Biology subjects

Gerlee, P.

Publications and source records attributed to Gerlee, P..

12 recordsLinked to original sources

bioRxiv2022

A hole in Turing's theory: pattern formation on the sphere with a hole

The formation of buds on the cell membrane of budding yeast cells is thought to be driven by reactions and diffusion involving the protein Cdc42. These processes can be described by a coupled system of partial differential equations known as the Schnakenberg system. The Schnakenberg system is known to exhibit diffusion-driven pattern formation, thus providing a mechanism for bud formation. However, it is not known how the accumulation of bud scars on the cell membrane affect the ability of the Schnakenberg system to form patterns. We have approached this problem by modelling a bud scar on the cell membrane with a hole on the sphere. We have studied how the spectrum of the Laplace-Beltrami operator, which determines the resulting pattern, is affected by the size of the hole, and by numerically solving the Schnakenberg system on a sphere with a hole using the finite element method. Both theoretical predictions and numerical solutions show that pattern formation is robust to the introduction of a bud scar of considerable size, which lends credence to the hypothesis that bud formation is driven by diffusion-driven instability.

cell biology↗

bioRxiv2022

Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems

Theoretical and applied cancer studies that use individual-based models (IBMs) have been limited by the lack of a mathematical formulation that enables rigorous analysis of these models. However, spatial cumulant models (SCMs), which have arisen from theoretical ecology, describe population dynamics generated by a specific family of IBMs, namely spatio-temporal point processes (STPPs). SCMs are spatially resolved population models formulated by a system of differential equations that approximate the dynamics of two STPP-generated summary statistics: first-order spatial cumulants (densities), and second-order spatial cumulants (spatial covariances). We exemplify how SCMs can be used in mathematical oncology by modelling theoretical cancer cell populations comprising interacting growth factor-producing and non-producing cells. To formulate model equations, we use computational tools that enable the generation of STPPs, SCMs and mean-field population models (MFPMs) from user-defined model descriptions (Cornell et al., 2019). To calculate and compare STPP, SCM and MFPM-generated summary statistics, we develop an application-agnostic computational pipeline. Our results demonstrate that SCMs can capture STPP-generated population density dynamics, even when MFPMs fail to do so. From both MFPM and SCM equations, we derive treatment-induced death rates required to achieve non-growing cell populations. When testing these treatment strategies in STPP-generated cell populations, our results demonstrate that SCM-informed strategies outperform MFPM-informed strategies in terms of inhibiting population growths. We thus demonstrate that SCMs provide a new framework in which to study cell-cell interactions, and can be used to describe and perturb STPP-generated cell population dynamics. We, therefore, argue that SCMs can be used to increase IBMs applicability in cancer research. Statements and DeclarationsThe authors have no competing interests to declare that are relevant to the content of this article.

cancer biology↗

bioRxiv2021

Weak selection and the separation of eco-evo time scales using perturbation analysis

We show that under the assumption of weak frequency-dependent selection a wide class of population dynamical models can be analysed using perturbation theory. The inner solution corresponds to the ecological dynamics, where to zeroth order, the genotype frequencies remain constant. The outer solution provides the evolutionary dynamics and corresponds, to zeroth order, to a generalisation of the replicator equation. We apply this method to a model of public goods dynamics and construct, using matched asymptotic expansions, a composite solution valid for all times. We also analyse a Lotka-Volterra model of predator competition and show that to zeroth order the fraction of wild-type predators follows a replicator equation with a constant selection coefficient given by the predator death rate. For both models we investigate how the error between approximate solutions and the solution to the full model depend on the order of the approximation, and show using numerical comparison, for k = 1 and 2, that the error scales according to{varepsilon} k+1, where{varepsilon} is the strength of selection and k is the order of the approximation.

evolutionary biology↗

bioRxiv2021

Autocrine signaling explains the emergence of Allee effects in cancer cell populations

