Biology subjects

Simpson, M.

Publications and source records attributed to Simpson, M..

11 recordsLinked to original sources

bioRxiv2018

Using experimental data and information criteria to guide model selection for reaction--diffusion problems in mathematical biology

Reaction-diffusion models describing the movement, reproduction and death of individuals within a population are key mathematical modelling tools with widespread applications in mathematical biology. A diverse range of such continuum models have been applied in various biological contexts by choosing different flux and source terms in the reaction-diffusion framework. For example, to describe collective spreading of cell populations, the flux term may be chosen to reflect various movement mechanisms, such as random motion (diffusion), adhesion, haptotaxis, chemokinesis and chemotaxis. The choice of flux terms in specific applications, such as wound healing, is usually made heuristically, and rarely is it tested quantitatively against detailed cell density data. More generally, in mathematical biology, the questions of model validation and model selection have not received the same attention as the questions of model development and model analysis. Many studies do not consider model validation or model selection, and those that do often base the selection of the model on residual error criteria after model calibration is performed using nonlinear regression techniques. In this work, we present a model selection case study, in the context of cell invasion, with a very detailed experimental data set. Using Bayesian analysis and information criteria, we demonstrate that model selection and model validation should account for both residual errors and model complexity. These considerations are often overlooked in the mathematical biology literature. The results we present here provide a clear methodology that can be used to guide model selection across a range of applications. Furthermore, the case study we present provides a clear example where neglecting the role of model complexity can give rise to misleading outcomes.

biophysics↗

bioRxiv2018

Optimal control of acute myeloid leukaemia

Acute myeloid leukaemia (AML) is a blood cancer affecting the haematopoietic stem cells of the myeloid cell line. AML is routinely treated with chemotherapy, and so it is of great interest to develop optimal chemotherapy treatment strategies. In this work, we incorporate an immune response into a stem cell model of AML, since we find that previous models lacking an immune response are inappropriate for deriving optimal control strategies. Using optimal control theory, we produce continuous controls and bang-bang controls, corresponding to a range of objectives and parameter choices. Through example calculations, we provide a practical approach to applying optimal control using Pontryagins maximum principle. In particular, we describe and explore factors that have a profound influence on numerical convergence. We find that the convergence behaviour is sensitive to the method of control updating, the nature of the control, and to the relative weighting of terms in the objective function. All codes we use to implement optimal control are made available.

synthetic biology↗

bioRxiv2018

Self-organization controls expression more than abundance of molecular components of transcription and translation in confined cell-free gene expression

Cell-free gene expression using purified components or cell extracts has become an important platform for synthetic biology that is finding a growing numBer of practical applications. Unfortunately, at cell-relevant reactor volumes, cell-free expression suffers from excessive variability (noise) such that protein concentrations may vary by more than an order of magnitude across a population of identically constructed reaction chambers. Consensus opinion holds that variability in expression is due to the stochastic distribution of expression resources (DNA, RNAP, ribosomes, etc.) across the population of reaction chambers. In contrast, here we find that chamber-to-chamber variation in the expression efficiency generates the large variability in protein production. Through analysis and modeling, we show that chambers self-organize into expression centers that control expression efficiency. Chambers that organize into many centers, each having relatively few expression resources, exhibit high expression efficiency. Conversely, chambers that organize into just a few centers where each center has an abundance of resources, exhibit low expression efficiency. A particularly surprising finding is that diluting expression resources reduces the chamber-to-chamber variation in protein production. Chambers with dilute pools of expression resources exhibit higher expression efficiency and lower expression noise than those with more concentrated expression resources. In addition to demonstrating the means to tune expression noise, these results demonstrate that in cell-free systems, self-organization may exert even more influence over expression than the abundance of the molecular components of transcription and translation. These observations in cell-free platform may elucidate how self-organized, membrane-less structures emerge and function in cells.

biophysics↗

bioRxiv2018

Mechanistic and experimental models of cell migration reveal the importance of intercellular interactions in cell invasion

