Biology subjects

Philip K Maini

Publications and source records attributed to Philip K Maini.

7 recordsLinked to original sources

bioRxiv2016

Logistic proliferation of cells in scratch assays is delayed

Scratch assays are used to study how a population of cells re-colonises a vacant region on a two-dimensional substrate after a cell mono-layer is scratched. These experiments are used in many applications including drug design for the treatment of cancer and chronic wounds. To provide insights into the mechanisms that drive scratch assays, solutions of continuum reaction-diffusion models have been calibrated to data from scratch as-says. These models typically include a logistic source term to model carrying capacity-limited proliferation, however the choice of using a logistic source term is often made without examining whether it is valid. Here we study the proliferation of PC-3 prostate cancer cells in a scratch assay, and we focus on the proliferation of these cells far away from the scratch. All experimental results for the scratch assay are compared with equivalent results from a proliferation assay where the cell monolayer is not scratched. Visual inspection of the evolution of the cell density as a function of time reveals a series of sigmoid curves that could be naively calibrated to the solution of the logistic growth model. However, careful analysis of the per capita growth rate as a function of density reveals several key differences between the proliferation of cells in scratch and proliferation assays. The per capita growth rate in the proliferation assay decreases, approximately linearly, with density in the proliferation assay suggesting that the logistic growth model is valid for the entire duration of the proliferation assay. However, the per capita growth rate in the scratch assay increases with density when the density is sufficiently small in the scratch assay, suggesting that the logistic growth model does not apply. Instead, guided by data, we find that there are two phases of proliferation in a scratch assay. At short time we have a disturbance phase where proliferation is not logistic, and this is followed by a growth phase where proliferation appears to be logistic. Accounting for the differences in the growth and disturbance phase, we obtain biologically realistic estimates of the proliferation rate and carrying capacity density. In contrast, simply calibrating the solution of the logistic growth equation to all data from the scratch assays, we obtain an excellent match between the data and the model, but the parameter estimates vary wildly and are not biologically realistic. Overall our study shows that simply calibrating the solution of a continuum model to a scratch assay might produce misleading parameter estimates, and this issue can be resolved by making a distinction between the disturbance and growth phases. Repeating our procedure for other scratch assays will provide insight into the roles of the disturbance and growth phases for different cell lines and scratch assays performed on different substrates.

Biophysics↗

bioRxiv2016

A hierarchical Bayesian framework for understanding the spatiotemporal dynamics of the intestinal epithelium

Our work addresses two key challenges, one biological and one methodological. First, we aim to understand how proliferation and cellular migration rates in the intestinal epithelium are related under healthy, damaged (Ara-C treated) and recovering conditions, and how these relations can be used to identify mechanisms of repair and regeneration. We analyse new data, presented in more detail in a companion paper, in which BrdU/IdU cell-labelling experiments were performed under these respective conditions. Second, in considering how to more rigorously process these data and interpret them using mathematical models, we develop a probabilistic, hierarchical framework. This framework provides a best-practice approach for systematically modelling and understanding the uncertainties that can otherwise undermine drawing reliable conclusions - uncertainties in experimental measurement and treatment, difficult-to-compare mathematical models of underlying mechanisms, and unknown or unobserved parameters. Both discrete and continuous mechanistic models are considered and related via hierarchical conditional probability assumptions. This allows the incorporation of features of both continuum tissue models and discrete cellular models. We perform model checks on both in-sample and out-of-sample datasets and use these checks to illustrate how to test possible model improvements and assess the robustness of our conclusions. This allows us to consider - and ultimately decide against - the need to retain finite-cell-size effects to explain a small misfit appearing in one set of long-time, out-of-sample predictions. Our approach leads us to conclude, for the present set of experiments, that a primarily proliferation-driven model is adequate for predictions over most time-scales. We describe each stage of our framework in detail, and hope that the present work may also serve as a guide for other applications of the hierarchical approach to problems in computational and systems biology more generally.\n\nAuthor SummaryThe intestinal epithelium serves as an important model system for studying the dynamics and regulation of multicellular populations. It is characterised by rapid rates of self-renewal and repair; failure of the regulation of these processes is thought to explain, in part, why many tumours occur in the intestinal and similar epithelial tissues. These features have led to a large amount of work on estimating rate parameters in the intestine. There still remain, however, large gaps between the raw data collected, the experimental interpretation of these data, and speculative mechanistic models for underlying processes. In our view hierarchical statistical modelling provides an ideal, but currently underutilised, method to begin to bridge these gaps. This approach makes essential use of the distinction between measurement, process and parameter models, giving an explicit framework for combining experimental data and mechanistic modelling in the presence of multiple sources of uncertainty. As we illustrate, the hierarchical approach also provides a suitable framework for addressing other methodological questions of broader interest in systems biology: how to systematically relate discrete and continuous mechanistic models; how to formally interpret and visualise statistical evidence; and how to express causal assumptions in terms of conditional independence.

