Calibration of dynamic models of biological systems with KInfer

Biochemical Systems Theory: A Review

Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. This paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. The paper is intended as a guide for investigators entering the fascinating field of biological systems analysis and as a resource for practitioners and experts.

Modelling non-homogeneous stochastic reaction-diffusion systems: the case study of gemcitabine-treated non-small cell lung cancer growth

Background

Reaction-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.

Methods

We 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.

Results

Using 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 patterns follow the growth curves observed in patients.

Conclusions

s This model is able to reproduce the observed increment/decrement of tumor size in response to the pharmacological treatment with gemcitabine. The formal specification of the model in Redi can be easily extended in an incremental way to include other relevant biophysical processes, such as local extracellular matrix remodelling, active cell migration and traction, and reshaping of host tissue vasculature, in order to be even more relevant to support the experimental investigation of cancer.

Inferring biochemical reaction pathways: the case of the gemcitabine pharmacokinetics

BACKGROUND

The 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.

RESULTS

The 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.

CONCLUSIONS

Time-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.

A Bayesian framework for parameter estimation in dynamical models

Mathematical models in biology are powerful tools for the study and exploration of complex dynamics. Nevertheless, bringing theoretical results to an agreement with experimental observations involves acknowledging a great deal of uncertainty intrinsic to our theoretical representation of a real system. Proper handling of such uncertainties is key to the successful usage of models to predict experimental or field observations. This problem has been addressed over the years by many tools for model calibration and parameter estimation. In this article we present a general framework for uncertainty analysis and parameter estimation that is designed to handle uncertainties associated with the modeling of dynamic biological systems while remaining agnostic as to the type of model used. We apply the framework to fit an SIR-like influenza transmission model to 7 years of incidence data in three European countries: Belgium, the Netherlands and Portugal.

Network inference from time-dependent Omics data

We provide a commented overview of the available databases for the systematic collection of pathway information and biological models essential for the interpretation of Omics data. Then, we present both the state of the art and the future challenges of network inference, a research area dealing with the deduction of reaction mechanisms from experimental Omics data. This approach represents one of the most challenging instances for making use of the huge amount of information gathered in the Omics era.

Elucidation of functional consequences of signalling pathway interactions

BACKGROUND

A great deal of data has accumulated on signalling pathways. These large datasets are thought to contain much implicit information on their molecular structure, interaction and activity information, which provides a picture of intricate molecular networks believed to underlie biological functions. While tremendous advances have been made in trying to understand these systems, how information is transmitted within them is still poorly understood. This ever growing amount of data demands we adopt powerful computational techniques that will play a pivotal role in the conversion of mined data to knowledge, and in elucidating the topological and functional properties of protein - protein interactions.

RESULTS

A computational framework is presented which allows for the description of embedded networks, and identification of common shared components thought to assist in the transmission of information within the systems studied. By employing the graph theories of network biology - such as degree distribution, clustering coefficient, vertex betweenness and shortest path measures - topological features of protein-protein interactions for published datasets of the p53, nuclear factor kappa B (NF-kappaB) and G1/S phase of the cell cycle systems were ascertained. Highly ranked nodes which in some cases were identified as connecting proteins most likely responsible for propagation of transduction signals across the networks were determined. The functional consequences of these nodes in the context of their network environment were also determined. These findings highlight the usefulness of the framework in identifying possible combination or links as targets for therapeutic responses; and put forward the idea of using retrieved knowledge on the shared components in constructing better organised and structured models of signalling networks.

CONCLUSION

It is hoped that through the data mined reconstructed signal transduction networks, well developed models of the published data can be built which in the end would guide the prediction of new targets based on the pathway's environment for further analysis. Source code is available upon request.