Biology subjects

Maini, P. K.

Publications and source records attributed to Maini, P. K..

At least 19 recordsLinked to original sources

bioRxiv2026

RecA structure kinetics determine SOS dynamics and predict spontaneous cell death

Even under optimal growth conditions, bacterial cells experience endogenous stresses that threaten cellular function. Individual cells sporadically activate stress responses to restore homeostasis, but some cells ultimately die. The SOS response to DNA damage is particularly heterogeneous, but the origin of its spontaneous activation and its relationship to cell fate remain unclear. Here, we imaged fluorescently labelled RecA in single Escherichia coli cells under steady-state unperturbed growth using microfluidics. We find that RecA* structures assemble frequently near replication forks and precede SOS response pulses. RecA* structure lifetime quantitatively encodes the magnitude of SOS induction: longer-lived structures promote greater LexA degradation and larger SOS pulses. Thus, cell-to-cell variability in spontaneous SOS activation reflects differences in the repair kinetics of endogenous DNA damage events. By tracking cell lineages over time, we further show that RecA* structures are strong and early predictors of cell fate. Elevated RecA* structure presence emerges up to six generations before spontaneous cell death in over 75% of cases, before other physiological disturbances become detectable. Together, our results establish spontaneous SOS activation as a quantitative readout of endogenous DNA damage processing and identify failure to resolve such damage as a major route to spontaneous bacterial cell death.

biophysics↗

bioRxiv2026

Impact of oxygen fluctuation and consumption on the dynamics of a reduced go-or-grow model for tumor cell invasion

We propose a minimal mathematical framework to describe the go-or-grow dynamics of tumor cells comprising two phenotypically distinct populations. One population is migratory and undergoes constant diffusion, while the other proliferates in an oxygen-dependent manner. The local oxygen concentration governs transitions between these phenotypes. We then ask whether the time scale of cyclic hypoxia, where oxygen is spatially homogeneous but fluctuates between normoxic and hypoxic levels over time, alters the dynamics of the reduced generalist model in the fast phenotype-switching regime compared with the full go-or-grow model. We observe that the reduced generalist phenotype model fails to capture the go-or-grow dynamics under rapid oxygen fluctuations. Our results predict that the tumor growth rate increases in the generalist-phenotype model under rapid oxygen fluctuations compared with tumors of the proposed go-or-grow model. We then explore whether oxygen consumption, which leads to spatial heterogeneity in oxygen concentration, plays a role in distinguishing the dynamics of the reduced model from the proposed go-or-grow model. We demonstrate that the tumor in the proposed go-or-grow model exhibits a higher growth rate than the tumor in the reduced generalist-phenotype model under a slow oxygen consumption rate.

systems biology↗

bioRxiv2026

Traveling Wave Analysis of a Go-or-Grow Invasion Model with ECM-Regulated Phenotypic Switching

Experimental studies show that tumor cells adopt migratory or proliferative phenotypes depending on the local extracellular matrix (ECM). In this work, we propose a minimal go-or-grow invasion model, comprising two specialist cell phenotypes: proliferating and migratory, with phenotypic switching and cell migration depending on local ECM density. Numerical simulations of this model reveal that the spatial arrangement of proliferative and migratory cells depends on the choice of phenotypic switching function. We then ask whether this specialist cell-phenotype model can be reduced to a generalist cell-phenotype model. We derive a relationship between the reduced model and go-or-grow model in the fast phenotypic switching regime. We observe that the reduced model captures the dynamics of the original model, for a range of realistic phenotypic switching functions. We analytically derive the minimum traveling wave speed of the reduced model in a homogeneous ECM bed. Moreover, using linear stability analysis on the go-or-grow model, we recover the same wave speed expression. In addition, we numerically explore how the key parameters influence the traveling wave speed profile. Our analysis indicated the counter-intuitive result that the wave speed is independent of the matrix degradation rate, and our simulations show that, at most, the speed is weakly dependent on this parameter.

systems biology↗

bioRxiv2026

Tipping Points and Emergent Phases of Species Diversity in Mutualistic Ecological Networks under Global Warming

