Along the lines developed by Celada and Seiden, for simulating an immune system by means of cellular automata, we have constructed a 'thymus' where T cells undergo positive and negative selection. The populations thus 'matured' have been analyzed and their performance has been tested in machina. The key feature of this thymus is to allow chance meeting and possible interaction between newly born T cells and antigen presenting cells. The latter represent both the epithelial and the dendritic cells of the biological organ and are equipped with MHC molecules that can accommodate selected self peptides. All possible specificities are represented among the virgin T cells entering the thymus, but this diversity is drastically reduced by the time they exit as mature elements. In the model organ the fate of T cells, i.e. whether they will undergo proliferation or apoptosis, is governed by their capacity to recognize MHCs and the affinity of this interaction. Crucial parameters turn out to be the concentration of presenting cells, the number of types of MHC per cell, the 'size of self' in terms of the number of different peptides and their prevalence. According to the results, events in the automaton can realize unforeseen cooperations and competitions among receptors, depending upon the interaction order and frequency, and ultimately determine the rescue or the killing of thymocytes. Thus the making of the mature T repertoire has a random component and cannot be completely predicted.
Gemcitabine (2,2-difluorodeoxycytidine, dFdC) is a prodrug widely used for treating various carcinomas. Gemcitabine exerts its clinical effect by depleting the deoxyribonucleotide pools, and incorporating its triphosphate metabolite (dFdC-TP) into DNA, thereby inhibiting DNA synthesis. This process blocks the cell cycle in the early S phase, eventually resulting in apoptosis. The incorporation of gemcitabine into DNA takes place in competition with the natural nucleoside dCTP. The mechanisms of indirect competition between these cascades for common resources are given with the race for DNA incorporation; in clinical studies dedicated to singling out mechanisms of resistance, ribonucleotide reductase (RR) and deoxycytidine kinase (dCK) and human equilibrative nucleoside transporter1 (hENT1) have been associated to efficacy of gemcitabine with respect to their roles in the synthesis cascades of dFdC-TP and dCTP. However, the direct competition, which manifests itself in terms of inhibitions between these cascades, remains to be quantified. We propose an algorithmic model of gemcitabine mechanism of action, verified with respect to independent experimental data. We performed in silico experiments in different virtual conditions, otherwise difficult in vivo, to evaluate the contribution of the inhibitory mechanisms to gemcitabine efficacy. In agreement with the experimental data, our model indicates that the inhibitions due to the association of dCTP with dCK and the association of gemcitabine diphosphate metabolite (dFdC-DP) with RR play a key role in adjusting the efficacy. While the former tunes the catalysis of the rate-limiting first phosphorylation of dFdC, the latter is responsible for depletion of dCTP pools, thereby contributing to gemcitabine efficacy with a dependency on nucleoside transport efficiency. Our simulations predict the existence of a continuum of non-efficacy to high-efficacy regimes, where the levels of dFdC-TP and dCTP are coupled in a complementary manner, which can explain the resistance to this drug in some patients.
BackgroundThe representation of a biochemical system as a network is the precursor of any mathematical model of the processes driving the dynamics of that system. Pharmacokinetics uses mathematical models to describe the interactions between drug, and drug metabolites and targets and through the simulation of these models predicts drug levels and/or dynamic behaviors of drug entities in the body. Therefore, the development of computational techniques for inferring the interaction network of the drug entities and its kinetic parameters from observational data is raising great interest in the scientific community of pharmacologists. In fact, the network inference is a set of mathematical procedures deducing the structure of a model from the experimental data associated to the nodes of the network of interactions. In this paper, we deal with the inference of a pharmacokinetic network from the concentrations of the drug and its metabolites observed at discrete time points.ResultsThe method of network inference presented in this paper is inspired by the theory of time-lagged correlation inference with regard to the deduction of the interaction network, and on a maximum likelihood approach with regard to the estimation of the kinetic parameters of the network. Both network inference and parameter estimation have been designed specifically to identify systems of biotransformations, at the biochemical level, from noisy time-resolved experimental data. We use our inference method to deduce the metabolic pathway of the gemcitabine. The inputs to our inference algorithm are the experimental time series of the concentration of gemcitabine and its metabolites. The output is the set of reactions of the metabolic network of the gemcitabine.ConclusionsTime-lagged correlation based inference pairs up to a probabilistic model of parameter inference from metabolites time series allows the identification of the microscopic pharmacokinetics and pharmacodynamics of a drug with a minimal a priori knowledge. In fact, the inference model presented in this paper is completely unsupervised. It takes as input the time series of the concetrations of the parent drug and its metabolites. The method, applied to the case study of the gemcitabine pharmacokinetics, shows good accuracy and sensitivity.
BackgroundReaction-diffusion based models have been widely used in the literature for modeling the growth of solid tumors. Many of the current models treat both diffusion/consumption of nutrients and cell proliferation. The majority of these models use classical transport/mass conservation equations for describing the distribution of molecular species in tumor spheroids, and the Fick's law for describing the flux of uncharged molecules (i.e oxygen, glucose). Commonly, the equations for the cell movement and proliferation are first order differential equations describing the rate of change of the velocity of the cells with respect to the spatial coordinates as a function of the nutrient's gradient. Several modifications of these equations have been developed in the last decade to explicitly indicate that the tumor includes cells, interstitial fluids and extracellular matrix: these variants provided a model of tumor as a multiphase material with these as the different phases. Most of the current reaction-diffusion tumor models are deterministic and do not model the diffusion as a local state-dependent process in a non-homogeneous medium at the micro- and meso-scale of the intra- and inter-cellular processes, respectively. Furthermore, a stochastic reaction-diffusion model in which diffusive transport of the molecular species of nutrients and chemotherapy drugs as well as the interactions of the tumor cells with these species is a novel approach. The application of this approach to he scase of non-small cell lung cancer treated with gemcitabine is also novel.MethodsWe present a stochastic reaction-diffusion model of non-small cell lung cancer growth in the specification formalism of the tool Redi, we recently developed for simulating reaction-diffusion systems. We also describe how a spatial gradient of nutrients and oncological drugs affects the tumor progression. Our model is based on a generalization of the Fick's first diffusion law that allows to model diffusive transport in non-homogeneous media. The diffusion coefficient is explicitly expressed as a function depending on the local conditions of the medium, such as the concentration of molecular species, the viscosity of the medium and the temperature. We incorporated this generalized law in a reaction-based stochastic simulation framework implementing an efficient version of Gillespie algorithm for modeling the dynamics of the interactions between tumor cell, nutrients and gemcitabine in a spatial domain expressing a nutrient and drug concentration gradient.ResultsUsing the mathematical framework of model we simulated the spatial growth of a 2D spheroidal tumor model in response to a treatment with gemcitabine and a dynamic gradient of oxygen and glucose. The parameters of the model have been taken from recet literature and also inferred from real tumor shrinkage curves measured in patients suffering from non-small cell lung cancer. The simulations qualitatively reproduce the time evolution of the morphologies of these tumors as well as the morphological patt...
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