screens across hundreds of compounds, where visible effects of whole organisms are compared to gauge efficacy and possible modes of action. However, such analysis is often limited to human-defined and static features. Here, we introduce a novel framework that can characterize shape changes (morphodynamics) for cell-drug interactions directly from images, and use it to interpret perturbed development of Phakopsora pachyrhizi, the Asian soybean rust crop pathogen. We describe population development over a 2D space of shapes (morphospace) using two models with condition-dependent parameters: a top-down Fokker-Planck model of diffusive development over Waddington-type landscapes, and a bottom-up model of tip growth. We discover a variety of landscapes, describing phenotype transitions during growth, and identify possible perturbations in the tip growth machinery that cause this variation. This demonstrates a widely-applicable integration of unsupervised learning and biophysical modeling.

Comparison of solitary and collective foraging strategies of Caenorhabditis elegans in patchy food distributions.

Collective foraging has been shown to benefit organisms in environments where food is patchily distributed, but whether this is true in the case where organisms do not rely on long-range communications to coordinate their collective behaviour has been understudied. To address this question, we use the tractable laboratory model organism Caenorhabditis elegans, where a social strain (npr-1 mutant) and a solitary strain (N2) are available for direct comparison of foraging strategies. We first developed an on-lattice minimal model for comparing collective and solitary foraging strategies, finding that social agents benefit from feeding faster and more efficiently simply owing to group formation. Our laboratory foraging experiments with npr-1 and N2 worm populations, however, show an advantage for solitary N2 in all food distribution environments that we tested. We incorporated additional strain-specific behavioural parameters of npr-1 and N2 worms into our model and computationally identified N2's higher feeding rate to be the key factor underlying its advantage, without which it is possible to recapitulate the advantage of collective foraging in patchy environments. Our work highlights the theoretical advantage of collective foraging owing to group formation alone without long-range interactions and the valuable role of modelling to guide experiments. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Of Cell Shapes and Motion: The Physical Basis of Animal Cell Migration.

Motile cells have developed a variety of migration modes relying on diverse traction-force-generation mechanisms. Before the behavior of intracellular components could be easily imaged, cell movements were mostly classified by different types of cellular shape dynamics. Indeed, even though some types of cells move without any significant change in shape, most cell propulsion mechanisms rely on global or local deformations of the cell surface. In this review, focusing mostly on metazoan cells, we discuss how different types of local and global shape changes underlie distinct migration modes. We then discuss mechanical differences between force-generation mechanisms and finish by speculating on how they may have evolved.

Thermodynamics of switching in multistable non-equilibrium systems.

Multistable non-equilibrium systems are abundant outcomes of nonlinear dynamics with feedback, but still relatively little is known about what determines the stability of the steady states and their switching rates in terms of entropy and entropy production. Here, we will link fluctuation theorems for the entropy production along trajectories with the action obtainable from the Freidlin-Wentzell theorem to elucidate the thermodynamics of switching between states in the large volume limit of multistable systems. We find that the entropy production at steady state plays no role, but the entropy production during switching is key. Steady-state entropy and diffusive noise strength can be neglected in this limit. The relevance to biological, ecological, and climate models is apparent.

Growth-rate dependent resource investment in bacterial motile behavior quantitatively follows potential benefit of chemotaxis.

Microorganisms possess diverse mechanisms to regulate investment into individual cellular processes according to their environment. How these regulatory strategies reflect the inherent trade-off between the benefit and cost of resource investment remains largely unknown, particularly for many cellular functions that are not immediately related to growth. Here, we investigate regulation of motility and chemotaxis, one of the most complex and costly bacterial behaviors, as a function of bacterial growth rate. We show with experiment and theory that in poor nutritional conditions, Escherichia coli increases its investment in motility in proportion to the reproductive fitness advantage provided by the ability to follow nutrient gradients. Since this growth-rate dependent regulation of motility genes occurs even when nutrient gradients are absent, we hypothesize that it reflects an anticipatory preallocation of cellular resources. Notably, relative fitness benefit of chemotaxis could be observed not only in the presence of imposed gradients of secondary nutrients but also in initially homogeneous bacterial cultures, suggesting that bacteria can generate local gradients of carbon sources and excreted metabolites, and subsequently use chemotaxis to enhance the utilization of these compounds. This interplay between metabolite excretion and their chemotaxis-dependent reutilization is likely to play an important general role in microbial communities.

Maximal information transmission is compatible with ultrasensitive biological pathways.

Cells are often considered input-output devices that maximize the transmission of information by converting extracellular stimuli (input) via signaling pathways (communication channel) to cell behavior (output). However, in biological systems outputs might feed back into inputs due to cell motility, and the biological channel can change by mutations during evolution. Here, we show that the conventional channel capacity obtained by optimizing the input distribution for a fixed channel may not reflect the global optimum. In a new approach we analytically identify both input distributions and input-output curves that optimally transmit information, given constraints from noise and the dynamic range of the channel. We find a universal optimal input distribution only depending on the input noise, and we generalize our formalism to multiple outputs (or inputs). Applying our formalism to Escherichia coli chemotaxis, we find that its pathway is compatible with optimal information transmission despite the ultrasensitive rotary motors.

Persistent and polarized global actin flow is essential for directionality during cell migration.

Cell migration is hypothesized to involve a cycle of behaviours beginning with leading edge extension. However, recent evidence suggests that the leading edge may be dispensable for migration, raising the question of what actually controls cell directionality. Here, we exploit the embryonic migration of Drosophila macrophages to bridge the different temporal scales of the behaviours controlling motility. This approach reveals that edge fluctuations during random motility are not persistent and are weakly correlated with motion. In contrast, flow of the actin network behind the leading edge is highly persistent. Quantification of actin flow structure during migration reveals a stable organization and asymmetry in the cell-wide flowfield that strongly correlates with cell directionality. This organization is regulated by a gradient of actin network compression and destruction, which is controlled by myosin contraction and cofilin-mediated disassembly. It is this stable actin-flow polarity, which integrates rapid fluctuations of the leading edge, that controls inherent cellular persistence.

Screening by changes in stereotypical behavior during cell motility.

Stereotyped behaviors are series of postures that show very little variability between repeats. They have been used to classify the dynamics of individuals, groups and species without reference to the lower-level mechanisms that drive them. Stereotypes are easily identified in animals due to strong constraints on the number, shape, and relative positions of anatomical features, such as limbs, that may be used as landmarks for posture identification. In contrast, the identification of stereotypes in single cells poses a significant challenge as the cell lacks these landmark features, and finding constraints on cell shape is a non-trivial task. Here, we use the maximum caliber variational method to build a minimal model of cell behavior during migration. Without reference to biochemical details, we are able to make behavioral predictions over timescales of minutes using only changes in cell shape over timescales of seconds. We use drug treatment and genetics to demonstrate that maximum caliber descriptors can discriminate between healthy and aberrant migration, thereby showing potential applications for maximum caliber methods in automated disease screening, for example in the identification of behaviors associated with cancer metastasis.

Shared behavioral mechanisms underlie C. elegans aggregation and swarming.

In complex biological systems, simple individual-level behavioral rules can give rise to emergent group-level behavior. While collective behavior has been well studied in cells and larger organisms, the mesoscopic scale is less understood, as it is unclear which sensory inputs and physical processes matter a priori. Here, we investigate collective feeding in the roundworm C. elegans at this intermediate scale, using quantitative phenotyping and agent-based modeling to identify behavioral rules underlying both aggregation and swarming-a dynamic phenotype only observed at longer timescales. Using fluorescence multi-worm tracking, we quantify aggregation in terms of individual dynamics and population-level statistics. Then we use agent-based simulations and approximate Bayesian inference to identify three key behavioral rules for aggregation: cluster-edge reversals, a density-dependent switch between crawling speeds, and taxis towards neighboring worms. Our simulations suggest that swarming is simply driven by local food depletion but otherwise employs the same behavioral mechanisms as the initial aggregation.

Chromosome Translocation Inflates Bacillus Forespores and Impacts Cellular Morphology.

The means by which the physicochemical properties of different cellular components together determine bacterial cell shape remain poorly understood. Here, we investigate a programmed cell-shape change during Bacillus subtilis sporulation, when a rod-shaped vegetative cell is transformed to an ovoid spore. Asymmetric cell division generates a bigger mother cell and a smaller, hemispherical forespore. The septum traps the forespore chromosome, which is translocated to the forespore by SpoIIIE. Simultaneously, forespore size increases as it is reshaped into an ovoid. Using genetics, timelapse microscopy, cryo-electron tomography, and mathematical modeling, we demonstrate that forespore growth relies on membrane synthesis and SpoIIIE-mediated chromosome translocation, but not on peptidoglycan or protein synthesis. Our data suggest that the hydrated nucleoid swells and inflates the forespore, displacing ribosomes to the cell periphery, stretching septal peptidoglycan, and reshaping the forespore. Our results illustrate how simple biophysical interactions between core cellular components contribute to cellular morphology.

Entropy production selects nonequilibrium states in multistable systems.