Global warming poses a severe threat to ecosystem resilience and biodiversity, potentially driving species loss, declining diversity, and ecosystem collapse. Accurately predicting tipping points of ecological resilience under global warming remains a fundamental challenge. Here, we develop a theoretical framework to identify climate-induced tipping points in mutualistic ecological networks, capturing critical transitions under warming scenarios. We show that rising temperatures, increasing intraspecific competition, and deteriorating mutualistic interaction can drive ecosystems through three distinct dynamical phases of species diversity: stable full coexistence, stable partial coexistence, and total extinction. Notably, ecosystems with low species abundances are particularly vulnerable, facing heightened risks of diversity loss and extinction. Moreover, the warming rate modulates these transitions, as slower warming grants endangered species a window of time within which to adjust and attenuate the loss of resilience. Applying this framework to assess various emission mitigation pathways, we find that "pollute first, clean up later" scenarios pose a threat to biodiversity, leading to irreversible biodiversity losses even after subsequent emission reductions. Our findings offer critical insights into the timing and mechanisms of ecological tipping points under climate change and underscore the urgency of proactive mitigation strategies.

ecology↗

bioRxiv2025

Predicting Treatment Outcomes from Adaptive Therapy -- A New Mathematical Biomarker

Standard-of-care cancer therapy regimens are characterized by continuous treatment at the maximum tolerated dose; however, this approach often fails on metastatic cancers due to the emergence of drug resistance. An evolution-based treatment paradigm known as Adaptive Therapy has been proposed to counter this, dynamically adjusting treatment to control, rather than minimize, the tumor burden, thus suppressing the growth of treatment-resistant cell populations and hence delaying patient relapse. Promising clinical results in prostate cancer indicate the potential of adaptive treatment protocols, but demonstrate broad heterogeneity in patient response. This naturally leads to the question: why does this heterogeneity occur, and is a one-size-fits-all protocol best for patients across this spectrum of responses? Using a Lotka-Volterra representation of drug-sensitive and -resistant tumor populations dynamics, we obtain a predictive expression for the expected benefit from Adaptive Therapy and propose two new mathematical biomarkers (the Delta AT Score and the eTTP) that can identify the best responders in a clinical dataset after the first cycle of treatment. Based on prior theoretical analyses, we derive personalized and clinically-feasible optimal treatment strategies, based on individual patients tumor dynamics. These strategies vary significantly between patients, and so we present a framework to generate individual treatment schedules based on a patients response to the first treatment cycle. Finally, we develop metrics to identify which patients have the greatest sensitivity to unplanned schedule changes, such as delayed appointments, allowing clinicians to identify high-risk patients that need to be monitored more closely and potentially more frequently. Overall, the proposed strategies offer personalized treatment schedules that consistently outperform clinical standard-of-care protocols.

cancer biology↗

bioRxiv2025

Mathematical modelling predicts novel mechanisms of stream confinement from Trail/Colec12/Dan in the collective migration of cranial neural crest cells

BackgroundIn vertebrate embryogenesis, cranial neural crest cells (CNCCs) migrate along discrete pathways. Analyses in the chick have identified key molecular candidates for the confinement of CNCC migration to stereo-typical pathways as Colec12, Trail, and Dan. The effects of these factors on CNCCs in vitro are known, but how they confine migration to discrete streams in vivo remains poorly-understood. Here, we propose and test several hypothetical mechanisms by which these factors confine cell streams and maintain coherent migration, simulating an expanded agent-based model for collective CNCC migration. ResultsModel simulations suggest that Trail enhances adhesion between CNCCs, facilitating movement towards stereotypical migratory pathways, whereas Colec12 confines CNCCs by inducing longer, branched filopodia that facilitate movement down Colec12 gradients and re-connections with streams. Moreover, we find that Trail and Colec12 facilitate the exchange of CNCCs and the formation of CNCC-bridges between adjacent streams that are observed in vivo but poorly-understood mechanistically. Finally, we predict that Dan increases the coherence of streams by modulating the speed of CNCCs at the leading edge of collectives to prevent escape. ConclusionsOur work highlights the importance of Trail, Colec12, and Dan in CNCC migration and predicts novel mechanisms for the confinement of CNCCs to stereotypical pathways in vivo.

developmental biology↗

bioRxiv2024

Multiscale modelling shows how cell-ECM interactions impact ECM fibre alignment and cell detachment