Moving fronts of cells are essential for development, repair and disease progression. Therefore, understanding and quantifying the details of the mechanisms that drive the movement of cell fronts is of wide interest. Quantitatively identifying the role of intercellular interactions, and in particular the role of cell pushing, remains an open question. Indeed, perhaps the most common continuum mathematical idealization of moving cell fronts is to treat the population of cells, either implicitly or explicitly, as a population of point particles undergoing a random walk that neglects intercellular interactions. In this work, we report a combined experimental-modelling approach showing that intercellular interactions contribute significantly to the spatial spreading of a population of cells. We use a novel experimental data set with PC-3 prostate cancer cells that have been pretreated with Mitomycin-C to suppress proliferation. This allows us to experimentally separate the effects of cell migration from cell proliferation, thereby enabling us to focus on the migration process in detail as the population of cells recolonizes an initially-vacant region in a series of two-dimensional experiments. We quantitatively model the experiments using a stochastic modelling framework, based on Langevin dynamics, which explicitly incorporates random motility and various intercellular forces including: (i) long range attraction (adhesion); and (ii) finite size effects that drive short range repulsion (pushing). Quantitatively comparing the ability of this model to describe the experimentally observed population-level behaviour provides us with quantitative insight into the roles of random motility and intercellular interactions. To quantify the mechanisms at play, we calibrate the stochastic model to match experimental cell density profiles to obtain estimates of cell diffusivity, D, and the amplitude of intercellular forces, f0. Our analysis shows that taking a standard modelling approach which ignores intercellular forces provides a poor match to the experimental data whereas incorporating intercellular forces, including short-range pushing and longer range attraction, leads to a faithful representation of the experimental observations. These results demonstrate a significant role for intercellular interactions in cell invasion.\n\nAuthor summaryMoving cell fronts are routinely observed in various physiological processes, such as wound healing, malignant invasion and embryonic morphogenesis. We explore the effects of a previously overlooked mechanism that contributes to population-level front movement: pushing. Our framework is flexible and incorporates range of reasonable biological phenomena, such as random motility, cell-to-cell adhesion, and pushing. We find that neglecting finite size effects and intercellular forces, such as cell pushing, reduces our ability to mimic and predict our experimental observations.

biophysics↗

bioRxiv2018

A Bayesian sequential learning framework to parameterise continuum models of melanoma invasion into human skin

We present a novel framework to parameterise a mathematical model of cell invasion that describes how a population of melanoma cells invades into human skin tissue. Using simple experimental data extracted from complex experimental images, we estimate three model parameters:(i) the melanoma cell proliferation rate,{lambda} ; (ii) the melanoma cell diffusivity, D; and (iii){delta} , a constant that determines the rate that melanoma cells degrade the skin tissue. The Bayesian sequential learning frame-work involves a sequence of increasingly-sophisticated experimental data from:(i) a spatially uniform cell proliferation assay; (ii) a two-dimensional circular barrier assay; and, (iii) a three-dimensional invasion assay. The Bayesian sequential learning approach leads to well-defined parameter estimates. In contrast, taking a naive approach that attempts to estimate all parameters from a single set of images from the same experiment fails to produce meaningful results. Overall our approach to inference is simple-to-implement, computationally efficient, and well-suited for many cell biology phenomena that can be described by low dimensional continuum models using ordinary differential equations and partial differential equations. We anticipate that this Bayesian sequential learning framework will be relevant in other biological contexts where it is challenging to extract detailed, quantitative biological measurements from experimental images and so we must rely on using relatively simple measurements from complex images.

biophysics↗

bioRxiv2018

KLF6 activates complementary gene modules relevant to axon growth and promotes corticospinal tract regeneration after spinal injury

