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Mathematical modeling of signaling pathways and regulatory networks has been supporting experimental research for some time now. Sensitivity analysis, aimed at finding model parameters whose changes yield significantly altered cellular responses, is an important part of modeling work. However, sensitivity methods are often directly transplanted from analysis of technical systems, and thus, they may not serve the purposes of analysis of biological systems. This paper presents a novel sensitivity analysis method that is particularly suited to the task of searching for potential molecular drug targets in signaling pathways. Using two sample models of pathways, p53/Mdm2 regulatory module and IFN-β-induced JAK/STAT signaling pathway, we show that the method leads to biologically relevant conclusions, identifying processes suitable for targeted pharmacological inhibition, represented by the reduction of kinetic parameter values. That, in turn, facilitates subsequent search for active drug components.

The paper is concerned with modeling of tumor growth, taking into account chemo- and radiotherapy and metastasis. The model consists of two compartments, one representing the primary tumor, sensitive to chemo- and radiotherapy and another, representing metastatic tumor. A population of virtual patients is created by sampling model parameters. Kaplan-Meier survival curves are used to analyze the influence of model parameters on treatment efficacy, with one standard treatment protocol.

Virtual environments (VE) are commonly used in learning or training in many different areas. We are focused on the problem when a group of artificial agents are simulated at the same time; their behavior is easily recognized as ‘artificial’. To avoid this undesired property presented work was aimed at creating a virtual world with agents equipped with psychosomatic elements that occur in the real world. It has been chosen the implementation of basic needs based on Maslow's hierarchy of needs (MHN), since they are one of necessary elements for the development of simulation of the real world. It is shown that the VE design based on artificial intelligence (AI) planning algorithms and the theory of MHN can be efficiently applied to generate semi-realistic behavior of agents population. Models of coronavirus spread have been introduced into the simulated environment. It allowed to build cases related to the number of infected people and the rate of infection depending on the level of avatar activity associated with basic needs.

Intracellular processes are cascades of biochemical reactions, triggered in response to various types of stimuli. Mathematical models describing their dynamics have become increasingly popular in recent years, as tools supporting experimental work in analysis of pathways and regulatory networks. Not only do they provide insights into general properties of these systems, but also help in specific tasks, such as search for drug molecular targets or treatment protocols. Different tools and methods are used to model complex biological systems. In this work, we focus on ordinary differential equations (ODEs) and Petri nets. We consider specific methods of analysis of such models, i.e., sensitivity analysis (SA) and significance analysis. So far, they have been applied separately, with different goals. In this paper, we show that they can complement each other, combining the sensitivity of ODE models and the significance analysis of Petri nets. The former is used to find parameters, whose change results in the greatest quantitative and qualitative changes in the model response, while the latter is a structural analysis and allows indicating the most important subprocesses in terms of information flow in Petri net. Ultimately, both methods facilitate finding the essential processes in a given signaling pathway or regulatory network and may be used to support medical therapy development. In the paper, the use of dual modeling is illustrated with an example of ATM/p53/NF-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa$$\end{document}κB pathway. Each method was applied to analyze this system, resulting in finding different subsets of important processes that might be prospective targets for changing this system behavior. While some of the processes were indicated in each of the approaches, others were found by one method only and would be missed if only that method was applied. This leads to the conclusion about the complementarity of the methods under investigation. The dual modeling approach of comprehensive structural and parametric analysis yields results that would not be possible if these two modeling approaches were applied separately. The combined approach, proposed in this paper, facilitates finding not only key processes, with which significant parameters are associated, but also significant modules, corresponding to subsystems of regulatory networks. The results provide broader insight into therapy targets in diseases in which the natural control of intracellular processes is disturbed, leading to the development of more effective therapies in medicine.

This paper is concerned with analysis of two anticancer therapy models focused on sensitivity of therapy outcome with respect to model structure and parameters. Realistic periodic therapies are considered, combining cytotoxic and antiangiogenic agents, defined on a fixed time horizon. Tumor size at the end of therapy and average tumor size calculated over therapy horizon are chosen to represent therapy outcome. Sensitivity analysis has been performed numerically, concentrating on model parameters and structure at one hand, and on treatment protocol parameters, on the other. The results show that sensitivity of the therapy outcome highly depends on the model structure, helping to discern a good model. Moreover, it is possible to use this analysis to find a good protocol in case of heterogeneous tumors.