The extracellular matrix (ECM) is a dynamic network structure that surrounds, supports, and influences cell behaviour. It facilitates cell communication and plays an important role in cell functions such as growth and migration. One way that cells interact with the ECM is via focal adhesions, which enable them to sense and respond to matrix mechanical properties and exert traction forces that deform it. This mechanical interplay between cells and the ECM, many aspects of which remain incompletely understood, involves the coordination of processes acting at different spatial scales and is highly influenced by the mechanical properties of the cells, ECM and focal adhesion components. To gain a better understanding of these mechanical interactions, we have developed a multiscale agent-based model based on a mechanical description of forces that simultaneously integrates the mechanosensitive regulation of focal adhesions, cytoskeleton dynamics, and ECM deformation. We use our model to quantify cell-cell communication mediated by ECM deformation and to show how this process depends on the mechanical properties of cells, the ECM fibres and the topology of the ECM network. In particular, we analyse the influence of ECM stiffness and cell contraction activity in the transmission of mechanical cues between cells and how the distinct timescales associated with different processes influence cell-ECM interaction. Our model simulations predict increased ECM deformation for stronger cell contraction and a sweet spot of ECM stiffness for the transmission of mechanical cues along its fibres. We also show how the network topology affects the ability of stiffer ECMs to transmit deformation and how it can induce cell detachment from the ECM. Finally, we demonstrate that integrating processes across different spatial and temporal scales is crucial for understanding how mechanical communication influences cell behaviour. Author summaryThe cell surrounding is a dynamic fibrous network known as the extracellular matrix (ECM). It supports and influences cell behaviour, playing a key role in cell communication, growth, and migration. Cells sense the ECMs mechanical properties and exert traction forces on it, leading to the deformation of matrix fibres and the transmission of mechanical stress. These changes are transmitted along the ECM fibres, influencing the behaviour of neighbouring cells. Different subcellular structures and extracellular matrix components interact at various spatial and temporal scales, making mathematical modelling a valuable tool for analysing these interactions. We have developed a multiscale force-based model that quantifies mechanical stress transmission, captures cell detachment, and explores the impact of mechanical properties of both cells and the ECM. Our analysis shows that stronger cell contraction increases extracellular matrix deformation and suggests a range of extracellular matrix stiffness for effective mechanical cell-cell communication. We also use our model to investigate how ECM network topology can induce cell detachment by modifying the ability of stiff ECMs to transmit deformation when subject to cell-induced traction forces. Our results show the importance of coupling the processes occurring at different scales to capture the overall behaviour.

biophysics↗

bioRxiv2024

Will a large complex system form Turing patterns?

From atomic spins in magnets to galaxies, and from embryonic development to patchy vegetation in arid environments, the physical world is filled with complex systems that spontaneously form spatial patterns. While simple mathematical models, such as reaction-diffusion systems, can explain the formation of such patterns, the complexity of the physical systems these models aim to describe necessitates the analysis of model robustness. Our work utilizes random matrix theory to provide arguably the first definition of robustness that is analytically tractable, providing an easy guide for identifying spatial interactions that robustly generate spatial patterns. We illustrate our theory on examples from mathematical biology, showing that diffusion alone cannot robustly generate spatial Turing patterns in large and unstructured systems, while advection, chemotaxis and non-local interactions can robustly promote pattern formation. Furthermore, we use our theory to prove that the spinodal decompositon of soft condensed matter is dynamically robust and predict the dynamics beyond regimes permitted by the standard Landau-Ginzburg theory. By classifying different spatial interactions based on the robustness of pattern formation, this work provides insights into which mechanisms are fundamental for pattern formation in large and unstructured physical systems.

biophysics↗

bioRxiv2024

Identifiability of heterogeneous phenotype adaptation from low-cell-count experiments and a stochastic model

