Quantitative Biology

Atherosclerotic plaque growth is characterised by chronic inflammation that promotes accumulation of cellular debris and extracellular fat in the inner artery wall. This material is highly thrombogenic, and plaque rupture can lead to the formation of blood clots that occlude major arteries and cause myocardial infarction or stroke. In advanced plaques, vascular smooth muscle cells (SMCs) migrate from deeper in the artery wall to synthesise a cap of fibrous tissue that stabilises the plaque and sequesters the thrombogenic plaque content from the bloodstream. The fibrous cap provides crucial protection against the clinical consequences of atherosclerosis, but the mechanisms of cap formation are poorly understood. In particular, it is unclear why certain plaques become stable and robust while others become fragile and vulnerable to rupture. We develop a multiphase model with non-standard boundary conditions to investigate early fibrous cap formation in the atherosclerotic plaque. The model is parameterised using a range of in vitro and in vivo data, and includes highly nonlinear mechanisms of SMC proliferation and migration in response to an endothelium-derived chemical signal. We demonstrate that the model SMC population naturally evolves towards a steady-state, and predict a rate of cap formation and a final plaque SMC content consistent with experimental observations in mice. Parameter sensitivity simulations show that SMC proliferation makes a limited contribution to cap formation, and highlight that stable cap formation relies on a critical balance between SMC recruitment to the plaque, SMC migration within the plaque and SMC loss by apoptosis. The model represents the first detailed in silico study of fibrous cap formation in atherosclerosis, and establishes a multiphase modelling framework that can be readily extended to investigate many other aspects of plaque development.

We present a theoretical agent-based model of cell evolution under the action of cytotoxic treatments, such as radioteraphy or chemoteraphy. The major features of cell cycle and proliferation, cell damage and repair, and chemical diffusion are included. Cell evolution is based on a discrete Markov chain, with cells stepping along a sequence of discrete internal states from 'normal' to 'inactive'. Probabilistic laws are introduced for each type of event a cell can undergo during its life cycle: duplication, arrest, apoptosis, senescence, damage, healing. We adjust the model parameters on a series of cell irradiation experiments, carried out in a clinical LINAC at 20 MV, in which the damage and repair kinetics of single- and double-strand breaks are followed. Two showcase applications of the model are then presented. In the first one, we reconstruct the cell survival curves from a number of published low- and high-dose irradiation experiments. We reobtain a very good description of the data without assuming the well-known linear-quadratic model, but instead including a variable DSB repair probability, which is found to spontaneously saturate with an exponential decay at increasingly high doses. As a second test, we attempt to simulate the two extreme possibilities of the so-called 'bystander' effect in radiotherapy: the 'local' effect versus a 'global' effect, respectively activated by the short-range or long-range diffusion of some factor, presumably secreted by the irradiated cells. Even with an oversimplified simulation, we could demonstrate a sizeable difference in the proliferation rate of non-irradiated cells, the proliferation acceleration being much larger for the global than the local effect, for relatively small fractions of irradiated cells in the colony.

The unicellular biflagellate green alga {\it Chlamydomonas reinhardtii} has been an important model system in biology for decades, and in recent years it has started to attract growing attention also within the biophysics community. Here we provide a concise review of some of the aspects of {\it Chlamydomonas} biology and biophysics most immediately relevant to physicists that might be interested in starting to work with this versatile microorganism.

Three-dimensional cultures of cells are gaining popularity as an in vitro improvement over 2D Petri dishes. In many such experiments, cells have been found to organize in aggregates. We present new results of three-dimensional in vitro cultures of breast cancer cells exhibiting patterns. Understanding their formation is of particular interest in the context of cancer since metastases have been shown to be created by cells moving in clusters. In this paper, we propose that the main mechanism which leads to the emergence of patterns is chemotaxis, i.e., oriented movement of cells towards high concentration zones of a signal emitted by the cells themselves. Studying a Keller-Segel PDE system to model chemotactical auto-organization of cells, we prove that it is subject to Turing instability under a time-dependent condition. This result is illustrated by two-dimensional simulations of the model showing spheroidal patterns. They are qualitatively compared to the biological results and their variability is discussed both theoretically and numerically.

The chemotactic network of Escherichia coli has been studied extensively both biophysically and information-theoretically. Nevertheless, the connection between these two aspects is still elusive. In this work, we report such a connection by showing that a standard biochemical model of the chemotactic network is mathematically equivalent to an information-theoretically optimal filtering dynamics. Moreover, we demonstrate that an experimentally observed nonlinear response relation can be reproduced from the optimal dynamics. These results suggest that the biochemical network of E. coli chemotaxis is designed to optimally extract gradient information in a noisy condition.