Members of the KLF family of transcription factors can exert both positive and negative effects on axon regeneration in the central nervous system, but the underlying mechanisms are unclear. KLF6 and -7 share nearly identical DNA binding domains and stand out as the only known growth-promoting family members. Here we confirm that similar to KLF7, expression of KLF6 declines during postnatal cortical development and that forced re-expression of KLF6 in corticospinal tract neurons of adult female mice enhances axon regeneration after cervical spinal injury. Unlike KLF7, however, these effects were achieved with wildtype KLF6, as opposed constitutively active mutants, thus simplifying the interpretation of mechanistic studies. To clarify the molecular basis of growth promotion, RNA sequencing identified 454 genes whose expression changed upon forced KLF6 expression in cortical neurons. Network analysis of these genes revealed sub-networks of downregulated genes that were highly enriched for synaptic functions, and sub-networks of upregulated genes with functions relevant to axon extension including cytoskeleton remodeling, lipid synthesis and transport, and bioenergetics. The promoter regions of KLF6-sensitive genes showed enrichment for the binding sequence of STAT3, a previously identified regeneration-associated gene. Notably, co-expression of constitutively active STAT3 along with KLF6 in cortical neurons produced synergistic increases in neurite length. Finally, genome-wide ATAC-seq footprinting detected frequent co-binding by the two factors in pro-growth gene networks, indicating co-occupancy as an underlying mechanism for the observed synergy. These findings advance understanding of KLF-stimulated axon growth and indicate functional synergy of KLF6 transcriptional effects with those of STAT3.\n\nSIGNIFICANCE STATEMENTThe failure of axon regeneration in the CNS limits recovery from damage and disease. These findings show the transcription factor KLF6 to be a potent promoter of axon growth after spinal injury, and more importantly clarify the underlying transcriptional changes. In addition, bioinformatics analysis predicted a functional interaction between KLF6 and a second transcription factor, STAT3, and genome-wide footprinting confirmed frequent co-occupancy. Co-expression of the two factors yielded synergistic elevation of neurite growth in primary neurons. These data point the way toward novel transcriptional interventions to promote CNS regeneration.

neuroscience↗

bioRxiv2018

Three-dimensional experiments and individual based simulations show that cell proliferation drives melanoma nest formation in human skin tissue

BackgroundMelanoma can be diagnosed by identifying nests of cells on the skin surface. Understanding the processes that drive nest formation is important as these processes could be potential targets for new cancer drugs. Cell proliferation and cell migration are two potential mechanisms that could conceivably drive melanoma nest formation. However, it is unclear which one of these two putative mechanisms plays a dominant role in driving nest formation.\n\nResultsWe use a suite of three-dimensional (3D) experiments in human skin tissue and a parallel series of 3D individual-based simulations to explore whether cell migration or cell proliferation plays a dominant role in nest formation. In the experiments we measure nest formation in populations of irradiated (non-proliferative) and non-irradiated (proliferative) melanoma cells, cultured together with primary keratinocyte and fibroblast cells on a 3D experimental human skin model. Results show that nest size depends on initial cell number and is driven primarily by cell proliferation rather than cell migration.\n\nConclusionsWe find that nest size depends on initial cell number, and is driven primarily by cell proliferation rather than cell migration. All experimental results are consistent with simulation data from a 3D individual based model (IBM) of cell migration and cell proliferation.

cell biology↗

bioRxiv2017

Mathematical models for cell migration with real-time cell cycle dynamics

Fluorescent ubiquitination-based cell cycle indicator, also known as FUCCI, allows the visualisation of the G1 and S/G2/M cell cycle phases of individual cells. FUCCI consists of two fluorescent probes, so that cells in the G1 phase fluoresce red and cells in the S/G2/M phase fluoresce green. FUCCI reveals real-time information about cell cycle dynamics of individual cells, and can be used to explore how the cell cycle relates to the location of individual cells, local cell density, and different cellular microenvironments. In particular, FUCCI is used in experimental studies examining cell migration, such as malignant invasion and wound healing. Here we present new mathematical models which can describe cell migration and cell cycle dynamics as indicated by FUCCI. The fundamental model describes the two cell cycle phases, G1 and S/G2/M, which FUCCI directly labels. The extended model includes a third phase, early S, which FUCCI indirectly labels. We present experimental data from scratch assays using FUCCI-transduced melanoma cells, and show that the predictions of spatial and temporal patterns of cell density in the experiments can be described by the fundamental model. We obtain numerical solutions of both the fundamental and extended models, which can take the form of travelling waves. These solutions are mathematically interesting because they are a combination of moving wavefronts and moving pulses. We derive and confirm a simple analytical expression for the minimum wave speed, as well as exploring how the wave speed depends on the spatial decay rate of the initial condition.