Phenotypic plasticity contributes significantly to treatment failure in many cancers. Despite the increased prevalence of experimental studies that interrogate this phenomenon, there remains a lack of applicable quantitative tools to characterise data, and importantly to distinguish between resistance as a discrete phenotype and a continuous distribution of phenotypes. To address this, we develop a stochastic individual-based model of plastic phenotype adaptation through a continuously-structured phenotype space in low-cell-count proliferation assays. That our model corresponds probabilistically to common partial differential equation models of resistance allows us to formulate a likelihood that captures the intrinsic noise ubiquitous to such experiments. We apply our framework to assess the identifiability of key model parameters in several population-level data collection regimes; in particular, parameters relating to the adaptation velocity and cell-to-cell heterogeneity. Significantly, we find that cell-to-cell heterogeneity is practically non-identifiable from both cell count and proliferation marker data, implying that population-level behaviours may be well characterised by homogeneous ordinary differential equation models. Additionally, we demonstrate that population-level data are insufficient to distinguish resistance as a discrete phenotype from a continuous distribution of phenotypes. Our results inform the design of both future experiments and future quantitative analyses that probe phenotypic plasticity in cancer. Author SummaryMany cancers adaptively and reversibly develop resistance to treatment, adding complexity to predictive model development and, by extension, treatment design. While so-called drug challenge experiments are now commonly employed to interrogate phenotypic plasticity, there are very few quantitative tools available to interpret the biological data that arises. In particular, it remains unclear what is needed from drug challenge experiments in order to identify the phenotypic structure of a population that responds adaptively to treatment. In this work, we develop a new individual-level mathematical model of phenotypic plasticity in parallel with a structured model calibration process. Applying our framework to various existing and potential experimental designs reveals that experiments that yield only population-level data cannot distinguish between drug resistance as a distinct cell state, or drug resistance as a continuum of cell states. Consequentially, at the population-level, we demonstrate that common mathematical models that assume a set of distinct cell states can characterise the behaviour of cell populations that, in actuality, respond through a continuum of states. Importantly, our results shed light on both the mathematical models and experiments required to capture phenotypic plasticity in cancer.

cancer biology↗

bioRxiv2024

Characterising cancer cell responses to cyclic hypoxia using mathematical modelling

In vivo observations show that oxygen levels in tumours can fluctuate on fast and slow timescales. As a result, cancer cells can be periodically exposed to pathologically low oxygen levels; a phenomenon known as cyclic hypoxia. Yet, little is known about the response and adaptation of cancer cells to cyclic, rather than, constant hypoxia. Further, existing in vitro models of cyclic hypoxia fail to capture the complex and heterogeneous oxygen dynamics of tumours growing in vivo. Mathematical models can help to overcome current experimental limitations and, in so doing, offer new insights into the biology of tumour cyclic hypoxia by predicting cell responses to a wide range of cyclic dynamics. We develop an individual-based model to investigate how cell cycle progression and cell fate determination of cancer cells are altered following exposure to cyclic hypoxia. Our model can simulate standard in vitro experiments, such as clonogenic assays and cell cycle experiments, allowing for efficient screening of cell responses under a wide range of cyclic hypoxia conditions. Simulation results show that the same cell line can exhibit markedly different responses to cyclic hypoxia depending on the dynamics of the oxygen fluctuations. We also use our model to investigate the impact of changes to cell cycle checkpoint activation and damage repair on cell responses to cyclic hypoxia. Our simulations suggest that cyclic hypoxia can promote heterogeneity in cellular damage repair activity within vascular tumours.

systems biology↗

bioRxiv2023

Enhanced perfusion following exposure to radiotherapy: a theoretical investigation

Tumour angiogenesis leads to the formation of blood vessels that are structurally and spatially heterogeneous. Poor blood perfusion, in conjunction with increased hypoxia and oxygen heterogeneity, impairs a tumours response to radiotherapy. The optimal strategy for enhancing tumour perfusion remains unclear, preventing its regular deployment in combination therapies. In this work, we first identify vascular architectural features that correlate with enhanced perfusion following radiotherapy, using in vivo imaging data from vascular tumours. Then, we present a novel computational model to determine the relationship between these architectural features, blood perfusion, and tumour response to radiotherapy in silico. If perfusion is defined to be the proportion of vessels that support blood flow, we find that vascular networks with small mean diameters and large numbers of angiogenic sprouts show the largest increases in perfusion post-irradiation for both biological and synthetic tumours. We also identify cases where perfusion increases due to the pruning of hypoperfused vessels, rather than blood being rerouted. These results indicate the importance of considering network composition when determining the optimal irradiation strategy. In the future, we aim to use our findings to identify tumours that are good candidates for perfusion enhancement and to improve the efficacy of combination therapies. Author summaryDysregulated tumour vasculature often contains hypoperfused blood vessels which inhibit the delivery of blood-borne anticancer therapies. Radiotherapy, used to treat more than half of all cancer patients, causes DNA damage to vascular endothelial cells, preferentially impacting smaller vessels, leading to their death and vessel pruning. At the same time, experiments measuring changes in tumour perfusion post-irradiation produce varying outcomes and, therefore, the impact of irradiation-induced vessel pruning on network-scale perfusion remains unclear. In this study, we use recent (in vivo) imaging data to identify features of tumour vascular architectures that impact perfusion change post-irradiation. We then use a newly-developed computational framework, directly informed by the experimental observations, to elucidate the relationship between the vascular geometry and topology prior to radiotherapy and the irradiation-induced changes to network perfusion. We find that perfusion increases most significantly for networks of blood vessels with small mean diameters and large numbers of angiogenic sprouts. Our results also distinguish different mechanisms of perfusion increase and we identify cases where rerouting of blood flow causes previously hypoperfused vessels to become perfused. Our study sheds more light on the impact of radiotherapy on tumour blood flow; these insights could be useful for improving anti-cancer treatments.