Systems Biology↗

bioRxiv2016

Architecture of a minimal signalling pathway explains the T cell response to a 1,000,000-fold variation in antigen affinity and dose

T cells must respond differently to antigens of varying affinity presented at different doses. Previous attempts to map pMHC affinity onto T cell responses have produced inconsistent patterns of responses preventing formulations of canonical models of T cell signalling. Here, a systematic analysis of T cell responses to 1,000,000-fold variations in both pMHC affinity and dose produced bell-shaped dose-response curves and different optimal pMHC affinities at different pMHC doses. Using sequential model rejection/identification algorithms, we identified a unique, minimal model of cellular signalling incorporating kinetic proofreading with limited signalling coupled to an incoherent feed forward loop (KPL-IFF), that reproduces these observations. We show that the KPL-IFF model correctly predicts the T cell response to antigen co-presentation. Our work offers a general approach for studying cellular signalling that does not require full details of biochemical pathways.\n\nSignificance statementT cells initiate and regulate adaptive immune responses when their T cell antigen receptors recognise antigens. The T cell response is known to depend on the antigen affinity/dose but the precise relationship, and the mechanisms underlying it, are debated. To resolve the debate, we stimulated T cells with antigens spanning a 1,000,000-fold range in affinity/dose. We found that a different antigen (and hence different affinity) produced the largest T cell response at different doses. Using model identification algorithms, we report a simple mechanistic model that can predict the T cell response from the physiological low affinity regime into the high affinity regime applicable to therapeutic receptors.

Immunology↗

bioRxiv2015

Spatial metrics of tumour vascular organisation predict radiation efficacy in a computational model

Intratumoural heterogeneity is known to contribute to poor therapeutic response. Variations in oxygen tension in particular have been correlated with changes in radiation response in vitro and at the clinical scale with overall survival. Heterogeneity at the microscopic scale in tumour blood vessel architecture has been described, and is one source of the underlying variations in oxygen tension. We endeavour to determine whether histologic scale measures of the erratic distribution of blood vessels within a tumour can be used to predict differing radiation response. Using a two-dimensional hybrid cellular automaton model of tumour growth, we evaluate the effect of vessel distribution on cell survival outcomes of simulated radiation therapy. Using the standard equations for the oxygen enhancement ratio for cell survival probability under differing oxygen tensions, we calculate average radiation effect over a range of different vessel densities and organisations. We go on to quantify the vessel distribution heterogeneity and measure spatial organization using Ripleys L function, a measure designed to detect deviations from spatial homogeneity. We find that under differing regimes of vessel density the correlation coefficient between the measure of spatial organization and radiation effect changes sign. This provides not only a useful way to understand the differences seen in radiation effect for tissues based on vessel architecture, but also an alternate explanation for the vessel normalization hypothesis.\n\nAuthor SummaryIn this paper we use a mathematical model, called a hybrid cellular automaton, to study the effect of different vessel distributions on radiation therapy outcomes at the cellular level. We show that the correlation between radiation outcome and spatial organization of vessels changes signs between relatively low and high vessel density. Specifically, that for relatively low vessel density, radiation efficacy is decreased when vessels are more homogeneously distributed, and the opposite is true, that radiation efficacy is improved, when vessel organisation is normalised in high densities. This result suggests an alteration to the vessel normalization hypothesis which states that normalisation of vascular beds should improve radio- and chemo-therapeutic response, but has failed to be validated in clinical studies. In this alteration, we provide a metric that differentiates between vascular architectures in different density regimes in which the hypothesis holds and does not and that could be used for quantitative histologic analysis of tumours, and for radiation dose personalisation.\n\nAuthor ContributionsConceived and designed the experiments: JGS, AGF, ARAA, PKM\n\nPerformed the experiments: JGS\n\nAnalyzed the data: JGS, AGF, ARAA, PKM\n\nWrote the paper: JGS, AGF, ARAA, PKM