Far-from-equilibrium thermodynamics underpins the emergence of life, but how has been a long-outstanding puzzle. Best candidate theories based on the maximum entropy production principle could not be unequivocally proven, in part due to complicated physics, unintuitive stochastic thermodynamics, and the existence of alternative theories such as the minimum entropy production principle. Here, we use a simple, analytically solvable, one-dimensional bistable chemical system to demonstrate the validity of the maximum entropy production principle. To generalize to multistable stochastic system, we use the stochastic least-action principle to derive the entropy production and its role in the stability of nonequilibrium steady states. This shows that in a multistable system, all else being equal, the steady state with the highest entropy production is favored, with a number of implications for the evolution of biological, physical, and geological systems.

Drift and Behavior of E. coli Cells.

Chemotaxis of the bacterium Escherichia coli is well understood in shallow chemical gradients, but its swimming behavior remains difficult to interpret in steep gradients. By focusing on single-cell trajectories from simulations, we investigated the dependence of the chemotactic drift velocity on attractant concentration in an exponential gradient. Whereas maxima of the average drift velocity can be interpreted within analytical linear-response theory of chemotaxis in shallow gradients, limits in drift due to steep gradients and finite number of receptor-methylation sites for adaptation go beyond perturbation theory. For instance, we found a surprising pinning of the cells to the concentration in the gradient at which cells run out of methylation sites. To validate the positions of maximal drift, we recorded single-cell trajectories in carefully designed chemical gradients using microfluidics.

A model of cell-wall dynamics during sporulation in Bacillus subtilis.

To survive starvation, Bacillus subtilis forms durable spores. After asymmetric cell division, the septum grows around the forespore in a process called engulfment, but the mechanism of force generation is unknown. Here, we derived a novel biophysical model for the dynamics of cell-wall remodeling during engulfment based on a balancing of dissipative, active, and mechanical forces. By plotting phase diagrams, we predict that sporulation is promoted by a line tension from the attachment of the septum to the outer cell wall, as well as by an imbalance in turgor pressures in the mother-cell and forespore compartments. We also predict that significant mother-cell growth hinders engulfment. Hence, relatively simple physical principles may guide this complex biological process.

How cells engulf: a review of theoretical approaches to phagocytosis.

Phagocytosis is a fascinating process whereby a cell surrounds and engulfs particles such as bacteria and dead cells. This is crucial both for single-cell organisms (as a way of acquiring nutrients) and as part of the immune system (to destroy foreign invaders). This whole process is hugely complex and involves multiple coordinated events such as membrane remodelling, receptor motion, cytoskeleton reorganisation and intracellular signalling. Because of this, phagocytosis is an excellent system for theoretical study, benefiting from biophysical approaches combined with mathematical modelling. Here, we review these theoretical approaches and discuss the recent mathematical and computational models, including models based on receptors, models focusing on the forces involved, and models employing energetic considerations. Along the way, we highlight a beautiful connection to the physics of phase transitions, consider the role of stochasticity, and examine links between phagocytosis and other types of endocytosis. We cover the recently discovered multistage nature of phagocytosis, showing that the size of the phagocytic cup grows in distinct stages, with an initial slow stage followed by a much quicker second stage starting around half engulfment. We also address the issue of target shape dependence, which is relevant to both pathogen infection and drug delivery, covering both one-dimensional and two-dimensional results. Throughout, we pay particular attention to recent experimental techniques that continue to inform the theoretical studies and provide a means to test model predictions. Finally, we discuss population models, connections to other biological processes, and how physics and modelling will continue to play a key role in future work in this area.

A critical-like collective state leads to long-range cell communication in Dictyostelium discoideum aggregation.

The transition from single-cell to multicellular behavior is important in early development but rarely studied. The starvation-induced aggregation of the social amoeba Dictyostelium discoideum into a multicellular slug is known to result from single-cell chemotaxis towards emitted pulses of cyclic adenosine monophosphate (cAMP). However, how exactly do transient, short-range chemical gradients lead to coherent collective movement at a macroscopic scale? Here, we developed a multiscale model verified by quantitative microscopy to describe behaviors ranging widely from chemotaxis and excitability of individual cells to aggregation of thousands of cells. To better understand the mechanism of long-range cell-cell communication and hence aggregation, we analyzed cell-cell correlations, showing evidence of self-organization at the onset of aggregation (as opposed to following a leader cell). Surprisingly, cell collectives, despite their finite size, show features of criticality known from phase transitions in physical systems. By comparing wild-type and mutant cells with impaired aggregation, we found the longest cell-cell communication distance in wild-type cells, suggesting that criticality provides an adaptive advantage and optimally sized aggregates for the dispersal of spores.