Model reduction and process analysis of biological models

International audienceUnderstanding the dynamical behavior of biological networks is complicated due to their large number of components and interactions. We present a method to analyse key processes for the system behavior, based on the a priori knowledge of the system trajectory and the simplification of mathematical models of these networks. The method consists of the model decomposition into biologically meaningful processes, whose activity or inactivity is evaluated during the time evolution of the system. The structure of the model is reduced to the core mechanisms involving active processes only. We assess the quality of the reduction by means of global relative errors and apply our method to two models of the circadian rhythm in Drosophila and the influence of RKIP on the ERK signaling pathway

A stochastic model of corneal epithelium maintenance and recovery following perturbation

Various biological studies suggest that the corneal epithelium is maintained by active stem cells located in the limbus, the so-called limbal epithelial stem cell hypothesis. While numerous mathematical models have been developed to describe corneal epithelium wound healing, only a few have explored the process of corneal epithelium homeostasis. In this paper we present a purposefully simple stochastic mathematical model based on a chemical master equation approach, with the aim of clarifying the main factors involved in the maintenance process. Model analysis provides a set of constraints on the numbers of stem cells, division rates, and the number of division cycles required to maintain a healthy corneal epithelium. In addition, our stochastic analysis reveals noise reduction as the epithelium approaches its homeostatic state, indicating robustness to noise. Finally, recovery is analysed in the context of perturbation scenarios

Process Control of Activated Sludge Treatment

General feed forward controllers, conforming to standard control modes, have been derived for an activated sludge process. The analysis indicated that the appropriate controllers are proportional control with measurement of substrate flow rate, and derivative control with measurement of inlet substrate concentration, and manipulation of the rate of return sludge by both controllers. The performance of these controllers was tested by computer simulation of five dynamic aerator models with and without sludge storage, and with two settling basin models. In all cases significant reduction of the maximum exit substrate concentration was achieved. Additional improvement resulted from the use of sludge storage. As the aerator model became more linear the control results also improved. The first dynamic results were obtained using a perfect steady state settler model, the remainder assumed that the settler dynamics could be represented by a variable time delay. The addition of the settler dynamics caused the control to degrade somewhat. Finally the generality of the two controllers was proved mathematically for the five biological kinetic models for substrate utilization and bacterial growth

Flux Analysis in Process Models via Causality

We present an approach for flux analysis in process algebra models of biological systems. We perceive flux as the flow of resources in stochastic simulations. We resort to an established correspondence between event structures, a broadly recognised model of concurrency, and state transitions of process models, seen as Petri nets. We show that we can this way extract the causal resource dependencies in simulations between individual state transitions as partial orders of events. We propose transformations on the partial orders that provide means for further analysis, and introduce a software tool, which implements these ideas. By means of an example of a published model of the Rho GTP-binding proteins, we argue that this approach can provide the substitute for flux analysis techniques on ordinary differential equation models within the stochastic setting of process algebras

Using Bayesian model selection and calibration to improve the DayCent ecosystem model

2020 Fall.Includes bibliographical references.Process-based biogeochemical models have been developed and used for decades to predict the outcomes of real-world ecological processes. These models are based on a theoretical understanding of relevant ecological processes and approximated using highly complex mathematical equations and hundreds of unknown parameters—requiring calibration using physical observations of the system. These models are then used to test scientific understanding, estimate pools and fluxes, make predictions for future scenarios, and to evaluate management and policy outcomes. To provide a better understanding of the ecological processes, these models need to be simple, make accurate predictions, and account for all sources of uncertainty. The focus of this dissertation is to develop a Bayesian model analysis framework to meet the goal of developing simple and accurate models that fully address uncertainty. This framework includes variance-based global sensitivity analysis (GSA) to identify influential model parameters, a Bayesian calibration method using sampling importance resampling (SIR) to estimate the posterior distribution of unknown model parameters and hyperparameters, and a Monte Carlo analysis to estimate the posterior predictive distribution of model outputs. The framework accounts for all sources of uncertainty, including the remaining uncertainty over the fitted parameters. Additionally, Bayesian model selection is also implemented in the framework to determine the most appropriate level of complexity during model development. The framework is applied to improve the DayCent ecosystem model in agricultural applications. The DayCent model was improved with several model developments, including NH3 volatilization, the release of nitrogen (N) from controlled-release N fertilizers (CRNFs) and the inhibition of the biological process of nitrification and delay the transformation of NH+4 to NO-3 with nitrification inhibitor (NIs). The model development incorporates key 4R management practices that mitigate NH3 and N2O emissions in fertilized upland agricultural soils. In addition, I recalibrated the soil organic matter submodel to improve estimation of soil organic carbon (C) sequestration potentials to a 30 cm depth for several management practices, including organic matter amendment, adoption of no-till management, and addition of synthetic N fertilizers. The results showed that the DayCent model predictions of C sequestration and reduction in N2O flux as well as NH3 volatilization from several management practices were consistent with the field observations. The model result suggested that addition of organic amendments and adoption of no-till are viable management option for C sequestration, however, the addition of synthetic N fertilizer did not produce a significant level of C sequestration. For NH3 volatilization, the model also adequately captures the reduction potential of urease inhibitor along with the incorporation of urea by mechanical means or with immediate irrigation/rainfall. The model also shows promising results in mitigating N2O emissions with both CRNFs and NIs in comparison to field observations. The model prediction focuses on estimating greenhouse gas (GHG) mitigation potential and estimation of uncertainty arising during model prediction—enhancing DayCent as a tool for scientific understanding, regional to global assessments, policy implementation, and carbon emission trading. Overall, the model improvements enhanced the ability of the DayCent model in providing a stronger basis to support policy and management decisions associated with GHG mitigation in agricultural soils

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers