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Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and Partial Differential Equation (PDE) trajectories. Our method is designed to identify underlying local rules that govern large scale dynamic emergent behaviours. Previous work on NCA focuses on learning rules that give stationary emergent structures. We extend NCA to capture both transient and stable structures within the same system, as well as learning rules that capture the dynamics of Turing pattern formation in nonlinear PDEs. We demonstrate that NCA can generalise very well beyond their PDE training data, we show how to constrain NCA to respect given symmetries, and we explore the effects of associated hyperparameters on model performance and stability. Being able to learn arbitrary dynamics gives NCA great potential as a data driven modelling framework, especially for modelling biological pattern formation., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Richardson et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Analysis across a growing number of single-cell perturbation datasets is hampered by poor data interoperability. To facilitate development and benchmarking of computational methods, we collect a set of 44 publicly available single-cell perturbation-response datasets with molecular readouts, including transcriptomics, proteomics and epigenomics. We apply uniform quality control pipelines and harmonize feature annotations. The resulting information resource, scPerturb, enables development and testing of computational methods, and facilitates comparison and integration across datasets. We describe energy statistics (E-statistics) for quantification of perturbation effects and significance testing, and demonstrate E-distance as a general distance measure between sets of single-cell expression profiles. We illustrate the application of E-statistics for quantifying similarity and efficacy of perturbations. The perturbation-response datasets and E-statistics computation software are publicly available at scperturb.org. This work provides an information resource for researchers working with single-cell perturbation data and recommendations for experimental design, including optimal cell counts and read depth., (© 2024. The Author(s), under exclusive licence to Springer Nature America, Inc.)

Collective cell migration is a multicellular phenomenon that arises in various biological contexts, including cancer and embryo development. 'Collectiveness' can be promoted by cell-cell interactions such as co-attraction and contact inhibition of locomotion. These mechanisms act on cell polarity, pivotal for directed cell motility, through influencing the intracellular dynamics of small GTPases such as Rac1. To model these dynamics we introduce a biased random walk model, where the bias depends on the internal state of Rac1, and the Rac1 state is influenced by cell-cell interactions and chemoattractive cues. In an extensive simulation study we demonstrate and explain the scope and applicability of the introduced model in various scenarios. The use of a biased random walk model allows for the derivation of a corresponding partial differential equation for the cell density while still maintaining a certain level of intracellular detail from the individual based setting., (© 2024. The Author(s).)

Clonal hematopoiesis of indeterminate potential (CHIP) increases rapidly in prevalence beyond age 60 and has been associated with increased risk for malignancy, heart disease and ischemic stroke. CHIP is driven by somatic mutations in hematopoietic stem and progenitor cells (HSPCs). Because mutations in HSPCs often drive leukemia, we hypothesized that HSPC fitness substantially contributes to transformation from CHIP to leukemia. HSPC fitness is defined as the proliferative advantage over cells carrying no or only neutral mutations. If mutations in different genes lead to distinct fitness advantages, this could enable patient stratification. We quantified the fitness effects of mutations over 12 years in older age using longitudinal sequencing and developed a filtering method that considers individual mutational context alongside mutation co-occurrence to quantify the growth potential of variants within individuals. We found that gene-specific fitness differences can outweigh inter-individual variation and, therefore, could form the basis for personalized clinical management., (© 2022. The Author(s).)

Apoptosis of cells and their subsequent removal through efferocytosis occurs in nearly all tissues during development, homeostasis, and disease. However, it has been difficult to track cell death and subsequent corpse removal in vivo. We developed a genetically encoded fluorescent reporter, CharON (Caspase and pH Activated Reporter, Fluorescence ON), that could track emerging apoptotic cells and their efferocytic clearance by phagocytes. Using Drosophila expressing CharON, we uncovered multiple qualitative and quantitative features of coordinated clearance of apoptotic corpses during embryonic development. When confronted with high rates of emerging apoptotic corpses, the macrophages displayed heterogeneity in engulfment behaviors, leading to some efferocytic macrophages carrying high corpse burden. Overburdened macrophages were compromised in clearing wound debris. These findings reveal known and unexpected features of apoptosis and macrophage efferocytosis in vivo.