In many human cancers, the rate of cell growth depends crucially on the size of the tumour cell population. Low, zero, or negative growth at low population densities is known as the Allee effect; this effect has been studied extensively in ecology, but so far lacks a good explanation in the cancer setting. Here, we formulate and analyze an individual-based model of cancer, in which cell division rates are increased by the local concentration of an autocrine growth factor produced by the cancer cells themselves. We show, analytically and by simulation, that autocrine signaling suffices to cause both strong and weak Allee effects. Whether low cell densities lead to negative (strong effect) or reduced (weak effect) growth rate depends directly on the ratio of cell death to proliferation, and indirectly on cellular dispersal. Our model is consistent with experimental observations of brain tumor cells grown at different densities. We propose that further studying and quantifying population-wide feedback, impacting cell growth, will be central for advancing our understanding of cancer dynamics and treatment, potentially exploiting Allee effects for therapy.

cancer biology↗

bioRxiv2020

Cell polarisation in a bulk-surface model can be driven by both classic and non-classic Turing instability

The GTPase Cdc42 is the master regulator of eukaryotic cell polarisation. During this process the active form of Cdc42 is accumulated at a particular site on the cell membrane called the pole. It is believed that the accumulation of the active Cdc42 resulting in a pole is driven by a combination of activation-inactivation reactions and diffusion. It has been proposed using mathematical modelling that this is the result of diffusion-driven instability, originally proposed by Alan Turing. In this study we developed, analysed and validated a 3D bulk-surface model of the dynamics of Cdc42. We show that the model can undergo both classic and non-classic Turing instability by deriving necessary conditions for which this occurs and conclude that the non-classic case can be viewed as a limit case of the classic case of diffusion driven instability. We thoroughly investigate the parameter space. Using three-dimensional spatio-temporal simulation we predicted pole size and time to polarisation, suggesting that cell polarisation is mainly driven by the reaction strength parameter and that the size of the pole is determined by the relative diffusion.

systems biology↗

bioRxiv2019

Quantifying cell line specific proliferation and migration rates in glioblastoma cells

We have characterised the migration and proliferation rates of a large number of patient-derived glioblastoma cell lines using an individual-based model coupled to an Approximate Bayesian Computation algorithm. We found that the cell lines exhibited a negative correlation between the rate of migration and rate of division. This observation agrees with the Go or Grow hypothesis and highlights patient-specific differences in migration and proliferation.

cancer biology↗

bioRxiv2018

Extinction times in diffusive public good population dynamics

The co-evolutionary dynamics of competing populations can be strongly affected by frequency-dependent selection and population structure in space. As co-evolving populations grow into a spatial domain, their initial spatial arrangement, as well as their growth rate differences determine the dynamics. Here, we are interested in the dynamics of producers and free-rider co-evolution in the context of an ecological public good that is produced by a sub-population but evokes growth benefits to all individuals. We consider the spatial growth dynamics in one, two and three dimensions by modeling producer cell, free-rider cell and public good densities in space, driven by birth, death and diffusion. Typically, one population goes extinct. We find that uncorrelated initial spatial structures do not influence the time to extinction in comparison to the well-mixed system. We derive a slow manifold solution in order to estimate the time to extinction of either free-riders or producers. For invading populations, i.e. for populations that are initially highly segregated, we observe a traveling wave, whose speed can be calculated to improve the extinction time estimate by a simple superposition of the two times. Our results show that local effects of spatial dynamics evolve independently of the dynamics of the mean populations. Our considerations provide quantitative predictions for the transient dynamics of cooperative traits under pressure of extinction, and a potential experiment to derive elusive details of the fitness function of an ecological public goods game through extinction time observations.\n\nAuthor SummaryEcological public goods (PG) relationships emerge in growing cellular populations, for example between bacteria and cancer cells. We study the eco-evolutionary dynamics of a PG in populations that grow in space. In our model, public good-producer cells and free-rider cells can grow according to their own birth and death rates. Co-evolution occurs due to public good-driven surplus in the intrinsic growth rates and a cost to producers. A net growth rate benefit to free-riders leads to the well-known tragedy of the commons in which producers go extinct. What is often omitted from discussions is the time scale on which this extinction can occur, especially in spatial populations. We derive analytical estimates of the time to extinction in different spatial settings, and identify spatial scenarios in which extinction takes long enough such that the tragedy of the commons never occurs within the lifetime of the populations. Using numerical simulations we analyze the deviations from analytical predictions. Our results have direct implications for inferring ecological public good game properties from in vitro and in vivo experimental observations.