systems biology↗

bioRxiv2023

Turing pattern formation in reaction-cross-diffusion systems with a bilayer geometry

Conditions for self-organisation via Turings mechanism in biological systems represented by reaction-diffusion or reaction-cross-diffusion models have been extensively studied. Nonetheless, the impact of tissue stratification in such systems is under-explored, despite its ubiquity in the context of a thin epithelium overlying connective tissue, for instance the epidermis and underlying dermal mesenchyme of embryonic skin. In particular, each layer can be subject to extensively different biochemical reactions and transport processes, with chemotaxis - a special case of cross- diffusion - often present in the mesenchyme, contrasting the solely molecular transport typically found in the epidermal layer. We study Turing patterning conditions for a class of reaction-cross- diffusion systems in bilayered regions, with a thin upper layer and coupled by a linear transport law. In particular, the role of differential transport through the interface is explored together with the presence of asymmetry between the homogeneous equilibria of the two layers. A linear stability analysis is carried out around a spatially homogeneous equilibrium state in the asymptotic limit of weak and strong coupling strengths, where quantitative approximations of the bifurcation curve can be computed. Our theoretical findings, for an arbitrary number of reacting species, reveal quantitative Turing conditions, highlighting when the coupling mechanism between the layered regions can either trigger patterning or stabilize a homogeneous equilibrium regardless of the inde- pendent patterning state of each layer. We support our theoretical results through direct numerical simulations, and provide an open source code to explore such systems further.

developmental biology↗

bioRxiv2023

Gap junctions in Turing-type periodic feather pattern formation

Periodic patterning requires coordinated cell-cell interactions at the tissue level. Turing showed, using mathematical modeling, how spatial patterns could arise from the reactions of a diffusive activator-inhibitor pair in an initially homogenous two-dimensional field. Most activators and inhibitors studied in biological systems are proteins, and the roles of cell-cell interaction, ions, bioelectricity, etc. are only now being identified. Gap junctions (GJs) mediate direct exchanges of ions or small molecules between cells, enabling rapid long-distance communications in a cell collective. They are therefore good candidates for propagating non-protein-based patterning signals that may act according to the Turing principles. Here, we explore the possible roles of GJs in Turing-type patterning using feather pattern formation as a model. We found seven of the twelve investigated GJ isoforms are highly dynamically expressed in the developing chicken skin. In ovo functional perturbations of the GJ isoform, connexin 30, by siRNA and the dominant-negative mutant applied before placode development led to disrupted primary feather bud formation, including patches of smooth skin and buds of irregular sizes. Later, after the primary feather arrays were laid out, inhibition of gap junctional intercellular communication in the ex vivo skin explant culture allowed the emergence of new feather buds in temporal waves at specific spatial locations relative to the existing primary buds. The results suggest that gap junctional communication may facilitate the propagation of long-distance inhibitory signals. Thus, the removal of GJ activity would enable the emergence of new feather buds if the local environment is competent and the threshold to form buds is reached. We propose Turing-based computational simulations that can predict the appearance of these ectopic bud waves. Our models demonstrate how a Turing activator-inhibitor system can continue to generate patterns in the competent morphogenetic field when the level of intercellular communication at the tissue scale is modulated.

