Journal of the Royal Society Interface

Organisms and machines must use measured sensory cues to estimate unknown information about themselves or their environment. Cleverly applied sensor motion can be exploited to enrich the quality of sensory data and improve estimation. However, a major barrier to modeling such active sensing problems is the lack of empirical, yet rigorous, tools for quantifying the relationship between movement and estimation performance. Here, we introduce "BOUNDS: Bounding Observability for Uncertain Nonlinear Dynamic Systems". BOUNDS can discover patterns of sensor motion that increase information and reduce uncertainty in either real or simulated data. Crucially, it is suitable for high dimensional and partially observable nonlinear systems with sensor noise. We demonstrate BOUNDS through a case study on how flying insects estimate wind properties, showing that specific active sensing motifs improve estimation. Additionally, we present a framework to refine sporadic estimates from active sensing. When combined with an artificial neural network, we show that the information gained via active sensing in real Drosophila flight trajectories is suitable for precise wind direction estimation. Collectively, our work will help decode active sensing in organisms and inform the design of estimation algorithms for machines.

Cybergenetics is an advancing field that seeks to implement control theory within biological systems. When applying feedback control for the regulation of gene expression or cell proliferation, model-based control strategies can be applied; in this context, online adaptive mathematical models can be used to keep models in tune with the current behaviour of the biological system. Controllers are often constrained by their sampling rate, which is usually relatively low when using microfluidics/microscopy platforms. Current adaptive filters can lead to an inaccurate predictive model when operating with a low sampling rate, leading to sub-optimal control. Here, we propose a kernel filter that can fit model parameters online to produce a more accurate predictive model that can be included within an adaptive model predictive control scheme. The use of the kernel filter is demonstrated in in silico and in vitro experiments, where we control a synthetic gene oscillator and a P53 oscillator, and observe a synthetic toggle switch. Our results show that the kernel filter outperforms a particle filter when used for parameter estimation in both the predictive model accuracy and when included within an adaptive model-based controller.

The structure of social networks strongly affects how different phenomena spread in human society, from the transmission of information to the propagation of contagious diseases. It is well-known that heterogeneous connectivity strongly favors spread, but a precise characterization of the redundancy present in social networks and its effect on the robustness of transmission is still lacking. This gap is addressed by the metric backbone, a weight- and connectivity-preserving subgraph that is sufficient to compute all shortest paths of weighted graphs. This subgraph is obtained via algebraically-principled axioms and does not require statistical sampling based on null-models. We show that the metric backbones of nine contact networks obtained from proximity sensors in a variety of social contexts are generally very small, 49% of the original graph for one and ranging from about 6% to 20% for the others. This reflects a surprising amount of redundancy and reveals that shortest paths on these networks are very robust to random attacks and failures. We also show that the metric backbone preserves the full distribution of shortest paths of the original contact networks--which must include the shortest inter- and intra-community distances that define any community structure--and is a primary subgraph for epidemic transmission based on pure diffusion processes. This suggests that the organization of social contact networks is based on large amounts of shortest-path redundancy which shapes epidemic spread in human populations. Thus, the metric backbone is an important subgraph with regard to epidemic spread, the robustness of social networks, and any communication dynamics that depend on complex network shortest paths. Author summaryIt is through social networks that contagious diseases spread in human populations, as best illustrated by the current pandemic and efforts to contain it. Measuring such networks from human contact data typically results in noisy and dense graphs that need to be simplified for effective analysis, without removal of their essential features. Thus, the identification of a primary subgraph that maintains the social interaction structure and likely transmission pathways is of relevance for studying epidemic spreading phenomena as well as devising intervention strategies to hinder spread. Here we propose and study the metric backbone as an optimal subgraph for sparsification of social contact networks in the study of simple spreading dynamics. We demonstrate that it is a unique, algebraically-principled network subgraph that preserves all shortest paths. We also discover that nine contact networks obtained from proximity sensors in a variety of social contexts contain large amounts of redundant interactions that can be removed with very little impact on community structure and epidemic spread. This reveals that epidemic spread on social networks is very robust to random interaction removal. However, extraction of the metric backbone subgraph reveals which interventions--strategic removal of specific social interactions--are likely to result in maximum impediment to epidemic spread.

