Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

The role of space in homeostasis and preneoplasia in stratified squamous epithelia

A major subject of study in biological research is the dynamics of stem cells in squamous epithelia. Given that most common human cancers develop from epithelia, understanding the rules of cell fate decision in these systems is key to explaining not only healthy tissue growth and maintenance but also the processes of mutagenesis and cancer. The aim of my project was to investigate the dynamics in squamous epithelial tissues both in homeostasis and preneoplasia, using cellular automata (CA) models. Stem cell dynamics has been shown to be accurately described by a simple mathematical model, the single progenitor (SP) model. Reliable parameterisation of this model would give access to valuable quantitative information on epithelial tissue maintenance and enable investigating how mutations affect tissue dynamics. I initially identified the most appropriate method for accurately parameterising the homeostatic system. I then sought to account for the spatial patterning of cells by implementing the SP model in two-dimensional space. The spatial model was able to reproduce the key signatures of homeostatic dynamics, thus showing that restrictions imposed by tissue organization do not alter the neutral dynamics. Furthermore, I studied non-homeostatic dynamics in stratified squamous epithelial tissues by spatially modelling the growth and competition of non-neutral mutations as well as the effects of wounding in the tissue. The studied dynamics of Notch and p53 mutant clones in mouse epithelia has been found to be highly distinct, with the former fully colonizing the tissue whereas the latter only partially. I demonstrated that the two mutants’ tissue takeover dynamics can be recapitulated by two distinct spatial feedback rules, on the basis of response to crowding, providing a mechanistic explanation of the observed distinct growth modes. Finally, mutant competition was explored. A striking effect resulting from the spatial interaction of the two mutations in a wild-type background is that the p53 mutant cell population was always outcompeted by the Notch mutant population and appeared to shrink. Considering this consistent emergent behaviour in the competition simulations and given the paucity of Notch mutations in human cancer datasets, it is tempting to speculate that the aggressive fitness of Notch may offer a tumour-protective effect

Spatiotemporal Identification of Cell Divisions Using Symmetry Properties in Time-Lapse Phase Contrast Microscopy

A variety of biological and pharmaceutical studies, such as for anti-cancer drugs, require the quantification of cell responses over long periods of time. This is performed with time-lapse video microscopy that gives a long sequence of frames. For this purpose, phase contrast imaging is commonly used since it is minimally invasive. The cell responses of interest in this study are the mitotic cell divisions. Their manual measurements are tedious, subjective, and restrictive. This study introduces an automated method for these measurements. The method starts with preprocessing for restoration and reconstruction of the phase contrast time-lapse sequences. The data are first restored from intensity non-uniformities. Subsequently, the circular symmetry of the contour of the mitotic cells in phase contrast images is used by applying a Circle Hough Transform (CHT) to reconstruct the entire cells. The CHT is also enhanced with the ability to “vote” exclusively towards the center of curvature. The CHT image sequence is then registered for misplacements between successive frames. The sequence is subsequently processed to detect cell centroids in individual frames and use them as starting points to form spatiotemporal trajectories of cells along the positive as well as along the negative time directions, that is, anti-causally. The connectivities of different trajectories enhanced by the symmetry of the trajectories of the daughter cells provide as topological by-products the events of cell divisions together with the corresponding entries into mitoses as well as exits from cytokineses. The experiments use several experimental video sequences from three different cell lines with many cells undergoing mitoses and divisions. The quantitative validations of the results of the processing demonstrate the high performance and efficiency of the method

Taking aim at moving targets in computational cell migration

Cell migration is central to the development and maintenance of multicellular organisms. Fundamental understanding of cell migration can, for example, direct novel therapeutic strategies to control invasive tumor cells. However, the study of cell migration yields an overabundance of experimental data that require demanding processing and analysis for results extraction. Computational methods and tools have therefore become essential in the quantification and modeling of cell migration data. We review computational approaches for the key tasks in the quantification of in vitro cell migration: image pre-processing, motion estimation and feature extraction. Moreover, we summarize the current state-of-the-art for in silico modeling of cell migration. Finally, we provide a list of available software tools for cell migration to assist researchers in choosing the most appropriate solution for their needs