Successful progression from bench to bedside for regenerative medicine products is challenging and requires a multidisciplinary approach. What has not yet been fully recognised is the potential for quantitative data analysis and mathematical modelling approaches to support this process. In this review, we highlight the wealth of opportunities for embedding mathematical and computational approaches within all stages of the regenerative medicine pipeline. We explore how exploiting quantitative mathematical and computational approaches, alongside state-of-the-art regenerative medicine research, can lead to therapies that potentially can be more rapidly translated into the clinic.

The deluge of single-cell data obtained by sequencing, imaging and epigenetic markers has led to an increasingly detailed description of cell state. However, it remains challenging to identify how cells transition between different states, in part because data are typically limited to snapshots in time. A prerequisite for inferring cell state transitions from such snapshots is to distinguish whether transitions are coupled to cell divisions. To address this, we present two minimal branching process models of cell division and differentiation in a well-mixed population. These models describe dynamics where differentiation and division are coupled or uncoupled. For each model, we derive analytic expressions for each subpopulation's mean and variance and for the likelihood, allowing exact Bayesian parameter inference and model selection in the idealised case of fully observed trajectories of differentiation and division events. In the case of snapshots, we present a sample path algorithm and use this to predict optimal temporal spacing of measurements for experimental design. We then apply this methodology to an in vitro dataset assaying the clonal growth of epiblast stem cells in culture conditions promoting self-renewal or differentiation. Here, the larger number of cell states necessitates approximate Bayesian computation. For both culture conditions, our inference supports the model where cell state transitions are coupled to division. For culture conditions promoting differentiation, our analysis indicates a possible shift in dynamics, with these processes becoming more coupled over time.

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'.

Models of cranial neural crest cell migration in cell-induced (or self-generated) gradients have included a division of labour into leader and follower migratory states, which undergo chemotaxis and contact guidance, respectively. Despite validated utility of these models through experimental perturbation of migration in the chick embryo and gene expression analysis showing relevant heterogeneity at the single cell level, an often raised question has been whether the discrete cell states are necessary, or if a continuum of cell behaviours offers a functionally equivalent description. Here we argue that this picture is supported by recent single-cell transcriptome data. Motivated by this, we implement two versions of a continuous-state model: (1) signal choice and (2) signal combination. We find that the cell population migrates further than in the discrete-state model and than in experimental observations. We further show that the signal combination model, but not the signal choice model, can be successfully adjusted to experimentally plausible regimes by reducing the chemoattractant consumption parameter. Thus we show an equivalently plausible, experimentally motivated, model of neural crest cell migration., (Copyright © 2019 Elsevier Ltd. All rights reserved.)

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.

Heterogeneity within cell populations can be an important aspect affecting their collective movement and tissue-mechanical properties, determining for example their effective viscoelasticity. Differences in cell-level properties and behaviour within a group of moving cells can give rise to unexpected and non-intuitive behaviours at the tissue level. Such emergent phenomena often manifest themselves through spatiotemporal patterns at an intermediate 'mesoscale' between cell and tissue scales, typically involving tens of cells. Focussing on the development of embryonic animal tissues, we review recent evidence for the importance of heterogeneity at the mesoscale for collective cell migration and convergence and extension movements. We further discuss approaches to incorporate heterogeneity into computational models to complement experimental investigations., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

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., Competing Interests: SD, LS, AJ, RE, AB No competing interests declared, (© 2019, Ding et al.)