Eukaryotes and prokaryotes exploit the ability of genetically identical cells to exhibit different phenotypes in order to enhance their survival. However, the mechanisms by which cells transition from one phenotype to another remain unclear. Canonical models of this dynamic posit that molecular fluctuations provide the noise that drives the cell out of one stable state and into another. Stochastic processes generated by canonical models should, therefore, be good descriptors of phenotype dynamics and between-state transitions should become more likely at greater noise amplitude, for instance at higher extracellular temperatures. To test these predictions, we observed temporal expression dynamics of the promoter of a flagellum gene, fliC, in a microfluidic device using Salmonella enterica serovar Typhimurium and green fluorescent protein (GFP). Our observations show that while cells can exhibit multistable phenotypes, including stable fliC-OFF and fliC-ON states characterised by low and high GFP levels, respectively, between-state transitions can exhibit oscillatory dynamics whose return statistics do not conform to canonical theories. For example, here the fliC-ON state was more frequent following a temperature increase. To better understand our data we developed different dynamical frameworks to predict fliC expression data. We conclude that a stochastic dynamical system tailored to the genetic network of fliC is better suited to our data than prior theories where dynamical features, like oscillations and pulsing, are driven by inevitable delays in the post-translational regulation of fliC. Thus, while transcriptional noise promotes phenotypic heterogeneity, as we show here, regular features like oscillatory heterogeneity can result from delays that fundamental molecular processes impose upon a cells gene regulatory architecture.

The environments inhabited by flying insects demand a balance between flight efficiency and flight manoeuvrability. In structural oscillators such as the insect indirect flight motor, efficiency (arising from resonance) and manoeuvrability (arising from kinematic modulation) are typically quid pro quo, with modulation incurring penalties to efficiency. Band-type resonance is a phenomenon that offers, in theory, a strategy to lessen these penalties via careful navigation through a band of efficient kinematic states. However, identifying this band is challenging: no methods exist to identify the complete band in realistic motor models, involving elasticity distributed across thorax and wing. Nor are the effects of elasticity distribution on the band known. In this work, we address both open topics. We present a suite of numerical methods for identifying the complete resonance band in general systems. Applying them to models of the insect flight motor with distributed elasticity--thoracic and wing flexion--reveals that distributed elasticity is moderate-risk but high-reward morphological feature. Well-tuned distributions expand the resonance band over fourfold whereas poorly-tuned distributions completely extinguish the resonance band. These results indicate that distributing elasticity across the insect flight motor can have adaptive value, and motivate broader work identifying distributions across species.

A key obstacle in the widespread application of microbial co-cultures in bioprocesses is their compositional instability, as faster-growing species outcompete and dominate the culture. While several synthetic biology approaches have demonstrated control over co-culture composition, there has been an increased interest in computer-based cybernetic control approaches that can offload burdensome genetic control circuitry to computers and enable dynamic control and real-time noise rejection. This work extends that approach, demonstrating a cybernetic control method that is not reliant on any genetic engineering, instead interfacing cells with computers by exploiting their natural characteristics to measure and actuate the composition. We apply this to a Pseudomonas putida (P. putida) and Escherichia coli (E. coli) co-culture grown in Chi.Bio bioreactors, first showing how composition estimates calculated from different bioreactor measurements can be combined with a system model using an extended Kalman filter to generate accurate estimates of a noisy system. We also demonstrate that because the species have different optimal temperature niches, adjusting the temperature of the culture can drive the composition in either direction. By using a proportional-integral control algorithm to calculate the temperature that would bring the measured composition towards the desired composition, we are able to track dynamic references and stabilised the co-culture for 7 days ([~]250 generations), with the experiment ending before the cells could adapt out of the control. This cybernetic framework is broadly applicable, with different microbes unique features and specific growth niches enabling robust control over diverse co-cultures.