Several cellular activities, such as directed cell migration, are coordinated by an intricate network of biochemical reactions which lead to a polarised state of the cell, in which cellular symmetry is broken, causing the cell to have a well defined front and back. Recent work on balancing biological complexity with mathematical tractability resulted in the proposal and formulation of a famous minimal model for cell polarisation, known as the wave pinning model. In this study, we present a three-dimensional generalisation of this mathematical framework through the maturing theory of coupled bulk-surface semilinear partial differential equations in which protein compartmentalisation becomes natural. We show how a local perturbation over the surface can trigger propagating reactions, eventually stopped in a stable profile by the interplay with the bulk component. We describe the behavior of the model through asymptotic and local perturbation analysis, in which the role of the geometry is investigated. The bulk-surface finite element method is used to generate numerical simulations over simple and complex geometries, which confirm our analysis, showing pattern formation due to propagation and pinning dynamics. The generality of our mathematical and computational framework allows to study more complex biochemical reactions and biomechanical properties associated with cell polarisation in multi-dimensions.

Modeling cell interactions such as co-attraction and contact-inhibition of locomotion is essential for understanding collective cell migration. Here, we propose a novel deep reinforcement learning model for collective neural crest cell migration. We apply the deep deterministic policy gradient algorithm in association with a particle dynamics simulation environment to train agents to determine the migration path. Because of the different migration mechanisms of leader and follower neural crest cells, we train two types of agents (leaders and followers) to learn the collective cell migration behavior. For a leader agent, we consider a linear combination of a global task, resulting in the shortest path to the target source, and a local task, resulting in a coordinated motion along the local chemoattractant gradient. For a follower agent, we consider only the local task. First, we show that the self-driven forces learned by the leader cell point approximately to the placode, which means that the agent is able to learn to follow the shortest path to the target. To validate our method, we compare the total time elapsed for agents to reach the placode computed using the proposed method and the time computed using an agent-based model. The distributions of the migration time intervals calculated using the two methods are shown to not differ significantly. We then study the effect of co-attraction and contact-inhibition of locomotion to the collective leader cell migration. We show that the overall leader cell migration for the case with co-attraction is slower because the co-attraction mitigates the source-driven effect. In addition, we find that the leader and follower agents learn to follow a similar migration behavior as in experimental observations. Overall, our proposed method provides useful insight on how to apply reinforcement learning techniques to simulate collective cell migration.

We present a model for cell growth, division and packing under soft constraints that arise from the deformability of the cells as well as of a membrane that encloses them. Our treatment falls within the framework of diffuse interface methods, under which each cell is represented by a scalar phase field and the zero level set of the phase field represents the cell membrane. One crucial element in the treatment is the definition of a free energy density function that penalizes cell overlap, thus giving rise to a simple model of cell-cell contact. In order to properly represent cell packing and the associated free energy, we include a simplified representation of the anisotropic mechanical response of the underlying cytoskeleton and cell membrane through appropriate penalization of the cell shape change. Numerical examples are presented to demonstrate the evolution of multi-cell clusters, and the total free energy of the clusters as a consequence of growth, division and packing.

We propose a discrete in continuous mathematical model describing the in vitro growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters in the form of spheres (Cardiospheres). The approach is hybrid: discrete at cellular scale and continuous at molecular level. In the present model cells are subject to the self-organizing collective dynamics mechanism and, additionally, they can proliferate and differentiate, also depending on stochastic processes. The two latter processes are triggered and regulated by chemical signals present in the environment. Numerical simulations show the structure and the development of the clustered progenitors and are in a good agreement with the results obtained from in vitro experiments.

We analyse a minimal model for the primary response in the adaptive immune system comprising three different players: antigens, T and B cells. We assume B-T interactions to be diluted and sampled locally from heterogeneous degree distributions, which mimic B cells receptors' promiscuity. We derive dynamical equations for the order parameters quantifying the B cells activation and study the nature and stability of the stationary solutions using linear stability analysis and Monte Carlo simulations.The system's behaviour is studied in different scaling regimes of the number of B cells, dilution in the interactions and number of antigens. Our analysis shows that: (i) B cells activation depends on the number of receptors in such a way that cells with an insufficient number of triggered receptors cannot be activated; (ii) idiotypic (i.e. B-B) interactions enhance parallel activation of multiple clones, improving the system's ability to fight different pathogens in parallel; (iii) the higher the fraction of antigens within the host the harder is for the system to sustain parallel signalling to B cells, crucial for the homeostatic control of cell numbers.