Using approximate Bayesian computation to quantify cell-cell adhesion parameters in a cell migratory process

Calibration of agent based models for monophasic and biphasic tumour growth using approximate Bayesian computation

Agent-based models (ABMs) are readily used to capture the stochasticity in tumour evolution; however, these models are often challenging to validate with experimental measurements due to model complexity. The Voronoi cell-based model (VCBM) is an off-lattice agent-based model that captures individual cell shapes using a Voronoi tessellation and mimics the evolution of cancer cell proliferation and movement. Evidence suggests tumours can exhibit biphasic growth in vivo. To account for this phenomena, we extend the VCBM to capture the existence of two distinct growth phases. Prior work primarily focused on point estimation for the parameters without consideration of estimating uncertainty. In this paper, approximate Bayesian computation is employed to calibrate the model to in vivo measurements of breast, ovarian and pancreatic cancer. Our approach involves estimating the distribution of parameters that govern cancer cell proliferation and recovering outputs that match the experimental data. Our results show that the VCBM, and its biphasic extension, provides insight into tumour growth and quantifies uncertainty in the switching time between the two phases of the biphasic growth model. We find this approach enables precise estimates for the time taken for a daughter cell to become a mature cell. This allows us to propose future refinements to the model to improve accuracy, whilst also making conclusions about the differences in cancer cell characteristics.

Designing optimal behavioral experiments using machine learning

Computational models are powerful tools for understanding human cognition and behavior. They let us express our theories clearly and precisely and offer predictions that can be subtle and often counter-intuitive. However, this same richness and ability to surprise means our scientific intuitions and traditional tools are ill-suited to designing experiments to test and compare these models. To avoid these pitfalls and realize the full potential of computational modeling, we require tools to design experiments that provide clear answers about what models explain human behavior and the auxiliary assumptions those models must make. Bayesian optimal experimental design (BOED) formalizes the search for optimal experimental designs by identifying experiments that are expected to yield informative data. In this work, we provide a tutorial on leveraging recent advances in BOED and machine learning to find optimal experiments for any kind of model that we can simulate data from, and show how by-products of this procedure allow for quick and straightforward evaluation of models and their parameters against real experimental data. As a case study, we consider theories of how people balance exploration and exploitation in multi-armed bandit decision-making tasks. We validate the presented approach using simulations and a real-world experiment. As compared to experimental designs commonly used in the literature, we show that our optimal designs more efficiently determine which of a set of models best account for individual human behavior, and more efficiently characterize behavior given a preferred model. At the same time, formalizing a scientific question such that it can be adequately addressed with BOED can be challenging and we discuss several potential caveats and pitfalls that practitioners should be aware of. We provide code to replicate all analyses as well as tutorial notebooks and pointers to adapt the methodology to different experimental settings.

Human Stem Cells for Ophthalmology: Recent Advances in Diagnostic Image Analysis and Computational Modelling

Purpose of Review

To explore the advances and future research directions in image analysis and computational modelling of human stem cells (hSCs) for ophthalmological applications.

Recent Findings

hSCs hold great potential in ocular regenerative medicine due to their application in cell-based therapies and in disease modelling and drug discovery using state-of-the-art 2D and 3D organoid models. However, a deeper characterisation of their complex, multi-scale properties is required to optimise their translation to clinical practice. Image analysis combined with computational modelling is a powerful tool to explore mechanisms of hSC behaviour and aid clinical diagnosis and therapy.

Summary

Many computational models draw on a variety of techniques, often blending continuum and discrete approaches, and have been used to describe cell differentiation and self-organisation. Machine learning tools are having a significant impact in model development and improving image classification processes for clinical diagnosis and treatment and will be the focus of much future research.

Model-based inference of a plant-specific dual role for HOPS in regulating guard cell vacuole fusion

Stomata are the pores on a leaf surface that regulate gas exchange. Each stoma consists of two guard cells whose movements regulate pore opening and thereby control CO2 fixation and water loss. Guard cell movements depend in part on the remodeling of vacuoles, which have been observed to change from a highly fragmented state to a fused morphology during stomata opening. This change in morphology requires a membrane fusion mechanism that responds rapidly to environmental signals, allowing plants to respond to diurnal and stress cues. With guard cell vacuoles being both large and responsive to external signals, stomata represent a unique system in which to delineate mechanisms of membrane fusion. Fusion of vacuole membranes is a highly conserved process in eukaryotes, with key roles played by two multi-subunit complexes: HOPS (homotypic fusion and vacuolar protein sorting) and SNARE (soluble NSF attachment protein receptor). HOPS is a vacuole tethering factor that is thought to chaperone SNAREs from apposing vacuole membranes into a fusion-competent complex capable of rearranging membranes. To resolve a counter-intuitive observation regarding the role of HOPS in regulating plant vacuole morphology, we derived a quantitative model of vacuole fusion dynamics and used it to generate testable predictions about HOPS-SNARE interactions. We derived our model by applying simulation-based inference to integrate prior knowledge about molecular interactions with limited, qualitative observations of emergent vacuole phenotypes. By constraining the model parameters to yield the emergent outcomes observed for stoma opening - as induced by two distinct chemical treatments - we predicted a dual role for HOPS and identified a stalled form of the SNARE complex that differs from phenomena reported in yeast. We predict that HOPS has contradictory actions at different points in the fusion signaling pathway, promoting the formation of SNARE complexes, but limiting their activity.

Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art

Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterizing stochastic effects in biochemical systems is essential to understand the complex dynamics of living things. Mathematical idealizations of biochemically reacting systems must be able to capture stochastic phenomena. While robust theory exists to describe such stochastic models, the computational challenges in exploring these models can be a significant burden in practice since realistic models are analytically intractable. Determining the expected behaviour and variability of a stochastic biochemical reaction network requires many probabilistic simulations of its evolution. Using a biochemical reaction network model to assist in the interpretation of time-course data from a biological experiment is an even greater challenge due to the intractability of the likelihood function for determining observation probabilities. These computational challenges have been subjects of active research for over four decades. In this review, we present an accessible discussion of the major historical developments and state-of-the-art computational techniques relevant to simulation and inference problems for stochastic biochemical reaction network models. Detailed algorithms for particularly important methods are described and complemented with Matlab^® implementations. As a result, this review provides a practical and accessible introduction to computational methods for stochastic models within the life sciences community.

Pulling in models of cell migration

There are numerous biological scenarios in which populations of cells migrate in crowded environments. Typical examples include wound healing, cancer growth, and embryo development. In these crowded environments cells are able to interact with each other in a variety of ways. These include excluded-volume interactions, adhesion, repulsion, cell signaling, pushing, and pulling. One popular way to understand the behavior of a group of interacting cells is through an agent-based mathematical model. A typical aim of modellers using such representations is to elucidate how the microscopic interactions at the cell-level impact on the macroscopic behavior of the population. At the very least, such models typically incorporate volume-exclusion. The more complex cell-cell interactions listed above have also been incorporated into such models; all apart from cell-cell pulling. In this paper we consider this under-represented cell-cell interaction, in which an active cell is able to "pull" a nearby neighbor as it moves. We incorporate a variety of potential cell-cell pulling mechanisms into on- and off-lattice agent-based volume exclusion models of cell movement. For each of these agent-based models we derive a continuum partial differential equation which describes the evolution of the cells at a population level. We study the agreement between the agent-based models and the continuum, population-based models and compare and contrast a range of agent-based models (accounting for the different pulling mechanisms) with each other. We find generally good agreement between the agent-based models and the corresponding continuum models that worsens as the agent-based models become more complex. Interestingly, we observe that the partial differential equations that we derive differ significantly, depending on whether they were derived from on- or off-lattice agent-based models of pulling. This hints that it is important to employ the appropriate agent-based model when representing pulling cell-cell interactions.

Neural crest migration with continuous cell states

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.

Bayesian Parameter Identification for Turing Systems on Stationary and Evolving Domains

In this study, we apply the Bayesian paradigm for parameter identification to a well-studied semi-linear reaction-diffusion system with activator-depleted reaction kinetics, posed on stationary as well as evolving domains. We provide a mathematically rigorous framework to study the inverse problem of finding the parameters of a reaction-diffusion system given a final spatial pattern. On the stationary domain the parameters are finite-dimensional, but on the evolving domain we consider the problem of identifying the evolution of the domain, i.e. a time-dependent function. Whilst others have considered these inverse problems using optimisation techniques, the Bayesian approach provides a rigorous mathematical framework for incorporating the prior knowledge on uncertainty in the observation and in the parameters themselves, resulting in an approximation of the full probability distribution for the parameters, given the data. Furthermore, using previously established results, we can prove well-posedness results for the inverse problem, using the well-posedness of the forward problem. Although the numerical approximation of the full probability is computationally expensive, parallelised algorithms make the problem solvable using high-performance computing.