Biological organisation is inherently multi-level: molecular processes, membrane dynamics, cellular geometry and tissue context reciprocally constrain one another, often through boundary-mediated feedback. A recurring theme in theoretical biology is that such organisation is not well captured by models that assume a fixed repertoire of variables and a pre-given state space: what counts as a relevant state description can depend on organisational context and history. The principle of biological relativity further sharpens the same challenge from a different angle, emphasising that no level is causally privileged and that cross-level feedback can close into circular causality. These lines of work motivates for a structural multi-level semantics for modeling the biological pathways. We introduce a constraint-based semantic framework that distinguishes an evolving organisational scaffold--the admissible multi-level patterns and interfaces--from the pathways that traverse and coordinate them. This separation yields mathematical, loop-level diagnostics for boundary-driven circular causality: it identifies when organisational trajectories induce persistent reparameterisations of local state descriptions, and it classifies cyclic regimes into reversible loops, stable history-dependent loops, and unique (rare) organisational reconfigurations. The framework is accompanied by a systematic crosswalk to mainstream causal, dynamical and computational approaches, clarifying what is gained when interfaces and local-global consistency are treated as semantic, rather than purely parametric, structure. We demonstrate the approach on a canonical excitable-cell exemplar by modelling a single Hodgkin spike as a cross-level interface loop coupling membrane, molecular and cellular constraints. Without re-deriving Hodgkin-Huxley kinetics, the resulting diagnostics provide an explicit semantics for boundary-mediated feedback and spike-induced history dependence, including when cyclic activity imprints persistent changes in effective excitability. Together, the case study and comparisons position constraint semantics as a practical mathematical layer for multi-level biological organisation: compatible with existing mechanistic models, yet designed to expose circular causal closure and organisation-dependent state descriptions that standard formalisms typically leave implicit. AMS subject classifications92C30, 92C46, 92B05, 55U10, 55R10

Understanding structural similarities across dynamical systems at different scales remains a central problem in nonlinear science [1, 3]. Here we propose a modeling framework for cross-scale morphogenetic dynamics, termed Generalized Morphogenesis Theory (GMT), based on a flow-inertia formulation: O_FD O_INLINEFIG[Formula 1]C_INLINEFIGM_FD(1)C_FD where S denotes system state, E environmental input, F (E, S) a driving function, and {micro}(S) an inertia function representing resistance to change. This formulation provides a structural representation that encompasses several classical dynamical models--including Newtonian relaxation, logistic growth, and reaction-diffusion systems [13]--under appropriate parameterizations. Non-dimensionalization reveals a small set of control parameters governing regime transitions. Empirical validation is performed across two independent scales. At the organism scale, crop growth time-series datasets from multiple species exhibit consistent multiplicative dynamics F (E, S) = f (E) {middle dot} S, statistically preferred over additive alternatives in 5 of 6 independently tested systems ({Delta}AIC ranging from +2 to +891; R2 up to 0.98). Independently estimated inertia time constants agree in two plant systems (cucumber:{tau} = 3.7 days, CV=3.3%; maize:{tau} = 36.8 days, CV=17.3%), with the 10-fold ratio consistent with structural complexity differences. At the molecular scale, publicly available perturbation transcriptomics datasets (Perturb-seq) show directional response structures consistent with the proposed flow-inertia decomposition (93% causal direction agreement across three independent datasets; p < 10-25). Across domains, recurrent dynamical motifs are organized into 12 canonical design patterns, derived from a 2 x 2 x 3 orthogonal structure (4 elementary operations x 3 temporal scales), associated with stability classes and bifurcation conditions. These results suggest that the flow-inertia formulation functions as a domain-independent structural modeling principle for dissipative morphogenesis.

The timing of biochemical events is often determined by the accumulation of a protein or chemical species to a critical threshold level. In a stochastic model, we define event timing as the first-passage time for the level to cross the threshold from zero or random initial conditions. This first-passage time can be modulated by implementing feedback in synthesis, that is, making the production rate an arbitrary function of the current species level. We aim to find the optimal feedback strategy that reduces the timing noise around a given mean first-passage time. Previous results have shown that while a no-feedback strategy (i.e., an independent constant production rate) is optimal in the absence of degradation and zero-molecules initial condition, a negative feedback is optimal when the process starts at random initial conditions. We show that when the species can be degraded and the synthesis rates are set to depend linearly on the number of molecules, a positive feedback strategy (the production rate increases with the level of the molecule) minimizes timing noise. However, if no constraints on the feedback are imposed, the optimal strategy involves a mixed feedback approach, which consists of an initial positive feedback followed by a sharp negative feedback (the production rate decreases with the level) near the threshold. Finally, we quantify the fundamental limits of timing noise reduction with and without feedback control when time-keeping species are subject to degradation.