Neural crest cells are both highly migratory and significant to vertebrate organogenesis. However, the signals that regulate neural crest cell migration remain unclear. In this study, we test the function of differential screening-selected gene aberrant in neuroblastoma (DAN), a bone morphogenetic protein (BMP) antagonist we detected by analysis of the chick cranial mesoderm. Our analysis shows that, before neural crest cell exit from the hindbrain, DAN is expressed in the mesoderm, and then it becomes absent along cell migratory pathways. Cranial neural crest and metastatic melanoma cells avoid DAN protein stripes in vitro. Addition of DAN reduces the speed of migrating cells in vivo and in vitro, respectively. In vivo loss of function of DAN results in enhanced neural crest cell migration by increasing speed and directionality. Computer model simulations support the hypothesis that DAN restrains cell migration by regulating cell speed. Collectively, our results identify DAN as a novel factor that inhibits uncontrolled neural crest and metastatic melanoma invasion and promotes collective migration in a manner consistent with the inhibition of BMP signaling., (© 2017 McLennan et al.)

Cell population heterogeneity is increasingly a focus of inquiry in biological research. For example, cell migration studies have investigated the heterogeneity of invasiveness and taxis in development, wound healing, and cancer. However, relatively little effort has been devoted to exploring when heterogeneity is mechanistically relevant and how to reliably measure it. Statistical methods from the animal movement literature offer the potential to analyze heterogeneity in collections of cell tracking data. A popular measure of heterogeneity, which we use here as an example, is the distribution of delays in directional cross-correlation. Employing a suitably generic, yet minimal, model of collective cell movement in three dimensions, we show how using such measures to quantify heterogeneity in tracking data can result in the inference of heterogeneity where there is none. Our study highlights a potential pitfall in the statistical analysis of cell population heterogeneity, and we argue that this can be mitigated by the appropriate choice of null models., (Copyright © 2017 Elsevier Inc. All rights reserved.)

Organoids made from dissociated progenitor cells undergo tissue-like organization. This in vitro self-organization process is not identical to embryonic organ formation, but it achieves a similar phenotype in vivo. This implies genetic codes do not specify morphology directly; instead, complex tissue architectures may be achieved through several intermediate layers of cross talk between genetic information and biophysical processes. Here we use newborn and adult skin organoids for analyses. Dissociated cells from newborn mouse skin form hair primordia-bearing organoids that grow hairs robustly in vivo after transplantation to nude mice. Detailed time-lapse imaging of 3D cultures revealed unexpected morphological transitions between six distinct phases: dissociated cells, cell aggregates, polarized cysts, cyst coalescence, planar skin, and hair-bearing skin. Transcriptome profiling reveals the sequential expression of adhesion molecules, growth factors, Wnts, and matrix metalloproteinases (MMPs). Functional perturbations at different times discern their roles in regulating the switch from one phase to another. In contrast, adult cells form small aggregates, but then development stalls in vitro. Comparative transcriptome analyses suggest suppressing epidermal differentiation in adult cells is critical. These results inspire a strategy that can restore morphological transitions and rescue the hair-forming ability of adult organoids: ( i ) continuous PKC inhibition and ( ii ) timely supply of growth factors (IGF, VEGF), Wnts, and MMPs. This comprehensive study demonstrates that alternating molecular events and physical processes are in action during organoid morphogenesis and that the self-organizing processes can be restored via environmental reprogramming. This tissue-level phase transition could drive self-organization behavior in organoid morphogenies beyond the skin., Competing Interests: The authors declare no conflict of interest.

Mathematical models are becoming increasingly integrated with experimental efforts in the study of biological systems. Collective cell migration in developmental biology is a particularly fruitful application area for the development of theoretical models to predict the behaviour of complex multicellular systems with many interacting parts. In this context, mathematical models provide a tool to assess the consistency of experimental observations with testable mechanistic hypotheses. In this review, we showcase examples from recent years of multidisciplinary investigations of neural crest cell migration. The neural crest model system has been used to study how collective migration of cell populations is shaped by cell-cell interactions, cell-environmental interactions and heterogeneity between cells. The wide range of emergent behaviours exhibited by neural crest cells in different embryonal locations and in different organisms helps us chart out the spectrum of collective cell migration. At the same time, this diversity in migratory characteristics highlights the need to reconcile or unify the array of currently hypothesized mechanisms through the next generation of experimental data and generalized theoretical descriptions., (© 2016 The Authors.)

