Biology subjects

Fadai, N. T.

Publications and source records attributed to Fadai, N. T..

8 recordsLinked to original sources

bioRxiv2024

Understanding the regulation of chronic wounds by tissue inhibitors of matrix metalloproteinases through mathematical modelling

Understanding the biochemistry and pharmacodynamics of chronic wounds is of key importance, due to the millions of people in the UK affected and the significant cost to the NHS. Chronic wounds are characterised by elevated concentrations of matrix metalloproteinases (MMPs) that destroy the surrounding extracellular matrix (ECM). However, fibroblasts can produce tissue inhibitors of MMPs (TIMPs) in order to regulate wound healing. Therefore, the role of TIMPs in both acute and chronic wounds needs to be properly understood in order to develop therapeutic treatments. In this work, we propose a reaction-diffusion system of four partial differential equations that describe the interaction of the ECM, fibroblasts, MMPs, and TIMPs in a wound. We observe that, subject to biologically realistic parameter values, this mathematical model gives rise to travelling wave solutions. Using bifurcation analysis, we demonstrate that deregulated apoptosis in the ECM results in the emergence of chronic wounds, and the reversal of these chronic wounds is prohibited for lower TIMP production values. These results are replicated within a simplified model obtained via a parameter sensitivity analysis. This model is further extended to more realistic spatial domains where we demonstrate the effectiveness of a therapeutic hydrogel containing TIMPs as a treatment for chronic wounds.

cell biology↗

bioRxiv2024

A Rose by any Other Name: Towards a quantitative theory of neuroimmune interactions

Humanity has known about - and been fascinated by - the connection between mind and body since time immemorial, yet we have only been able to begin to quantitatively explore their interactions in recent years. Even so, the field of neuroimmunology is categorically in its infancy. Despite myriad and diverse experimental reports, no coherent theoretical approach to the neuroimmune system has been even attempted, which makes it difficult to make sense of the emerging body of empirical findings. Here, we take the first steps towards this goal by introducing a mathematical framework that describes the triggering and control of neurological memories (engrams) of immune challenges. Using peanut allergies as a model system, we show how a simple differential equation model of coupled immune-engram responses can explain a number of key observations regarding putative neurological control of focal inflammatory responses and failures thereof. Simulations of our model identify four areas of the parameter regime corresponding to distinct consequences of fake immune stimulation: a) resolution b) finite oscillations of inflammation, followed by resolution c) sustained, self-amplifying oscillations (cytokine storm-like phenomena) and d) resolution followed by the permanent establishment of a chronic higher-baseline inflammatory state. Importantly, we then show how our model recapitulates the key qualitative features of a recent experimental description of immune engram encoding and re-activation (respectively, suppression) in a mouse model of colitis. We conclude with remarks around clinical implications as well as directions for future work in theoretical neuroimmunology. O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=89 SRC="FIGDIR/small/605114v3_ufig1.gif" ALT="Figure 1"> View larger version (18K): org.highwire.dtl.DTLVardef@89ea55org.highwire.dtl.DTLVardef@778323org.highwire.dtl.DTLVardef@428edforg.highwire.dtl.DTLVardef@1b1deea_HPS_FORMAT_FIGEXP M_FIG C_FIG

immunology↗

bioRxiv2023

Modelling the effect of matrix metalloproteinases in dermal wound healing

With over 2 million people in the UK suffering from chronic wounds, understanding the biochemistry and pharmacology that underpins these wounds and wound healing is of high importance. Chronic wounds are characterised by high levels of matrix metalloproteinases (MMPs), which are necessary for the modification of healthy tissue in the healing process. Overexposure of MMPs, however, adversely affects healing of the wound by causing further destruction of the surrounding extracellular matrix. In this work, we propose a mathematical model that focuses on the interaction of MMPs with dermal cells using a system of partial differential equations. Using biologically realistic parameter values, this model gives rise to travelling waves corresponding to a front of healthy cells invading a wound. From the arising travelling wave analysis, we observe that deregulated apoptosis results in the emergence of chronic wounds, characterised by elevated MMP concentrations. We also observe hysteresis effects when both the apoptotic rate and MMP production rate are varied, providing further insight into the management (and potential reversal) of chronic wounds.

biophysics↗

bioRxiv2022

Pattern formation and travelling waves in a multiphase moving boundary model of tumour growth