Oscillators are fundamental to biological systems, underpinning essential processes such as cell division, circadian rhythms, and developmental cycles. While both natural and synthetic genetic oscillators have been extensively studied, oscillatory behaviors in cells can also emerge without dedicated genetic circuits. In earlier work, we uncovered sustained oscillations in phenotypic switching across diverse cellular systems and gene circuits, occurring spontaneously, without external forcing and linked them to the induction of slow-growing phenotypes. In this study, we identify the conditions that give rise to such intrinsic phenotypic instabilities, leading to population-level oscillations. We develop and analytically solve a simplified mathematical model of a stress-induced phenotype, mapping the range of continuous culture conditions that trigger oscillatory gene expression. This instability range, predicted by the model, was experimentally validated in Bacillus subtilis cultures. Our findings reveal that oscillations can arise in the complete absence of genetic oscillators or external perturbations. Although demonstrated here for a stress response in continuous culture, this phenomenon may occur in any long-term cultivation where environmental feedback links an inducer to the cellular system, broadening the landscape of possible oscillatory behaviors in microbiology and synthetic biology.

Molecular reactions within a cell are inherently stochastic, and cells often differ in morphological properties or interact with a heterogeneous environment. Consequently, cell populations exhibit heterogeneity both due to these intrinsic and extrinsic causes. Although state-of-the-art studies that focus on dissecting this heterogeneity use single-cell measurements, the bulk data that shows only the mean expression levels is still in routine use. The fingerprint of the heterogeneity is present also in bulk data, despite being hidden from direct measurement. In particular, this heterogeneity can affect the mean expression levels via bimolecular interactions with low-abundant environment species. We make this statement rigorous for the class of linear reaction systems that are embedded in a discrete state Markov environment. The analytic expression that we provide for the stationary mean depends on the reaction rate constants of the linear subsystem, as well as the generator and stationary distribution of the Markov environment. We demonstrate the effect of the environment on the stationary mean. Namely, we show how the heterogeneous case deviates from the quasi-steady state (Q.SS) case when the embedded system is fast compared to the environment.

Eukaryotic transcriptional networks are often large and contain several levels of feedback regulation. Many of these networks have the ability to generate and maintain several distinct transcriptional states across multiple cell divisions and to switch between them. In certain instances, switching between cell states is stochastic, occurring in a small subset of cells of an isogenic population in a seemingly homogenous environment. Given the scarcity and unpredictability of switching in these cases, investigating the determining molecular events is challenging. White-opaque switching in the fungal species Candida albicans is an example of stably inherited cell states that are determined by a complex transcriptional network and can serve as an experimentally accessible model system to study characteristics important for stochastic cell fate switching in eukaryotes. In standard lab media, genetically identical cells maintain their cellular identity (either "white" or "opaque") through thousands of cell divisions and switching between the states is rare. By isolating populations of white or opaque cells, previous studies have elucidated the many differences between the two stable cell states and identified a set of transcriptional regulators needed for cell type switching. Yet little is known about the molecular events that determine the rare, stochastic switching events that occur in single cells. We use microfluidics combined with fluorescent reporters to directly observe rare switching events between the white and opaque states. We investigate the stochastic nature of switching by beginning with white cells and monitoring the activation of Wor1, a master regulator and marker for the opaque state, in single cells and throughout cell pedigrees. Our results indicate that switching requires two stochastic steps; first an event occurs that predisposes a lineage of cells to switch. In the second step, some but not all, of those predisposed cells rapidly express high levels of Wor1 and commit to the opaque state. To further understand the rapid rise in Wor1, we used a synthetic inducible system in Saccharomyces cerevisiae into which a controllable C. albicans Wor1 and a reporter for its transcriptional control region have been introduced. We document that Wor1 positive autoregulation is highly cooperative (Hill coefficient > 3), leading to rapid activation and producing an "all or none" rather than a graded response. Taken together, our results suggest that reaching a threshold level of a master regulator is sufficient to drive cell type switching in single cells and that an earlier molecular event increases the probability of reaching that threshold in certain small lineages of cells. Quantitative molecular analysis of the white-opaque circuit can serve as a model for the general understanding of complex circuits.

Many organisms, ranging from modern humans to extinct species, exhibit movement patterns that can be described by Levy walk dynamics. It has been demonstrated that such behavior enables optimal foraging when resource distribution is sparse. Here, we analyze a dataset of football player trajectories, recorded during the matches of the Japanese football league to elucidate the presence of statistical signatures of Levy walks; such as the heavy-tailed distribution of distances traveled between significant turns and the characteristic superdiffusive behavior. We conjecture that the competitive environment of a football game leads to movement dynamics reminiscent of that observed in hunter-gathering populations and more broadly in any biological organisms foraging for resources, whose exact distribution is unknown to them. Apart from analyzing individual players movements, we investigate the dynamics of the whole team by studying the movements of its center of mass (teams centroid). Remarkably, the trajectory of the centroid also exhibits Levy walk properties, marking the first instance of such type of motion observed at the group level. Our work concludes with a comparative analysis of different teams and some discussion on the relevance of our findings to sports science and science more generally.