Cancer Biology↗

bioRxiv2014

Glucose-lactate metabolic cooperation in cancer: insights from a spatial mathematical model and implications for targeted therapy

A recent hypothesis has proposed a glucose-lactate metabolic symbiosis between adjacent hypoxic and oxygenated regions of a developing tumour, and proposed a treatment strategy to target this symbiosis. However, in vivo experimental support remains inconclusive. Here we develop a minimal spatial mathematical model of glucose-lactate metabolism to examine, in principle, whether metabolic symbiosis is plausible in human tumours, and to assess the potential impact of inhibiting it. We find that symbiosis is a robust feature of our model system--although on the length scale at which oxygen supply is diffusion-limited, its occurrence requires very high cellular metabolic activity--and that necrosis in the tumour core is reduced in the presence of symbiosis. Upon simulating therapeutic inhibition of lactate uptake, we predict that targeted treatment increases the extent of tissue oxygenation without increasing core necrosis. The oxygenation effect is correlated strongly with the extent of wildtype hypoxia and only weakly with wildtype symbiotic behaviour, and therefore may be promising for radiosensitisation of hypoxic, lactate-consuming tumours even if they do not exhibit a spatially well-defined symbiosis. Finally, we conduct a set of in vitro experiments on the U87 glioblastoma cell line to facilitate preliminary speculation as to where highly malignant tumours might fall in our parameter space, and find that these experiments suggest a weakly symbiotic regime for U87 cells, which raises the new question of what relationship exists between symbiosis--if indeed it occurs in vivo--and tumour malignancy.

Cancer Biology↗

bioRxiv2014

Exploiting evolutionary non-commutativity to prevent the emergence of bacterial antibiotic resistance