cell biology↗

bioRxiv2017

Extended logistic growth model for heterogeneous populations

Cell proliferation is the most important cellular-level mechanism responsible for regulating cell population dynamics in living tissues. Modern experimental procedures show that the proliferation rates of individual cells can vary significantly within the same cell line. However, in the mathematical biology literature, cell proliferation is typically modelled using a classical logistic equation which neglects variations in the proliferation rate. In this work, we consider a discrete mathematical model of cell migration and cell proliferation, modulated by volume exclusion (crowding) effects, with variable rates of proliferation across the total population. We refer to this variability as heterogeneity. Constructing the continuum limit of the discrete model leads to a generalisation of the classical logistic growth model. Comparing numerical solutions of the model to averaged data from discrete simulations shows that the new model captures the key features of the discrete process. Applying the extended logistic model to simulate a proliferation assay using rates from recent experimental literature shows that neglecting the role of heterogeneity can, at times, lead to misleading results.

cell biology↗

bioRxiv2017

Discrete and continuum approximations for collective cell migration in a scratch assay with cell size dynamics

Scratch assays are routinely used to study the collective spreading of cell populations. In general, the rate at which a population of cells spreads is driven by the combined effects of cell migration and proliferation. To examine the effects of cell migration separately from the effects of cell proliferation, scratch assays are often performed after treating the cells with a drug that inhibits proliferation. Mitomycin-C is a drug that is commonly used to suppress cell proliferation in this context. However, in addition to suppressing cell proliferation, Mitomycin-C also causes cells to change size during the experiment, as each cell in the population approximately doubles in size as a result of treatment. Therefore, to describe a scratch assay that incorporates the effects of cell-to-cell crowding, cell-to-cell adhesion, and dynamic changes in cell size, we present a new stochastic model that incorporates these mechanisms. Our agent-based stochastic model takes the form of a system of Langevin equations that is the system of stochastic differential equations governing the evolution of the population of agents. We incorporate a time-dependent interaction force that is used to mimic the dynamic increase in size of the agents. To provide a mathematical description of the average behaviour of the stochastic model we present continuum limit descriptions using both a standard mean-field approximation, and a more sophisticated moment dynamics approximation that accounts for the density of agents and density of pairs of agents in the stochastic model. Comparing the accuracy of the two continuum descriptions for a typical scratch assay geometry shows that the incorporation of agent growth in the system is associated with a decrease in accuracy of the standard mean-field description. In contrast, the moment dynamics description provides a more accurate prediction of the evolution of the scratch assay when the increase in size of individual agents is included in the model.

biophysics↗

bioRxiv2017

HIVs Feedback Circuit Breaks The Fundamental Limit On Noise Suppression To Stabilize Fate

Diverse biological systems utilize gene-expression fluctuations ( noise) to drive lineage-commitment decisions1-5. However, once a commitment is made, noise becomes detrimental to reliable function6,7 and the mechanisms enabling post-commitment noise suppression are unclear. We used time-lapse imaging and mathematical modeling, and found that, after a noise-driven event, human immunodeficiency virus (HIV) strongly attenuated expression noise through a non-transcriptional negative-feedback circuit. Feedback is established by serial generation of RNAs from post-transcriptional splicing, creating a precursor-product relationship where proteins generated from spliced mRNAs auto-deplete their own precursor un-spliced mRNAs. Strikingly, precursor auto-depletion overcomes the theoretical limits on conventional noise suppression--minimizing noise far better than transcriptional auto-repression--and dramatically stabilizes commitment to the active-replication state. This auto-depletion feedback motif may efficiently suppress noise in other systems ranging from detained introns to non-sense mediated decay.

cell biology↗