The paper is focused on sensitivity analysis of large-scale models of biological systems that describe dynamics of the so called signaling pathways. These systems are continuous in time but their models are based on discrete-time measurements. Therefore, if sensitivity analysis is used as a tool supporting model development and evaluation of its quality, it should take this fact into account. Such models are usually very complex and include many parameters difficult to estimate in an experimental way. Changes of many of those parameters have little effect on model dynamics, and therefore they are called sloppy. In contrast, other parameters, when changed, lead to substantial changes in model responses and these are called stiff parameters. While this is a well-known fact, and there are methods to discern sloppy parameters from the stiff ones, they have not been utilized, so far, to create parameter rankings and quantify the influence of single parameter changes on system time responses. These single parameter changes are particularly important in analysis of signalling pathways, because they may pinpoint parameters, associated with the processes to be targeted at the molecular level in laboratory experiments. In the paper we present a new, original method of creating parameter rankings, based on an Hessian of a cost function which describes the fit of the model to a discrete experimental data. Its application is explained with simple dynamical systems, representing two typical dynamics exhibited by the signaling pathways.

Pre- or post-operational chemo-radiotherapy have become one of the standard adjuvant therapies in recent years. Though both chemo- and radiotherapy protocols are standardized, the question about the order in which they should be applied, or concurrency, remains an open question. In this work we attempt to answer it with mathematical modeling and optimization of two-dimensional control that represents therapy in a control-theory based approach. In order to address this problem, two issues are discussed. First, two different ways of modeling tumor growth under therapy are compared. For each of them, the necessary conditions for optimal control representing the therapy are presented and discussed. Then, Kaplan-Meier survival curves are compared for standard therapy protocols used in clinics and different approaches to model tumor growth. Finally, a framework for analysis of treatment efficacy is presented, in which optimization and survival analysis are used sequentially.

Simple mathematical models of tumor growth are commonly used to predict efficiency of different therapy protocols and to optimize therapy outcome. Nowadays, the focus is on personalized oncology, in which treatment strategy is tailored to an individual patient. Simple models with minimal number of parameters can be used to find appropriate treatment strategy. The main idea of this study is to describe effects of combined radio-chemotherapy by two control actions. In this work we compare results of different control strategies (treatment protocols) for a family of models of tumor growth. Using simulations in silico we analyse responses of a thousand patients to three possible therapy protocols. Comparing Kaplan-Meier survival curves obtained for two different tumor growth models indicates that while Gompertz model is slightly less sensitive to changes in control action than exponential and logistic models, the difference is negligible. The important finding is that the shapes of survival curves are similar in all cases. It suggests that the family of models is structurally insensitive. Obtained results imply that more attention should be paid on estimation of parameters for a tumor growth model, than on model selection.

The paper deals with local sensitivity analysis of signaling pathway models, based on sensitivity functions. Though the methods are well known, their application to various models is always based on the assumption that the output of the system whose sensitivity is analyzed is given by absolute quantitative data. In signaling pathways models, however, this data is always normalized. In this paper we show what are the implications of the way the signaling pathways models are built for the interpretation of sensitivity functions and parameter rankings based on them. The reasoning is illustrated using simple first- and second order systems as well as an example of a simple regulatory module.

We present a system engineering approach to a problem of DNA damage-repair in human cells. We discuss chosen control systems existing in the cells and demonstrate that they constitute an almost perfect fault tolerant system. We discuss the consequences of gaps in this system and explain why it cannot be completely perfect.

This paper deals with development of signaling pathways models and using plasmid-based experiments to support parameter estimation. We show that if cells transfected with plasmids are used in experiments, the models should include additional components that describe explicitly effects induced by plasmids. Otherwise, when the model is used to analyze responses of wild type, i.e. non-transfected cells, it may not capture their dynamics properly or even lead to false conclusions. In order to illustrate this, an original mathematical model of miRNA-mediated control of gene expression in the NF$\kappa$B pathway is presented. The paper shows what artifacts might appear due to experimental procedures and how to develop the models in order to avoid pursuing these artifacts instead of real kinetics.

Analysis of the models presented in the preceding chapters may be focused on drawing conclusions of either qualitative or quantitative nature. In the first case, parameter values are not needed, as the goal is to determine, for example, stability properties or the form of the optimal control. Such conclusions subsequently provide the basis for quantitative analysis that concerns a particular cancer type and attempts to determine the outcome of a therapy, or, in more advanced studies, the optimal therapy protocol. The latter is of more value from the clinical point of view. However, applicability of modeling results depends on the ability to estimate correct parameter values for the models under consideration. In subsequent sections, estimation of the model parameters is discussed in the context of experimental and numerical procedures, relevant for the models described in previous chapters.