The increasing rate of antibiotic resistance and slowing discovery of novel antibiotic treatments presents a growing threat to public health. Here, we develop a Markov Chain model of evolution in asexually reproducing populations which is an encoding of the Strong Selection Weak Mutation model of evolution on fitness landscapes. This model associates the global properties of the fitness landscape with the algebraic properties of the Markov Chain transition matrix and allows us to derive general results on the non-commutativity and irreversibility of natural selection as well as antibiotic cycling strategies. Utilizing this formalism, we analyse 15 empirical fitness landscapes of E. coli under selection by di.erent beta-lactam antibiotics and demonstrate that the emergence of resistance to a given antibiotic can be both hindered and promoted by di.erent sequences of drug application. Further, we derive optimal drug application sequences with which we can probabilistically steer the population through genotype space to avoid the emergence of resistance. This suggests a new strategy in the war against antibiotic.therapy.resistant organisms: drug sequencing to shepherd evolution through genotype space to states from which resistance cannot emerge and by which to maximize the chance of successful therapy. BackgroundThe increasing rate of antibiotic resistance and slowing discovery of novel antibiotic treatments presents a growing threat to public health. Previous studies of bacterial evolutionary dynamics have shown that populations evolving on fitness landscapes follow predictable paths. In this article, we develop a general mathematical model of evolution and hypothesise that it can be used to understand, and avoid, the emergence of antibiotic resistance. Methods and FindingsWe develop a Markov Chain model of evolution in asexually reproducing populations which is an encoding of the Strong Selection Weak Mutation model of evolution on fitness landscapes. This model associates the global properties of the fitness landscape with the algebraic properties of the Markov Chain transition matrix and allows us to derive general results on the non-commutativity and irreversibility of natural selection as well as antibiotic cycling strategies. Utilizing this formalism, we analyse 15 empirical fitness landscapes of E. coli under selection by different {beta}-lactam antibiotics and demonstrate that the emergence of resistance to a given antibiotic can be both hindered and promoted by different sequences of drug application. We show that resistance to a given antibiotic is promoted in 61.4%, 68.6% and 70.3% of possible orderings of single, pair or triple prior drug administrations, respectively. Further, we derive optimal drug application sequences with which we can probabilistically steer the population through genotype space to avoid the emergence of resistance. ConclusionsOur model provides generalisable results of interest to theorists studying evolution as well as providing specific, testable predictions for experimentalists to validate our methods. Further, these results suggest a new strategy in the war against antibiotic-therapy-resistant organisms: drug sequencing to shepherd an evolving population through genotype space to states from which resistance cannot emerge and from which we can maximize the likelihood of successful therapy using existing drugs. While our results are derived using a specific class of antibiotics, the method is generalisable to other situations, including the emergence of resistance to targeted therapy in cancer and how species could change secondary to changing climate or geographical movement.

Evolutionary Biology↗

bioRxiv2013

A filter-flow perspective of hematogenous metastasis offers a non-genetic paradigm for personalized cancer therapy

Translational RelevanceSince the discovery of circulating tumor cells (CTC), we have struggled for ways to use them to inform treatment. The only currently accepted method for this is a more is worse paradigm by which clinicians measure CTC burden before and after treatment to assess efficacy. Research efforts are currently focused almost entirely on genetic classification of these cells, which has yet to bear any fruit translationally. We suggest that we should shift the focus of our investigation to one driven by a physical sciences perspective. Specifically, by understanding the vascular system as a network of interconnected organs and capillary beds as filters that capture CTCs. By ascertaining the distribution of CTCs in this network for individual patients, information about the existence of subclinical metastatic disease, and therefore metastatic propensity, will come to light, and allow for better staging, prognostication and rational use of organ-directed therapy in the setting of oligometastatic disease.\n\nAbstractO_ST_ABSPurposeC_ST_ABSResearch into mechanisms of hematogenous metastasis has largely become genetic in focus, attempting to understand the molecular basis of seed-soil relationships. However, preceding this biological mechanism is the physical process of dissemination of circulating tumour cells (CTCs) in the circulatory network. We utilize a novel, network perspective of hematogenous metastasis and a large dataset on metastatic patterns to shed new light on this process.\n\nExperimental DesignThe metastatic efficiency index (MEI), previously suggested by Weiss, quantifies the process of hematogenous metastasis by taking the ratio of metastatic incidence for a given primary-target organ pair and the relative blood flow between the two sites. In this paper we extend the methodology by taking into account the reduction in CTC number that occurs in capillary beds and a novel network model of CTC flow.\n\nResultsBy applying this model to a dataset of metastatic incidence, we show that the MEI depends strongly on the assumptions of micrometastatic lesions in the lung and liver. Utilizing this framework we can represent different configurations of metastatic disease and offer a rational method for identifying patients with oligometastatic disease for inclusion in future trials.\n\nConclusionsWe show that our understanding of the dynamics of CTC flow is significantly lacking, and that this specifically precludes our ability to predict metastatic patterns in individual patients. Our formalism suggests an opportunity to go a step further in metastatic disease characterization by including the distribution of CTCs at staging, offering a rational method of trial design for oligometastatic disease.

Cancer Biology↗