developmental biology↗

bioRxiv2021

A DNA-structured mathematical model of cell-cycle progression in cyclic hypoxia

New experimental data have shown how the periodic exposure of cells to low oxygen levels (i.e., cyclic hypoxia) impacts their progress through the cell-cycle. Cyclic hypoxia has been detected in tumours and linked to poor prognosis and treatment failure. While fluctuating oxygen environments can be reproduced in vitro, the range of oxygen cycles that can be tested is limited. By contrast, mathematical models can be used to predict the response to a wide range of cyclic dynamics. Accordingly, in this paper we develop a mechanistic model of the cell-cycle that can be combined with in vitro experiments, to better understand the link between cyclic hypoxia and cell-cycle dysregulation. A distinguishing feature of our model is the inclusion of impaired DNA synthesis and cell-cycle arrest due to periodic exposure to severely low oxygen levels. Our model decomposes the cell population into four compartments and a time-dependent delay accounts for the variability in the duration of the S phase which increases in severe hypoxia due to reduced rates of DNA synthesis. We calibrate our model against experimental data and show that it recapitulates the observed cell-cycle dynamics. We use the calibrated model to investigate the response of cells to oxygen cycles not yet tested experimentally. When the re-oxygenation phase is sufficiently long, our model predicts that cyclic hypoxia simply slows cell proliferation since cells spend more time in the S phase. On the contrary, cycles with short periods of re-oxygenation are predicted to lead to inhibition of proliferation, with cells arresting from the cell-cycle when they exit the S phase. While model predictions on short time scales (about a day) are fairly accurate (i.e, confidence intervals are small), the predictions become more uncertain over longer periods. Hence, we use our model to inform experimental design that can lead to improved model parameter estimates and validate model predictions.

cancer biology↗

bioRxiv2020

Spatial structure impacts adaptive therapy by shaping intra-tumoral competition

(1) Background: Adaptive therapy aims to tackle cancer drug resistance by leveraging intra-tumoral competition between drug-sensitive and resistant cells. Motivated by promising results in prostate cancer there is growing interest in extending this approach to other cancers. Here we present a theoretical study of intra-tumoral competition during adaptive therapy, to identify under which circumstances it will be superior to aggressive treatment; (2) Methods: We use a 2-D, on-lattice, agent-based tumour model to examine the impact of different microenvironmental factors on the comparison between continuous drug administration and adaptive therapy. (3) Results: We show that the degree of crowding, the initial resistance fraction, the presence of resistance costs, and the rate of tumour cell turnover are key determinants of the benefit of adaptive therapy, and we study in detail how these factors alter competition between cells. We find that intra-specific competition between resistant cells plays an unexpectedly important role in the ability to control resistance. To conclude we show how differences in resistance cost and turnover change the tumours spatial organisation and may explain differences in cycling speed observed in a cohort of 67 prostate cancer patients undergoing intermittent androgen deprivation therapy; (4) Conclusion: Our work provides insights into how adaptive therapy leverages inter- and intra-specific competition to control resistance, and shows that the tumours spatial architecture will likely be an important factor in determining the quantitative benefit of adaptive therapy in patients.

cancer biology↗

bioRxiv2020

A multiscale model of complex endothelial cell dynamics in early angiogenesis

We introduce a hybrid two-dimensional multiscale model of angiogenesis, the process by which endothelial cells (ECs) migrate from a pre-existing vascular bed in response to local environmental cues and cell-cell interactions, to create a new vascular network. Recent experimental studies have highlighted a central role of cell rearrangements in the formation of angiogenic networks. Our model accounts for this phenomenon via the heterogeneous response of ECs to their microenvironment. These cell rearrangements, in turn, dynamically remodel the local environment. The model reproduces characteristic features of angiogenic sprouting that include branching, chemotactic sensitivity, the brush border effect, and cell mixing. These properties, rather than being hardwired into the model, emerge naturally from the gene expression patterns of individual cells. After calibrating and validating our model against experimental data, we use it to predict how the structure of the vascular network changes as the baseline gene expression levels of the VEGF-Delta-Notch pathway, and the composition of the extracellular environment, vary. In order to investigate the impact of cell rearrangements on the vascular network structure, we introduce the mixing measure, a scalar metric that quantifies cell mixing as the vascular network grows. We calculate the mixing measure for the simulated vascular networks generated by ECs of different lineages (wild type cells and mutant cells with impaired expression of a specific receptor). Our results show that the time evolution of the mixing measure is directly correlated to the generic features of the vascular branching pattern, thus, supporting the hypothesis that cell rearrangements play an essential role in sprouting angiogenesis. Furthermore, we predict that lower cell rearrangement leads to an imbalance between branching and sprout elongation. Since the computation of this statistic requires only individual cell trajectories, it can be computed for networks generated in biological experiments, making it a potential biomarker for pathological angiogenesis. Author summaryAngiogenesis, the process by which new blood vessels are formed by sprouting from the pre-existing vascular bed, plays a key role in both physiological and pathological processes, including tumour growth. The structure of a growing vascular network is determined by the coordinated behaviour of endothelial cells in response to various signalling cues. Recent experimental studies have highlighted the importance of cell rearrangements as a driver for sprout elongation. However, the functional role of this phenomenon remains unclear. We formulate a new multiscale model of angiogenesis which, by accounting explicitly for the complex dynamics of endothelial cells within growing angiogenic sprouts, is able to produce generic features of angiogenic structures (branching, chemotactic sensitivity, cell mixing, etc.) as emergent properties of its dynamics. We validate our model against experimental data and then use it to quantify the phenomenon of cell mixing in vascular networks generated by endothelial cells of different lineages. Our results show that there is a direct correlation between the time evolution of cell mixing in a growing vascular network and its branching structure, thus paving the way for understanding the functional role of cell rearrangements in angiogenesis.

systems biology↗

bioRxiv2019

A mathematical dissection of the adaptation of cell populations to fluctuating oxygen levels

The disordered network of blood vessels that arises from tumour angiogenesis results in variations in the delivery of oxygen into the tumour tissue. This brings about regions of chronic hypoxia (i.e. sustained low oxygen levels) and regions with alternating phases of low and relatively higher oxygen levels within vascularised tumours, and makes it necessary for cancer cells to adapt to fluctuating environmental conditions. We use a phenotype-structured model to dissect the evolutionary dynamics of cell populations exposed to fluctuating oxygen levels. In this model, the phenotypic state of every cell is described by a continuous variable that provides a simple representation of its metabolic phenotype, ranging from fully oxidative to fully glycolytic, and cells are grouped into two competing populations that undergo heritable, spontaneous phenotypic variations at different rates. Model simulations indicate that, depending on the rate at which oxygen is consumed by the cells, nonlinear dynamic interactions between cells and oxygen can stimulate chronic hypoxia and cycling hypoxia. Moreover, the model supports the idea that under chronic-hypoxic conditions lower rates of phenotypic variation lead to a competitive advantage, whereas higher rates of phenotypic variation can confer a competitive advantage under cycling-hypoxic conditions. In the latter case, the numerical results obtained show that bet-hedging evolutionary strategies, whereby cells switch between oxidative and glycolytic phenotypes, can spontaneously emerge. We explain how these results can shed light on the evolutionary process that may underpin the emergence of phenotypic heterogeneity in vascularised tumours.

cancer biology↗

bioRxiv2019

Mix & Match: Phenotypic coexistence as a key facilitator of solid tumour invasion

Invasion of healthy tissue is a defining feature of malignant tumours. Traditionally, invasion is thought to be driven by cells that have acquired all the necessary traits to overcome the range of biological and physical defences employed by the body. However, in light of the ever-increasing evidence for geno- and phenotypic intra-tumour heterogeneity an alternative hypothesis presents itself: Could invasion be driven by a collection of cells with distinct traits that together facilitate the invasion process? In this paper, we use a mathematical model to assess the feasibility of this hypothesis in the context of acid-mediated invasion. We assume tumour expansion is obstructed by stroma which inhibits growth, and extra-cellular matrix (ECM) which blocks cancer cell movement. Further, we assume that there are two types of cancer cells: i) a glycolytic phenotype which produces acid that kills stromal cells, and ii) a matrix-degrading phenotype that locally remodels the ECM. We extend the Gatenby-Gawlinski reaction-diffusion model to derive a system of five coupled reaction-diffusion equations to describe the resulting invasion process. We characterise the spatially homogeneous steady states and carry out a simulation study in one spatial dimension to determine how the tumour develops as we vary the strength of competition between the two phenotypes. We find that overall tumour growth is most extensive when both cell types can stably coexist, since this allows the cells to locally mix and benefit most from the combination of traits. In contrast, when inter-species competition exceeds intra-species competition the populations spatially separate and invasion arrests either: i) rapidly (matrix-degraders dominate), or ii) slowly (acid-producers dominate). Overall, our work demonstrates that the spatial and ecological relationship between a heterogeneous population of tumour cells is a key factor in determining their ability to cooperate. Specifically, we predict that tumours in which different phenotypes coexist stably are more invasive than tumours in which phenotypes are spatially separated.

cancer biology↗