Fabian Spill

Impact of the physical microenvironment on tumor progression and metastasis.

The tumor microenvironment is increasingly understood to contribute to cancer development and progression by affecting the complex interplay of genetic and epigenetic changes within the cells themselves. Moreover, recent research has highlighted that, besides biochemical cues from the microenvironment, physical cues can also greatly alter cellular behavior such as proliferation, cancer stem cell properties, and metastatic potential. Whereas initial assays have focused on basic ECM physical properties, such as stiffness, novel in vitro systems are becoming increasingly sophisticated in differentiating between distinct physical cues-ECM pore size, fiber alignment, and molecular composition-and elucidating the different roles these properties play in driving tumor progression and metastasis. Combined with advances in our understanding of the mechanisms responsible for how cells sense these properties, a new appreciation for the role of mechanics in cancer is emerging.

Mesoscopic and continuum modelling of angiogenesis

Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which processes that include proliferation and cell movement are considered as stochastic events. By studying the dependence of the model on the lattice spacing and the number of cells involved, we are able to derive the deterministic continuum limit of our equations and compare it to similar existing models of angiogenesis. We further identify conditions under which the use of continuum models is justified, and others for which stochastic or discrete effects dominate. We also compare different stochastic models for the movement of endothelial tip cells which have the same macroscopic, deterministic behaviour, but lead to markedly different behaviour in terms of production of new vessel cells.

Hybrid approaches for multiple-species stochastic reaction-diffusion models

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

A Computational Model of YAP/TAZ Mechanosensing

In cell proliferation, stem cell differentiation, chemoresistance, and tissue organization, the ubiquitous role of YAP/TAZ continues to impact our fundamental understanding in numerous physiological and disease systems. YAP/TAZ is an important signaling nexus integrating diverse mechanical and biochemical signals, such as ECM stiffness, adhesion ligand density, or cell-cell contacts, and thus strongly influences cell fate. Recent studies show that YAP/TAZ mechanical sensing is dependent on RhoA-regulated stress fibers. However, current understanding of YAP/TAZ remains limited due to the unknown interaction between the canonical Hippo pathway and cell tension. Furthermore, the multiscale relationship connecting adhesion signaling to YAP/TAZ activity through cytoskeleton dynamics remains poorly understood. To identify the roles of key signaling molecules in mechanical signal sensing and transduction, we present a, to our knowledge, novel computational model of the YAP/TAZ signaling pathway. This model converts extracellular-matrix mechanical properties to biochemical signals via adhesion, and integrates intracellular signaling cascades associated with cytoskeleton dynamics. We perform perturbations of molecular levels and sensitivity analyses to predict how various signaling molecules affect YAP/TAZ activity. Adhesion molecules, such as FAK, are predicted to rescue YAP/TAZ activity in soft environments via the RhoA pathway. We also found that changes of molecule concentrations result in different patterns of YAP/TAZ stiffness response. We also investigate the sensitivity of YAP/TAZ activity to ECM stiffness, and compare with that of SRF/MAL, which is another important regulator of differentiation. In addition, the model shows that the unresolved synergistic effect of YAP/TAZ activity between the mechanosensing and the Hippo pathways can be explained by the interaction of LIM-kinase and LATS. Overall, our model provides a, to our knowledge, novel platform for studying YAP/TAZ activity in the context of integrating different signaling pathways. This platform can be used to gain, to our knowledge, new fundamental insights into roles of key molecular and mechanical regulators on development, tissue engineering, or tumor progression.

Controlling uncertainty in aptamer selection

Significance Oligonucleotide aptamers have increasing applications as a class of molecules that bind with high affinity and specificity to a target. Aptamers are typically selected from a large pool of random candidate nucleic acid libraries through competition for the target. Using a stochastic hybrid model, we are able to study the combined impact of important evolutionary success factors such as competition, randomness, and changes in the environment. Whereas the environment may be tuned with experimental parameters such as target concentration, competition varies with differences in the initial distribution of aptamer–target binding affinities, and random events can eliminate even the ligands with the highest affinity. The search for high-affinity aptamers for targets such as proteins, small molecules, or cancer cells remains a formidable endeavor. Systematic Evolution of Ligands by EXponential Enrichment (SELEX) offers an iterative process to discover these aptamers through evolutionary selection of high-affinity candidates from a highly diverse random pool. This randomness dictates an unknown population distribution of fitness parameters, encoded by the binding affinities, toward SELEX targets. Adding to this uncertainty, repeating SELEX under identical conditions may lead to variable outcomes. These uncertainties pose a challenge when tuning selection pressures to isolate high-affinity ligands. Here, we present a stochastic hybrid model that describes the evolutionary selection of aptamers to explore the impact of these unknowns. To our surprise, we find that even single copies of high-affinity ligands in a pool of billions can strongly influence population dynamics, yet their survival is highly dependent on chance. We perform Monte Carlo simulations to explore the impact of environmental parameters, such as the target concentration, on selection efficiency in SELEX and identify strategies to control these uncertainties to ultimately improve the outcome and speed of this time- and resource-intensive process.