In many organisms, interactions among genes lead to multiple functional states, and changes to interactions can lead to transitions into new states. These transitions can be related to bifurcations (or critical points) in dynamical systems theory. Characterizing these collective transitions is a major challenge for systems biology. Here, we develop a statistical method for identifying bistability near a continuous transition directly from high-dimensional gene expression data. We apply the method to data from honey bees, where a known developmental transition occurs between bees performing tasks in the nest and leaving the nest to forage. Our method, which makes use of the expected shape of the distribution of gene expression levels near a transition, successfully identifies the emergence of bistability and links it to genes that are known to be involved in the behavioral transition. This proof of concept demonstrates that going beyond correlative analysis to infer the shape of gene expression distributions might be used more generally to identify collective transitions from gene expression data.

Recent experiments suggested that sizer-like division strategy, a deviation from the adder paradigm might be produced by additional degradation events of cell division machinery molecules. We revisited single cell size data from a recently microfluidics setup using the above model. We observed that such additional degradation process, although reproduces size observations in the mean sense, it is unable to capture cell size fluctuations. We further extended recently proposed power law models to include commitment size. Our proposal is in agreement of both mean and fluctuation profiles seen in experiments. Our approach suggests further uses of noise profiles on dissecting cell size regulatory mechanisms. SIGNIFICANCEWe contrast cell division models against bacteria cell size data in minimal media. Our results seems to support the idea that division starts once bacteria meet a given commitment size.

Cell dynamics are powered by patterns of activity, but it is not straightforward to quantify these patterns or compare them across different environmental conditions or cell-types. Here we digitize the long-term shape fluctuations of metazoan cells grown on micropatterned fibronectin islands to define and extract statistical features of cell dynamics without the need for genetic modification or fluorescence imaging. These shape fluctuations generate single-cell morphological signals that can be decomposed into two major components: a continuous, slow-timescale meandering of morphology about an average steady-state shape; and short-lived "events" of rapid morphology change that sporadically occur throughout the timecourse. By developing statistical metrics for each of these components, we used thousands of hours of single-cell data to quantitatively define how each axis of cell dynamics was impacted by environmental conditions or cell-type. We found the size and spatial complexity of the micropattern island modulated the statistics of morphological events--lifetime, frequency, and orientation--but not its baseline shape fluctuations. Extending this approach to profile a panel of triple negative breast cancer cell-lines, we found that different cell-types could be distinguished from one another along specific and unique statistical axes of their behavior. Our results suggest that micropatterned substrates provide a generalizable method to build statistical profiles of cell dynamics to classify and compare emergent cell behaviors.

Inflammatory responses occur within the complex spatial context of tissues and organs, and many questions remain about how tissue structure and cellular communication shape their spatiotemporal dynamics. Here, we use a multiplexed RNA in situ hybridization approach, together with analytical tools, to study inflammatory gene expression in the larval zebrafish tailfin in response to a bath of lipopolysaccharide (LPS). We use this model system to address whether spatial structure emerges in the tissue response even absent the spatial variation introduced by a pathogen. We find that epithelial cells in the tailfin express several pro-inflammatory genes, and that across these genes, the uniform stimulus triggers a spatially non-uniform response. We use a graph-based spectral decomposition method to analyze its structure, and find that long modes dominate, creating zones of activation. Overall, these zones account for a majority of the variation in gene expression. Our results show that epithelial cells are important producers of pro-inflammatory effector molecules in this system, and that tissue induces spatial correlations even absent a structured input.

