Summary Local cell contraction pulses play important roles in tissue and cell morphogenesis. Here, we improve a chemo-optogenetic approach and apply it to investigate the signal network that generates these pulses. We use these measurements to derive and parameterize a system of ordinary differential equations describing temporal signal network dynamics. Bifurcation analysis and numerical simulations predict a strong dependence of oscillatory system dynamics on the concentration of GEF-H1, an Lbc-type RhoGEF, which mediates the positive feedback amplification of Rho activity. This prediction is confirmed experimentally via optogenetic tuning of the effective GEF-H1 concentration in individual living cells. Numerical simulations show that pulse amplitude is most sensitive to external inputs into the myosin component at low GEF-H1 concentrations and that the spatial pulse width is dependent on GEF-H1 diffusion. Our study offers a theoretical framework to explain the emergence of local cell contraction pulses and their modulation by biochemical and mechanical signals.
The first case of COVID-19 was reported in Kenya in March 2020 and soon after non-pharmaceutical interventions (NPIs) were established to control the spread of the disease. The NPIs consisted, and continue to consist, of mitigation measures followed by a period of relaxation of some of the measures. In this paper, we use a deterministic mathematical model to analyze the dynamics of the disease, during the first wave, and relate it to the intervention measures. In the process, we develop a new method for estimating the disease parameters. Our solutions yield a basic reproduction number, R0 = 2.76, which is consistent with other solutions. The results further show that the initial mitigation reduced disease transmission by 40% while the subsequent relaxation increased transmission by 25%. We also propose a mathematical model on how interventions of known magnitudes collectively affect disease transmission rates. The modelled positivity rate curve compares well with observations. If interventions of unknown magnitudes have occurred, and data is available on the positivity rate, we use the method of planar envelopes around a curve to deduce the modelled positivity rate and the magnitudes of the interventions. Our solutions deduce mitigation and relaxation effects of 42.5% and 26%, respectively; these percentages are close to values obtained by the solution of the SIRD system. Our methods so far apply to a single wave; there is a need to investigate the possibility of extending them to handle multiple waves.
Crime data provides information on the nature and location of the crime but, in general, does not include information on the number of criminals operating in a region. By contrast, many approaches to crime reduction necessarily involve working with criminals or individuals at risk of engaging in criminal activity and so the dynamics of the criminal population is important. With this in mind, we develop a mechanistic, mathematical model which combines the number of crimes and number of criminals to create a dynamical system. Analysis of the model highlights a threshold for criminal efficiency, below which criminal numbers will settle to an equilibrium level that can be exploited to reduce crime through prevention. This efficiency measure arises from the initiation of new criminals in response to observation of criminal activity; other initiation routes -via opportunism or peer pressure -do not exhibit such thresholds although they do impact on the level of criminal activity observed. We used data from Cape Town, South Africa, to obtain parameter estimates and predicted that the number of criminals in the region is tending towards an equilibrium point but in a heterogeneous manner -a drop in the number of criminals from low crime neighbourhoods is being offset by an increase from high crime neighbourhoods.
The process of revitalising quiescent cells in order for them to proliferate plays a pivotal role in the repair of warn out tissues as well as for tissue homeostasis. This process is also crucial in the growth, development and well-being of higher multi-cellular organisms such as mammals. Deregulation of quiescent-proliferation transition is related to many diseases, in particular cancer. Recent studies have revealed that this process is regulated tightly by the Rb−E2F bistable switch mechanism. Based on experimental observations, in this study, we formulate a mathematical model to examine the effect of the growth factor concentration on the proliferation-quiescence transition in human cells. Working with a non-dimensionalised model, we prove positivity, boundedness and uniqueness of solutions. To understand model solution behaviour close to bifurcation points, we carry out bifurcation analysis, which is further verified by use of numerical bifurcation analysis, sensitivity analysis and numerical simulations. Indeed, bifurcation and numerical analysis of the model predicted a transition between stable, bistable and stable states, which are dependent on the growth factor concentration parameter (GF). The derived predictions confirm experimental observations.
<p style='text-indent:20px;'>Recent experimental observations reveal that local cellular contraction pulses emerge via a combination of fast positive and slow negative feedbacks based on a signal network composed of Rho, GEF and Myosin interactions [<xref ref-type="bibr" rid="b22">22</xref>]. As an examplary, we propose to study a plausible, hypothetical temporal model that mirrors general principles of fast positive and slow negative feedback, a hallmark for activator-inhibitor models. The methodology involves (ⅰ) a qualitative analysis to unravel system switching between different states (stable, excitable, oscillatory and bistable) through model parameter variations; (ⅱ) a numerical bifurcation analysis using the positive feedback mediator concentration as a bifurcation parameter, (ⅲ) a sensitivity analysis to quantify the effect of parameter uncertainty on the model output for different dynamic regimes of the model system; and (ⅳ) numerical simulations of the model system for model predictions. Our methodological approach supports the role of mathematical and computational models in unravelling mechanisms for molecular and developmental processes and provides tools for analysis of temporal models of this nature.</p>
The process of revitalising quiescent cells in order for them to proliferate plays a pivotal role in the repair of worn-out tissues as well as for tissue homeostasis. This process is also crucial in the growth, development and well-being of higher multi-cellular organisms such as mammals. Deregulation of proliferation-quiescence transition is related to many diseases, such as cancer. Recent studies have revealed that this proliferation–quiescence process is regulated tightly by the Rb−E2F bistable switch mechanism. Based on experimental observations, in this study, we formulate a mathematical model to examine the effect of the growth factor concentration on the proliferation–quiescence transition in human cells. Working with a non-dimensionalised model, we prove the positivity, boundedness and uniqueness of solutions. To understand model solution behaviour close to bifurcation points, we carry out bifurcation analysis, which is further illustrated by the use of numerical bifurcation analysis, sensitivity analysis and numerical simulations. Indeed, bifurcation and numerical analysis of the model predicted a transition between bistable and stable states, which are dependent on the growth factor concentration parameter (GF). The derived predictions confirm experimental observations .
Dose calculation plays a critical role in radiotherapy (RT) treatment planning, and there is a growing need to develop accurate dose deposition models that incorporate heterogeneous tumour properties. Deterministic models have demonstrated their capability in this regard, making them the focus of recent treatment planning studies as they serve as a basis for simplified models in RT treatment planning. In this study, we present a simplified deterministic model for photon transport based on the Boltzmann transport equation (BTE) as a proof‐of‐concept to illustrate the impact of heterogeneous tumour properties on RT treatment planning. We employ the finite element method (FEM) to simulate the photon flux and dose deposition in real cases of diffuse intrinsic pontine glioma (DIPG) and neuroblastoma (NB) tumours. Importantly, in light of the availability of pipelines capable of extracting tumour properties from magnetic resonance imaging (MRI) data, we highlight the significance of such data. Specifically, we utilise cellularity data extracted from DIPG and NB MRI images to demonstrate the importance of heterogeneity in dose calculation. Our model simplifies the process of simulating a RT treatment system and can serve as a useful starting point for further research. To simulate a full RT treatment system, one would need a comprehensive model that couples the transport of electrons and photons.
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