The effects of intrinsic noise on the behaviour of bistable cell regulatory systems under quasi-steady state conditions.

We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady state approximation based on the semi-classical approximation of the partial differential equation for the generating function associated with the chemical master equation. Such approximation proceeds by optimising an action functional whose associated set of Euler-Lagrange (Hamilton) equations provides the most likely fluctuation path. We show that, under appropriate conditions granting time scale separation, the Hamiltonian can be re-scaled so that the set of Hamilton equations splits up into slow and fast variables, whereby the quasi-steady state approximation can be applied. We analyse two particular examples of systems whose mean-field limit has been shown to exhibit bi-stability: an enzyme-catalysed system of two mutually inhibitory proteins and a gene regulatory circuit with self-activation. Our theory establishes that the number of molecules of the conserved species is order parameters whose variation regulates bistable behaviour in the associated systems beyond the predictions of the mean-field theory. This prediction is fully confirmed by direct numerical simulations using the stochastic simulation algorithm. This result allows us to propose strategies whereby, by varying the number of molecules of the three conserved chemical species, cell properties associated to bistable behaviour (phenotype, cell-cycle status, etc.) can be controlled.

Effects of 3D geometries on cellular gradient sensing and polarization

During cell migration, cells become polarized, change their shape, and move in response to various internal and external cues. Cell polarization is defined through the spatio-temporal organization of molecules such as PI3K or small GTPases, and is determined by intracellular signaling networks. It results in directional forces through actin polymerization and myosin contractions. Many existing mathematical models of cell polarization are formulated in terms of reaction-diffusion systems of interacting molecules, and are often defined in one or two spatial dimensions. In this paper, we introduce a 3D reaction-diffusion model of interacting molecules in a single cell, and find that cell geometry has an important role affecting the capability of a cell to polarize, or change polarization when an external signal changes direction. Our results suggest a geometrical argument why more roundish cells can repolarize more effectively than cells which are elongated along the direction of the original stimulus, and thus enable roundish cells to turn faster, as has been observed in experiments. On the other hand, elongated cells preferentially polarize along their main axis even when a gradient stimulus appears from another direction. Furthermore, our 3D model can accurately capture the effect of binding and unbinding of important regulators of cell polarization to and from the cell membrane. This spatial separation of membrane and cytosol, not possible to capture in 1D or 2D models, leads to marked differences of our model from comparable lower-dimensional models.

Dynamic interplay between tumour, stroma and immune system can drive or prevent tumour progression

In the tumour microenvironment, cancer cells directly interact with both the immune system and the stroma. It is firmly established that the immune system, historically believed to be a major part of the bodys defence against tumour progression, can be reprogrammed by tumour cells to be ineffective, inactivated, or even acquire tumour promoting phenotypes. Likewise, stromal cells and extracellular matrix can also have pro-and anti-tumour properties. However, there is strong evidence that the stroma and immune system also directly interact, therefore creating a tripartite interaction that exists between cancer cells, immune cells and tumour stroma. This interaction contributes to the maintenance of a chronically inflamed tumour microenvironment with pro-tumorigenic immune phenotypes and facilitated metastatic dissemination. A comprehensive understanding of cancer in the context of dynamical interactions of the immune system and the tumour stroma is therefore required to truly understand the progression toward and past malignancy.

Stochastic multi-scale models of competition within heterogeneous cellular populations:: Simulation methods and mean-field analysis

We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age (i.e. time elapsed since they were born). The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. Once the birth rate is determined, we formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size (carrying capacity): cells consume oxygen which in turn fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. Besides the fact that this simple behaviour emerges from a rather complex model, this allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance to therapy since the rescued population is less sensitive to therapy.

Optimisation of simulations of stochastic processes by removal of opposing reactions

Models invoking the chemical master equation are used in many areas of science, and, hence, their simulation is of interest to many researchers. The complexity of the problems at hand often requires considerable computational power, so a large number of algorithms have been developed to speed up simulations. However, a drawback of many of these algorithms is that their implementation is more complicated than, for instance, the Gillespie algorithm, which is widely used to simulate the chemical master equation, and can be implemented with a few lines of code. Here, we present an algorithm which does not modify the way in which the master equation is solved, but instead modifies the transition rates. It works for all models in which reversible reactions occur by replacing such reversible reactions with effective net reactions. Examples of such systems include reaction-diffusion systems, in which diffusion is modelled by a random walk. The random movement of particles between neighbouring sites is then replaced with a net random flux. Furthermore, as we modify the transition rates of the model, rather than its implementation on a computer, our method can be combined with existing algorithms that were designed to speed up simulations of the stochastic master equation. By focusing on some specific models, we show how our algorithm can significantly speed up model simulations while maintaining essential features of the original model.