ecology↗

bioRxiv2018

Inferring rates of metastatic dissemination using stochastic network models

The formation of metastases is driven by the ability of cancer cells to disseminate from the site of the primary tumour to target organs. The process of dissemination is constrained by anatomical features such as the flow of blood and lymph in the circulatory system. We exploit this fact in a stochastic network model of metastasis formation, in which only anatomically feasible routes of dissemination are considered. By fitting this model to two different clinical datasets (tongue & ovarian cancer) we show that incidence data can be modelled using a small number of biologically meaningful parameters. The fitted models reveal site specific relative rates of dissemination and also allow for patient-specific predictions of metastatic involvement based on primary tumour location and stage. Applied to other data sets this type of model could yield insight about seed-soil effects, and could also be used in a clinical setting to provide personalised predictions about the extent of metastatic spread. AUTHOR SUMMARYFor most cancer patients the occurrence of metastases equals incurable disease. Despite this fact our quantitative knowledge about the process of metastatic dissemination is limited. In this manuscript we improve on a previously published mathematical model by incorporating known biological facts about metastatic spread and also consider the temporal dimension of dissemination. The model is fit to two different cancer types with very different patterns of spread, which highlights the versatility of our framework. Properly parametrised this type of model can be used for making personalised predictions about metastatic burden.

cancer biology↗

bioRxiv2018

Finite size effects in diffusive public goods games

A particular challenge in the co-evolutionary dynamics of growing populations is to determine the effects of population assortment on growth advantage of cooperative traits. Here we study the coevolution of cooperators that are public good producers and consumers, and free riders that are only public good consumers. Using an individual-based model and its continuum limit we show that the differential growth rate between producers and free-riders depends on the spatial Fourier decomposition of their respective densities. Further, we derive a finite-size correction, which scales as the cell size, which accurately describes the dynamics of a randomly assorted population. Using this result we are also able to derive an effective benefit to cost relation, which provides a criterion that relates the parameters of the model (e.g. diffusion constant of the public good, decay rate and cost) to the long-term persistence of cooperation. Our findings provide a powerful tool for the analysis of diffusive public goods games, and can explain commonly observed patterns of cooperation, rather than the tragedy of the commons, based on the derived finite-size correction.

ecology↗

bioRxiv2018

Neighborhood size-effects in nonlinear public goods games

Ecological and evolutionary dynamics can be strongly affected by population assortment and frequency-dependent selection. In growing populations, a particular challenge is to disentangle global ecological effects from local frequency-dependent effects. Here we implement a logistic growth and death model on the global scale, coupled to frequency-dependent growth rates influenced by a public goods game between cooperators and defectors. For each individual, the public good is only effective within a neighborhood of other individuals, and the public good-growth rate relationship can be nonlinear. At low numbers of cooperators, increases of public good accumulate synergistically; at high numbers, increases in public good only provide diminishing returns-the inflection point of this pattern is given by the strength of frequency-dependent selection in relation to the background fitness effect. We observed complex critical behavior in the evolutionary dynamics equilibria, determined by the relative magnitude of frequency-dependent to constant (background) growth benefits. We predict neighborhood-size-driven state changes, hysteresis between polymorphic and monomorphic equilibria, and observed that type-dependent differences in neighborhood sizes can destabilize monomorphic cooperative states but increase coexistence of cooperators and defectors. Stochastic neighborhood size fluctuations also led to coexistence and could stabilize the purely cooperative equilibrium. Our results quantify the role of assortment through neighborhood-size effects and nonlinearity of the gains function in eco-evolutionary dynamics, which is relevant for a variety of microbial and cellular public goods games.

ecology↗

bioRxiv2018

Using neural networks to bridge scales in cancer: Mapping signaling pathways to phenotypes

Cancer is an evolving system subject to mutation and selection. Selection is driven by the microenvironment that the cancer cells are growing in and acts on the cell phenotype, which is in turn modulated by intracellular signaling pathways regulated by the cell genotype. Integrating all of these processes requires bridging different biological scales. We present a mathematical model that uses a neural network as a means to connecting these scales. In particular, we consider the mapping from intracellular pathway activity to phenotype under different microenvironmental conditions.

cancer biology↗

bioRxiv2017

Extinction Times In Tumor Public Goods Games

Cancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumor cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the timescales, in particular in co-evolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell type specific rates have to be accounted for explicitly.

cancer biology↗