Embryonic neural crest cells travel in discrete streams to precise locations throughout the head and body. We previously showed that cranial neural crest cells respond chemotactically to vascular endothelial growth factor (VEGF) and that cells within the migratory front have distinct behaviors and gene expression. We proposed a cell-induced gradient model in which lead neural crest cells read out directional information from a chemoattractant profile and instruct trailers to follow. In this study, we show that migrating chick neural crest cells do not display distinct lead and trailer gene expression profiles in culture. However, exposure to VEGF in vitro results in the upregulation of a small subset of genes associated with an in vivo lead cell signature. Timed addition and removal of VEGF in culture reveals the changes in neural crest cell gene expression are rapid. A computational model incorporating an integrate-and-switch mechanism between cellular phenotypes predicts migration efficiency is influenced by the timescale of cell behavior switching. To test the model hypothesis that neural crest cellular phenotypes respond to changes in the VEGF chemoattractant profile, we presented ectopic sources of VEGF to the trailer neural crest cell subpopulation and show diverted cell trajectories and stream alterations consistent with model predictions. Gene profiling of trailer cells that diverted and encountered VEGF revealed upregulation of a subset of 'lead' genes. Injection of neuropilin1 (Np1)-Fc into the trailer subpopulation or electroporation of VEGF morpholino to reduce VEGF signaling failed to alter trailer neural crest cell trajectories, suggesting trailers do not require VEGF to maintain coordinated migration. These results indicate that VEGF is one of the signals that establishes lead cell identity and its chemoattractant profile is critical to neural crest cell migration., (Copyright © 2015 Elsevier Inc. All rights reserved.)

Neural crest (NC) cell migration is crucial to the formation of peripheral tissues during vertebrate development. However, how NC cells respond to different microenvironments to maintain persistence of direction and cohesion in multicellular streams remains unclear. To address this, we profiled eight subregions of a typical cranial NC cell migratory stream. Hierarchical clustering showed significant differences in the expression profiles of the lead three subregions compared with newly emerged cells. Multiplexed imaging of mRNA expression using fluorescent hybridization chain reaction (HCR) quantitatively confirmed the expression profiles of lead cells. Computational modeling predicted that a small fraction of lead cells that detect directional information is optimal for successful stream migration. Single-cell profiling then revealed a unique molecular signature that is consistent and stable over time in a subset of lead cells within the most advanced portion of the migratory front, which we term trailblazers. Model simulations that forced a lead cell behavior in the trailing subpopulation predicted cell bunching near the migratory domain entrance. Misexpression of the trailblazer molecular signature by perturbation of two upstream transcription factors agreed with the in silico prediction and showed alterations to NC cell migration distance and stream shape. These data are the first to characterize the molecular diversity within an NC cell migratory stream and offer insights into how molecular patterns are transduced into cell behaviors., (© 2015. Published by The Company of Biologists Ltd.)

We examine the ability of intrinsic noise to produce complex temporal dynamics in Turing pattern formation systems, with particular emphasis on the Schnakenberg kinetics. Using power spectral methods, we characterize the behavior of the system using stochastic simulations at a wide range of points in parameter space and compare with analytical approximations. Specifically, we investigate whether polarity switching of stochastic patterns occurs at a defined frequency. We find that it can do so in individual realizations of a stochastic simulation, but that the frequency is not defined consistently across realizations in our samples of parameter space. Further, we examine the effect of noise on deterministically predicted traveling waves and find them increased in amplitude and decreased in speed.

Using the Index of Attitudes Toward Homosexuals to study the attitudes of 34 Asian students and 32 American students toward lesbians and gay men showed these Asian students were more likely to harbor homophobic attitudes than these American students. There were no significant sex differences between groups.