The impact of experimental design choices on parameter inference for models of growing cell colonies

To better understand development, repair and disease progression, it is useful to quantify the behaviour of proliferative and motile cell populations as they grow and expand to fill their local environment. Inferring parameters associated with mechanistic models of cell colony growth using quantitative data collected from carefully designed experiments provides a natural means to elucidate the relative contributions of various processes to the growth of the colony. In this work, we explore how experimental design impacts our ability to infer parameters for simple models of the growth of proliferative and motile cell populations. We adopt a Bayesian approach, which allows us to characterize the uncertainty associated with estimates of the model parameters. Our results suggest that experimental designs that incorporate initial spatial heterogeneities in cell positions facilitate parameter inference without the requirement of cell tracking, while designs that involve uniform initial placement of cells require cell tracking for accurate parameter inference. As cell tracking is an experimental bottleneck in many studies of this type, our recommendations for experimental design provide for significant potential time and cost savings in the analysis of cell colony growth.

Modeling persistence of motion in a crowded environment: The diffusive limit of excluding velocity-jump processes

Persistence of motion is the tendency of an object to maintain motion in a direction for short time scales without necessarily being biased in any direction in the long term. One of the most appropriate mathematical tools to study this behavior is an agent-based velocity-jump process. In the absence of agent-agent interaction, the mean-field continuum limit of the agent-based model (ABM) gives rise to the well known hyperbolic telegraph equation. When agent-agent interaction is included in the ABM, a strictly advective system of partial differential equations (PDEs) can be derived at the population level. However, no diffusive limit of the ABM has been obtained from such a model. Connecting the microscopic behavior of the ABM to a diffusive macroscopic description is desirable, since it allows the exploration of a wider range of scenarios and establishes a direct connection with commonly used statistical tools of movement analysis. In order to connect the ABM at the population level to a diffusive PDE at the population level, we consider a generalization of the agent-based velocity-jump process on a two-dimensional lattice with three forms of agent interaction. This generalization allows us to take a diffusive limit and obtain a faithful population-level description. We investigate the properties of the model at both the individual and population levels and we elucidate some of the models' key characteristic features. In particular, we show an intrinsic anisotropy inherent to the models and we find evidence of a spontaneous form of aggregation at both the micro- and macroscales.

Approximate Bayesian computation reveals the importance of repeated measurements for parameterising cell-based models of growing tissues

The growth and dynamics of epithelial tissues govern many morphogenetic processes in embryonic development. A recent quantitative transition in data acquisition, facilitated by advances in genetic and live-imaging techniques, is paving the way for new insights to these processes. Computational models can help us understand and interpret observations, and then make predictions for future experiments that can distinguish between hypothesised mechanisms. Increasingly, cell-based modelling approaches such as vertex models are being used to help understand the mechanics underlying epithelial morphogenesis. These models typically seek to reproduce qualitative phenomena, such as cell sorting or tissue buckling. However, it remains unclear to what extent quantitative data can be used to constrain these models so that they can then be used to make quantitative, experimentally testable predictions. To address this issue, we perform an in silico study to investigate whether vertex model parameters can be inferred from imaging data, and explore methods to quantify the uncertainty of such estimates. Our approach requires the use of summary statistics to estimate parameters. Here, we focus on summary statistics of cellular packing and of laser ablation experiments, as are commonly reported from imaging studies. We find that including data from repeated experiments is necessary to generate reliable parameter estimates that can facilitate quantitative model predictions.

Understanding interactions between populations: Individual based modelling and quantification using pair correlation functions

Understanding the underlying mechanisms that produce the huge variety of swarming and aggregation patterns in animals and cells is fundamental in ecology, developmental biology, and regenerative medicine, to name but a few examples. Depending upon the nature of the interactions between individuals (cells or animals), a variety of different large-scale spatial patterns can be observed in their distribution; examples include cell aggregates, stripes of different coloured skin cells, etc. For the case where all individuals are of the same type (i.e., all interactions are alike), a considerable literature already exists on how the collective organisation depends on the inter-individual interactions. Here, we focus on the less studied case where there are two different types of individuals present. Whilst a number of continuum models of this scenario exist, it can be difficult to compare these models to experimental data, since real cells and animals are discrete. In order to overcome this problem, we develop an agent-based model to simulate some archetypal mechanisms involving attraction and repulsion. However, with this approach (as with experiments), each realisation of the model is different, due to stochastic effects. In order to make useful comparisons between simulations and experimental data, we need to identify the robust features of the spatial distributions of the two species which persist over many realisations of the model (for example, the size of aggregates, degree of segregation or intermixing of the two species). In some cases, it is possible to do this by simple visual inspection. In others, the features of the pattern are not so clear to the unaided eye. In this paper, we introduce a pair correlation function (PCF), which allows us to analyse multi-species spatial distributions quantitatively. We show how the differing strengths of inter-individual attraction and repulsion between species give rise to different spatial patterns, and how the PCF can be used to quantify these differences, even when it might be impossible to recognise them visually.