Biofilms, surface attached communities of microbes, grow in a wide variety of environments. Often, the size of these microbial community is constrained by their physical surroundings. However, little is known about how size constraints of a colony impact the outcome of microbial competitions. Here, we use individual-based models to simulate contact killing between two bacterial strains with different killing rates in a wide range of community sizes. We found that community size has a substantial impact on outcomes; in fact, in some competitions the identity of the most fit strain differs in large and small environments. Specifically, when at a numerical disadvantage, the strain with the slow killing rate is more successful in smaller environments than in large environments. The improved performance in small spaces comes from finite size effects; stochastic fluctuations in the initial relative abundance of each strain in small environments lead to dramatically different outcomes. However, when the slow killing strain has a numerical advantage, it performs better in large spaces than in small spaces, where stochastic fluctuations now aid the fast killing strain in small communities. Finally, we experimentally validate these results by confining contact killing strains of Vibrio cholerae in transmission electron microscopy grids. The outcomes of these experiments are consistent with our simulations. When rare, the slow killing strain does better in small environments; when common, the slow killing strain does better in large environments. Together, this work demonstrates that finite size effects can substantially modify antagonistic competitions, suggesting that colony size may, at least in part, subvert the microbial arms race. Author summaryBiofilms are often crowded with many bacteria in direct contact. As a result, the competition for space and resources often turns deadly. Bacteria have evolved many mechanisms with which to kill each other; this bacterial warfare is often studied in large communities on agar plates or in flow cells [1]. However, in nature these colonies are often smaller, due to spatial constraints or shear forces. It is unclear how bacterial warfare proceeds in small systems. We performed individual based model simulations of bacterial warfare comprising two strains, each capable of killing the other on direct contact. We found that the community size played a substantial role in determining the outcome. When at a numerical disadvantage, the slow killing strain survived at much higher rates in small communities. In fact, there were many conditions in which the slow killing strain survives in small spaces but is completely eliminated in large ones. Conversely, when the slow killing strain is more common, it performs better in large spaces. Together, these observations demonstrate that finite size effects aid the strain that is at a disadvantage, and in some conditions, can even flip which strain increases its abundance. Finally, we experimentally tested the results of these simulations. Two mutual killing strains of V. cholerae were grown unconfined on agar plates (i.e., in large spaces) or confined within square holes with sides 7.5m long (i.e., in small spaces). In these experiments we found that the slow killing strain survived at significantly higher rates in confinement, validating simulation results.

The dynamic behavior of synthetic gene circuits plays a key role in ensuring their correct function. Although there has been substantial work on modeling dynamic behavior after circuit construction, the forward engineering of dynamic behavior remains a major challenge. Previous engineering methods have focused on quantifying average behaviors of circuits over an extended time window, however this provides a static characterization of behavior that is a poor predictor of dynamics. Here we present a method for characterizing the dynamic behavior of synthetic gene circuits, using parameter inference of dynamical system models applied to time-series measurements of cell cultures growing in microtiter plates. We demonstrate that the behaviors of simple devices can be characterized dynamically and used to predict the behaviors of more complex circuits. Specifically, we compose 23 biological parts into 9 devices and use them to design 9 synthetic gene circuits in E. coli that provide core functionality for engineering cell behavior at the population level, including relays, receivers and a degrader. We embody our method in a software package and corresponding programming language. Our method supports the notion of an inference graph for iterative inference of models as new circuits are constructed, without the need to infer all models from scratch, and lays the foundation for characterizing large libraries of synthetic gene circuits in a scalable manner.

AO_SCPLOWBSTRACTC_SCPLOWCell migration is a key biological process underlying wound healing, tissue development, and cancer metastasis, yet calibrating mathematical models of migration to experimental data remains a major challenge. Scratch and barrier assays are widely used to study collective cell spreading, and agent-based random walk models provide a natural stochastic description of these experiments. However, parameter inference for such models is hampered by intractable likelihoods, forcing researchers to rely on Approximate Bayesian Computation, which introduces biases and tuning difficulties, or surrogate models that require potentially erroneous noise model specifications. Here, we overcome these limitations using neural posterior estimation, a simulation-based inference framework that learns the full posterior distribution directly from stochastic simulations without surrogate approximations or explicit noise model specifications. We deploy this framework on four progressively complex random walk models of barrier assay experiments describing in vitro cell migration: an isotropic baseline, a model with directional bias (chemotaxis), a model with cell proliferation, and a combined model incorporating both bias and proliferation. For each model, we demonstrate inference in two settings: using one-dimensional summary statistics (column counts), and using a convolutional neural network that enables inference directly from raw two-dimensional spatial data. Neural posterior estimation performs well across all four models, recovering biologically interpretable parameters (e.g. cell motility, directional bias, proliferation rates) from cases where classical surrogate-based methods are adequate through to the combined model where the interplay of multiple mechanisms renders surrogate approximations unreliable. We validate all posteriors using simulation-based calibration diagnostics and provide an open-source implementation of our pipeline to facilitate its adoption and extension to more complex, spatially-structured biological models.