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The objective of this study is to evaluate the role of cooperativity, captured by the Hill coefficient, in a minimal mathematical model describing the interactions between p53 and miR-34a. The model equations are analyzed for negative, none and normal cooperativity using a specific version of bifurcation theory and they are solved numerically. Special attention is paid to the sign of so-called first Lyapunov value. Interpretations of the results are given, both according to dynamic theory and in biological terms. In terms of cell signaling, we propose the hypothesis that when the outgoing signal of a system spends a physiologically significant amount of time outside of its equilibrium state, then the value of that signal can be sampled at any point along the trajectory towards that equilibrium and indeed, at multiple points. Coupled with non-linear behavior, such as that caused by cooperativity, this feature can account for a complex and varied response, which p53 is known for. From dynamical point of view, we found that when cooperativity is negative, the system has only one stable equilibrium point. In the absence of cooperativity, there is a single unstable equilibrium point with a critical boundary of stability. In the case with normal cooperativity, the system can have one, two, or three steady states with both, bi-stability and bi-instability occurring.
This article was published in the following journal.
Name: Journal of theoretical biology
We attempted to create a mathematical model for neuronal differentiation. The present study was performed within the framework of self-organization with constraints by looking for an optimized informa...
Human glucokinase (GCK) is the prototypic example of an emerging class of proteins with allosteric-like behavior that originates from intrinsic polypeptide dynamics. High-resolution NMR investigations...
The attractive tail of the intermolecular interaction affects very weakly the structural properties of liquids, while it affects dramatically their dynamical ones. Via the numerical simulations of mod...
C-H∙∙∙π and N-H∙∙∙π interactions can have an important contribution for protein stability. However, direct measurements of these interactions in proteins are rarely reported. In this wor...
A huge variety of mathematical models have been used to investigate collective cell migration. The aim of this brief review is twofold: to present a number of modelling approaches that incorporate the...
The purpose of this study is to establish an ultrasound mathematical model using acoustic radiation force impulse (ARFI) and contrast-enhanced ultrasonography (CEUS) for diagnosing the sta...
This research study is studying a new schedule of radiation therapy for recurrent glioblastoma as a possible treatment for this diagnosis. This radiation schedule is based on a new model f...
The adoption of bolus calculators has been limited by the slow speed of the current trial and error approach. The goal of this project is to automate the determination of patient specific ...
This is a feasibility study evaluating the use of a mathematical model to predict response to standard neoadjuvant anthracycline / taxane based chemotherapy in patients with breast cancer.
This study evaluates the diagnostic efficiency of an automated method of noninvasive assessment of the fractional reserve of coronary blood flow. Fractional flow reserve is estimated with...
Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.
Computer-assisted interpretation and analysis of various mathematical functions related to a particular problem.
Theoretical models simulating behavior or activities in nursing, including nursing care, management and economics, theory, assessment, research, and education. Some examples of these models include Orem Self-Care Model, Roy Adaptation Model, and Rogers Life Process Model.
Biological systems as affected by time. Aging, biological rhythms, and cyclic phenomena are included. Statistical, computer-aided mathematical procedures are used to describe, in mathematical terminology, various biological functions over time.
A principle of estimation in which the estimates of a set of parameters in a statistical model are those quantities minimizing the sum of squared differences between the observed values of a dependent variable and the values predicted by the model.
Biological therapy involves the use of living organisms, substances derived from living organisms, or laboratory-produced versions of such substances to treat disease. Some biological therapies for cancer use vaccines or bacteria to stimulate the body&rs...