We analyse a multiphase, moving boundary model that describes solid tumour growth. We consider the evolution of a motile, viscous cell phase and an inviscid extracellular liquid phase. The model comprises two partial differential equations that govern the cell volume fraction and the cell velocity, together with a moving boundary condition for the tumour edge. Numerical simulations of the model indicate that patterned solutions can be obtained, which correspond to multiple regions of high cell density separated by regions of low cell density. In other parameter regimes, solutions of the model can develop into a forward- or backward-moving travelling wave, corresponding to tumour growth or extinction, respectively. A travelling-wave analysis allows us to find the corresponding wave speed, as well as criteria for the growth or extinction of the tumour. Furthermore, a stability analysis of these travelling-wave solutions provides us with criteria for the occurrence of patterned solutions. Finally, we discuss how the initial cell distribution, as well as parameters related to cellular motion and cell-liquid drag, control the qualitative features of patterned solutions.

cell biology↗

bioRxiv2021

Travelling wave and asymptotic analysis of a multiphase moving boundary model for engineered tissue growth

We derive a multiphase, moving boundary model to represent the development of tissue in vitro in a porous tissue engineering scaffold. We consider a cell, extra-cellular liquid and a rigid scaffold phase, and adopt Darcys law to relate the velocity of the cell and liquid phases to their respective pressures. Cell-cell and cell-scaffold interactions which can drive cellular motion are accounted for by utilising relevant constitutive assumptions for the pressure in the cell phase. We reduce the model to a nonlinear reaction-diffusion equation for the cell phase, coupled to a moving boundary condition for the tissue edge, the diffusivity being dependent on the cell and scaffold volume fractions, cell and liquid viscosities, and parameters that relate to cellular motion. Numerical simulations reveal that the reduced model admits three regimes for the evolution of the tissue edge at large-time: linear, logarithmic and stationary. Employing travelling wave and asymptotic analysis, we characterise these regimes in terms of parameters related to cellular production and motion. The results of our investigation allow us to suggest optimal values for the governing parameters, so as to stimulate tissue growth in an engineering scaffold.

cell biology↗

bioRxiv2020

Population dynamics with threshold effects give rise to a diverse family of Allee effects

The Allee effect describes populations that deviate from logistic growth models and arises in applications including ecology and cell biology. A common justification for incorporating Allee effects into population models is that the population in question has altered growth mechanisms at some critical density, often referred to as a threshold effect. Despite the ubiquitous nature of threshold effects arising in various biological applications, the explicit link between local threshold effects and global Allee effects has not been considered. In this work, we examine a continuum population model that incorporates threshold effects in the local growth mechanisms. We show that this model gives rise to a diverse family of Allee effects and we provide a comprehensive analysis of which choices of local growth mechanisms give rise to specific Allee effects. Calibrating this model to a recent set of experimental data describing the growth of a population of cancer cells provides an interpretation of the threshold population density and growth mechanisms associated with the population.

biophysics↗

bioRxiv2019

Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics

We present a solid theoretical foundation for interpreting the origin of Allee effects by providing the missing link in understanding how local individual-based mechanisms translate to global population dynamics. Allee effects were originally proposed to describe population dynamics that cannot be explained by exponential and logistic growth models. However, standard methods often calibrate Allee effect models to match observed global population dynamics without providing any mechanistic insight. By introducing a stochastic individual-based model, with proliferation, death, and motility rates that depend on local density, we present a modelling framework that translates particular global Allee effects to specific individual-based mechanisms. Using data from ecology and cell biology, we unpack individual-level mechanisms implicit in an Allee effect model and provide simulation tools for others to repeat this analysis.

biophysics↗

bioRxiv2019

Accurate and efficient discretisations for stochastic models of cell migration and cell proliferation with crowding

Understanding how cells proliferate, migrate, and die in various environments is essential in determining how organisms develop and repair themselves. Continuum mathematical models, such as the logistic equation and the Fisher-Kolmogorov equation, can describe the global characteristics observed in commonly-used cell biology assays, such as proliferation and scratch assays. However, these continuum models do not account for single-cell-level mechanics observed in high-throughput experiments. Mathematical modelling frameworks that represent individual cells, often called agent-based models, can successfully describe key single-cell-level features of these assays, but are computationally infeasible when dealing with large populations. In this work, we propose an agent-based model with crowding effects that is computationally efficient and matches the logistic and Fisher-Kolmogorov equations in parameter regimes relevant to proliferation and scratch assays, respectively. This stochastic agent-based model allows multiple agents to be contained within compartments on an underlying lattice, thereby reducing the computational storage compared to existing agent-based models that allow one agent per site only. We propose a systematic method to determine a suitable compartment size. Implementing this compartment-based model with this compartment size provides a balance between computational storage, local resolution of agent behaviour, and agreement with classical continuum descriptions.

biophysics↗