Capturing Within Host HIV-1 Evolution Dynamics Using Simulation Methods

The persistent latent reservoir of long-lived cells carrying integrated HIV DNA is the source of reinfection upon treatment interruption, and a primary focus for cure research. The reservoir is difficult to study because these cells are relatively rare or located in tissues that are difficult to sample. Sequencing proviral DNA in the latent reservoir is an important source of information about reservoir establishment and persistence, especially from the presence of identical (clonal) sequences. I evaluated the relationship between select measures of these clonal sequences and drivers of reservoir persistence, e.g., clonal expansion, by implementing a simulation model of within-host HIV dynamics in actively and latently infected cells. I implemented a discrete event simulation in the R package treeswithintrees, with four populations of cells corresponding to active, latent, replenishment and death compartments. To simulate molecular evolution on the resulting trees, I collapsed branches representing infected cells in a latent state and ran the program INDELible with parameters calibrated to HIV-1 on a representative env sequence. I propose a new clonality statistic (pairwise clonality) that can capture the genetic diversity of a sample with less information loss. I then evaluated the response of two clonality statistics used in literature (the proportion of identical sequences, Gini coefficient) and my proposed clonality statistic (number of identical pairwise comparisons) to changes in simulation parameter values by fitting a General linear Model (GLM). I found that the former clonality statistics were not as robust as the proposed pairwise clonality score. In addition, there were significant associations between clonality statistics and simulation parameters. Finally, I implemented a particle filtering method to evaluate non-linear relationships between simulation parameters and the clonality scores

Bayesian Inference for Genomic Data Analysis

High-throughput genomic data contain gazillion of information that are influenced by the complex biological processes in the cell. As such, appropriate mathematical modeling frameworks are required to understand the data and the data generating processes. This dissertation focuses on the formulation of mathematical models and the description of appropriate computational algorithms to obtain insights from genomic data. Specifically, characterization of intra-tumor heterogeneity is studied. Based on the total number of allele copies at the genomic locations in the tumor subclones, the problem is viewed from two perspectives: the presence or absence of copy-neutrality assumption. With the presence of copy-neutrality, it is assumed that the genome contains mutational variability and the three possible genotypes may be present at each genomic location. As such, the genotypes of all the genomic locations in the tumor subclones are modeled by a ternary matrix. In the second case, in addition to mutational variability, it is assumed that the genomic locations may be affected by structural variabilities such as copy number variation (CNV). Thus, the genotypes are modeled with a pair of (Q + 1)-ary matrices. Using the categorical Indian buffet process (cIBP), state-space modeling framework is employed in describing the two processes and the sequential Monte Carlo (SMC) methods for dynamic models are applied to perform inference on important model parameters. Moreover, the problem of estimating gene regulatory network (GRN) from measurement with missing values is presented. Specifically, gene expression time series data may contain missing values for entire expression values of a single point or some set of consecutive time points. However, complete data is often needed to make inference on the underlying GRN. Using the missing measurement, a dynamic stochastic model is used to describe the evolution of gene expression and point-based Gaussian approximation (PBGA) filters with one-step or two-step missing measurements are applied for the inference. Finally, the problem of deconvolving gene expression data from complex heterogeneous biological samples is examined, where the observed data are a mixture of different cell types. A statistical description of the problem is used and the SMC method for static models is applied to estimate the cell-type specific expressions and the cell type proportions in the heterogeneous samples

Inferring kinetic parameters of oscillatory gene regulation from single cell time-series data

This work was supported by a Wellcome Trust Four-Year PhD Studentship in Basic Science to J.B. (219992/Z/19/Z) and a Wellcome Trust Senior Research Fellowship to N.P. (090868/Z/09/Z). C.M. was supported by a Sir Henry Wellcome Fellowship (103986/Z/14/Z) and University of Manchester Presidential Fellowship. M.R.’s work was supported by a Wellcome Trust Investigator Award (204832/B/16/Z).Gene expression dynamics, such as stochastic oscillations and aperiodic fluctuations, have been associated with cell fate changes in multiple contexts, including development and cancer. Single cell live imaging of protein expression with endogenous reporters is widely used to observe such gene expression dynamics. However, the experimental investigation of regulatory mechanisms underlying the observed dynamics is challenging, since these mechanisms include complex interactions of multiple processes, including transcription, translation and protein degradation. Here, we present a Bayesian method to infer kinetic parameters of oscillatory gene expression regulation using an auto-negative feedback motif with delay. Specifically, we use a delay-adapted nonlinear Kalman filter within a Metropolis-adjusted Langevin algorithm to identify posterior probability distributions. Our method can be applied to time-series data on gene expression from single cells and is able to infer multiple parameters simultaneously. We apply it to published data on murine neural progenitor cells and show that it outperforms alternative methods. We further analyse how parameter uncertainty depends on the duration and time resolution of an imaging experiment, to make experimental design recommendations. This work demonstrates the utility of parameter inference on time course data from single cells and enables new studies on cell fate changes and population heterogeneity.Publisher PDFPeer reviewe