Theoretical Biology and Medical Modelling 

About: Theoretical Biology and Medical Modelling is an academic journal. The journal publishes majorly in the area(s): Population & Cancer. It has an ISSN identifier of 1742-4682. Over the lifetime, 638 publications have been published receiving 14871 citations.

Cosinor-based rhythmometry

Abstract: A brief overview is provided of cosinor-based techniques for the analysis of time series in chronobiology. Conceived as a regression problem, the method is applicable to non-equidistant data, a major advantage. Another dividend is the feasibility of deriving confidence intervals for parameters of rhythmic components of known periods, readily drawn from the least squares procedure, stressing the importance of prior (external) information. Originally developed for the analysis of short and sparse data series, the extended cosinor has been further developed for the analysis of long time series, focusing both on rhythm detection and parameter estimation. Attention is given to the assumptions underlying the use of the cosinor and ways to determine whether they are satisfied. In particular, ways of dealing with non-stationary data are presented. Examples illustrate the use of the different cosinor-based methods, extending their application from the study of circadian rhythms to the mapping of broad time structures (chronomes).

A method for the generation of standardized qualitative dynamical systems of regulatory networks

Abstract: Modeling of molecular networks is necessary to understand their dynamical properties. While a wealth of information on molecular connectivity is available, there are still relatively few data regarding the precise stoichiometry and kinetics of the biochemical reactions underlying most molecular networks. This imbalance has limited the development of dynamical models of biological networks to a small number of well-characterized systems. To overcome this problem, we wanted to develop a methodology that would systematically create dynamical models of regulatory networks where the flow of information is known but the biochemical reactions are not. There are already diverse methodologies for modeling regulatory networks, but we aimed to create a method that could be completely standardized, i.e. independent of the network under study, so as to use it systematically. We developed a set of equations that can be used to translate the graph of any regulatory network into a continuous dynamical system. Furthermore, it is also possible to locate its stable steady states. The method is based on the construction of two dynamical systems for a given network, one discrete and one continuous. The stable steady states of the discrete system can be found analytically, so they are used to locate the stable steady states of the continuous system numerically. To provide an example of the applicability of the method, we used it to model the regulatory network controlling T helper cell differentiation. The proposed equations have a form that permit any regulatory network to be translated into a continuous dynamical system, and also find its steady stable states. We showed that by applying the method to the T helper regulatory network it is possible to find its known states of activation, which correspond the molecular profiles observed in the precursor and effector cell types.

Bringing metabolic networks to life: convenience rate law and thermodynamic constraints.

Abstract: Translating a known metabolic network into a dynamic model requires rate laws for all chemical reactions The mathematical expressions depend on the underlying enzymatic mechanism; they can become quite involved and may contain a large number of parameters Rate laws and enzyme parameters are still unknown for most enzymes We introduce a simple and general rate law called "convenience kinetics" It can be derived from a simple random-order enzyme mechanism Thermodynamic laws can impose dependencies on the kinetic parameters Hence, to facilitate model fitting and parameter optimisation for large networks, we introduce thermodynamically independent system parameters: their values can be varied independently, without violating thermodynamical constraints We achieve this by expressing the equilibrium constants either by Gibbs free energies of formation or by a set of independent equilibrium constants The remaining system parameters are mean turnover rates, generalised Michaelis-Menten constants, and constants for inhibition and activation All parameters correspond to molecular energies, for instance, binding energies between reactants and enzyme Convenience kinetics can be used to translate a biochemical network – manually or automatically - into a dynamical model with plausible biological properties It implements enzyme saturation and regulation by activators and inhibitors, covers all possible reaction stoichiometries, and can be specified by a small number of parameters Its mathematical form makes it especially suitable for parameter estimation and optimisation Parameter estimates can be easily computed from a least-squares fit to Michaelis-Menten values, turnover rates, equilibrium constants, and other quantities that are routinely measured in enzyme assays and stored in kinetic databases

A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies.

Abstract: Radiotherapy outcomes are usually predicted using the Linear Quadratic model. However, this model does not integrate complex features of tumor growth, in particular cell cycle regulation. In this paper, we propose a multiscale model of cancer growth based on the genetic and molecular features of the evolution of colorectal cancer. The model includes key genes, cellular kinetics, tissue dynamics, macroscopic tumor evolution and radiosensitivity dependence on the cell cycle phase. We investigate the role of gene-dependent cell cycle regulation in the response of tumors to therapeutic irradiation protocols. Simulation results emphasize the importance of tumor tissue features and the need to consider regulating factors such as hypoxia, as well as tumor geometry and tissue dynamics, in predicting and improving radiotherapeutic efficacy. This model provides insight into the coupling of complex biological processes, which leads to a better understanding of oncogenesis. This will hopefully lead to improved irradiation therapy.

Pros and cons of estimating the reproduction number from early epidemic growth rate of influenza A (H1N1) 2009

Abstract: In many parts of the world, the exponential growth rate of infections during the initial epidemic phase has been used to make statistical inferences on the reproduction number, R, a summary measure of the transmission potential for the novel influenza A (H1N1) 2009. The growth rate at the initial stage of the epidemic in Japan led to estimates for R in the range 2.0 to 2.6, capturing the intensity of the initial outbreak among school-age children in May 2009. An updated estimate of R that takes into account the epidemic data from 29 May to 14 July is provided. An age-structured renewal process is employed to capture the age-dependent transmission dynamics, jointly estimating the reproduction number, the age-dependent susceptibility and the relative contribution of imported cases to secondary transmission. Pitfalls in estimating epidemic growth rates are identified and used for scrutinizing and re-assessing the results of our earlier estimate of R. Maximum likelihood estimates of R using the data from 29 May to 14 July ranged from 1.21 to 1.35. The next-generation matrix, based on our age-structured model, predicts that only 17.5% of the population will experience infection by the end of the first pandemic wave. Our earlier estimate of R did not fully capture the population-wide epidemic in quantifying the next-generation matrix from the estimated growth rate during the initial stage of the pandemic in Japan. In order to quantify R from the growth rate of cases, it is essential that the selected model captures the underlying transmission dynamics embedded in the data. Exploring additional epidemiological information will be useful for assessing the temporal dynamics. Although the simple concept of R is more easily grasped by the general public than that of the next-generation matrix, the matrix incorporating detailed information (e.g., age-specificity) is essential for reducing the levels of uncertainty in predictions and for assisting public health policymaking. Model-based prediction and policymaking are best described by sharing fundamental notions of heterogeneous risks of infection and death with non-experts to avoid potential confusion and/or possible misuse of modelling results.