Multi-scale modeling of follicular ovulation as a reachability problem

During each ovarian cycle, only a definite number of follicles ovulate, while the others undergo a degeneration process called atresia. We have designed a multi-scale mathematical model where ovulation and atresia result from a hormonal controlled selection process. A 2D-conservation law describes the age and maturity structuration of the follicular cell population. In this paper, we focus on the operating mode of the control, through the study of the characteristics of the conservation law. We describe in particular the set of microscopic initial conditions leading to the macroscopic phenomenon of either ovulation or atresia, in the framework of backwards reachable sets theory

Incorporating Time Delays in Process Hitting Framework for Dynamical Modeling of Large Biological Regulatory Networks

Modeling and simulation of molecular systems helps in understanding the behavioral mechanism of biological regulation. Time delays in production and degradation of expressions are important parameters in biological regulation. Constraints on time delays provide insight into the dynamical behavior of a Biological Regulatory Network (BRN). A recently introduced Process Hitting (PH) Framework has been found efficient in static analysis of large BRNs, however, it lacks the inference of time delays and thus determination of their constraints associated with the evolution of the expression levels of biological entities of BRN is not possible. In this paper we propose a Hybrid Process Hitting scheme for introducing time delays in Process Hitting Framework for dynamical modeling and analysis of Large Biological Regulatory Networks. It provides valuable insights into the time delays corresponding to the changes in the expression levels of biological entities thus possibly helping in identification of therapeutic targets. The proposed framework is applied to a well-known BRNs of Bacteriophage λ and ERBB Receptor-regulated G1/S transition involved in the breast cancer to demonstrate the viability of our approach. Using the proposed approach, we are able to perform goal-oriented reduction of the BRN and also determine the constraints on time delays characterizing the evolution (dynamics) of the reduced BRN

Systems Biology of Cancer: A Challenging Expedition for Clinical and Quantitative Biologists

A systems-biology approach to complex disease (such as cancer) is now complementing traditional experience-based approaches, which have typically been invasive and expensive. The rapid progress in biomedical knowledge is enabling the targeting of disease with therapies that are precise, proactive, preventive, and personalized. In this paper, we summarize and classify models of systems biology and model checking tools, which have been used to great success in computational biology and related fields. We demonstrate how these models and tools have been used to study some of the twelve biochemical pathways implicated in but not unique to pancreatic cancer, and conclude that the resulting mechanistic models will need to be further enhanced by various abstraction techniques to interpret phenomenological models of cancer progression

A Systems Biology Approach in Therapeutic Response Study for Different Dosing Regimens—a Modeling Study of Drug Effects on Tumor Growth using Hybrid Systems

Motivated by the frustration of translation of research advances in the molecular and cellular biology of cancer into treatment, this study calls for cross-disciplinary efforts and proposes a methodology of incorporating drug pharmacology information into drug therapeutic response modeling using a computational systems biology approach. The objectives are two fold. The first one is to involve effective mathematical modeling in the drug development stage to incorporate preclinical and clinical data in order to decrease costs of drug development and increase pipeline productivity, since it is extremely expensive and difficult to get the optimal compromise of dosage and schedule through empirical testing. The second objective is to provide valuable suggestions to adjust individual drug dosing regimens to improve therapeutic effects considering most anticancer agents have wide inter-individual pharmacokinetic variability and a narrow therapeutic index. A dynamic hybrid systems model is proposed to study drug antitumor effect from the perspective of tumor growth dynamics, specifically the dosing and schedule of the periodic drug intake, and a drug’s pharmacokinetics and pharmacodynamics information are linked together in the proposed model using a state-space approach. It is proved analytically that there exists an optimal drug dosage and interval administration point, and demonstrated through simulation study

Biological Networks

Networks of coordinated interactions among biological entities govern a myriad of biological functions that span a wide range of both length and time scales—from ecosystems to individual cells and from years to milliseconds. For these networks, the concept “the whole is greater than the sum of its parts” applies as a norm rather than an exception. Meanwhile, continued advances in molecular biology and high-throughput technology have enabled a broad and systematic interrogation of whole-cell networks, allowing the investigation of biological processes and functions at unprecedented breadth and resolution—even down to the single-cell level. The explosion of biological data, especially molecular-level intracellular data, necessitates new paradigms for unraveling the complexity of biological networks and for understanding how biological functions emerge from such networks. These paradigms introduce new challenges related to the analysis of networks in which quantitative approaches such as machine learning and mathematical modeling play an indispensable role. The Special Issue on “Biological Networks” showcases advances in the development and application of in silico network modeling and analysis of biological systems

A Study of the Synergies Between Control Mechanisms in the Immune System and the Variable Structure Control Paradigm

This thesis argues that variable structure control theory finds application in immunology. The immune system maintains a healthy state by using feedback to switch on and off immune responses. Experimental and mathematical work has analysed the dynamics of the immune response of T cells, relatively little attention has been paid to examine the underlying control paradigm. Besides, in modelling and simulation studies, it is necessary to evaluate the impact of uncertainty and perturbations on immunological dynamics. This is important to deliver robust predictions and insights. These facts motivate considering variable structure control techniques to investigate the control strategy and robustness of the immune system in the context of immunity to infection and tolerance. The results indicate that the dynamic response of T cells following foreign or self-antigen stimulation behaves as a naturally occurring switched control law. Further, the reachability analysis from sliding mode control highlights dynamical conditions to assess the performance and robustness of the T cell response dynamics. Additionally, this approach delivers dynamical conditions for the containment of Human Immunodeficiency Virus (HIV) infection by the HIV-specific CD8+ T cell response and antiretroviral therapy by enforcing a sliding mode on a manifold associated with the infection-free steady-state. This condition for immunity reveals particular patterns for early diagnosis of eventual success, marginal and failure cases of antiretroviral therapy. Together, the findings in this thesis evidence that variable structure control theory presents a useful framework to study health and disease dynamics as well as to monitor the performance of treatment regimes

A computational modelling of cellular and supra-cellular networks to unravel the control of EMT

"Over the last decade, Epithelial-to-Mesenchymal Transition (EMT) has gained the attention of cancer researchers due to its potential to promote cancer migration and metastasis. However, the complexity of EMT intertwined regulation and the involvement of multiple signals in the tumour microenvironment have been limiting the understanding of how this process can be controlled. Cell-cell adhesion and focal adhesion dynamics are two critical properties that change during EMT, which provide a simple way to characterize distinct modes of cancer migration. Therefore, the main focus of this thesis is to provide a framework to predict critical microenvironment and de-regulations in cancer that drive interconversion between adhesion phenotypes, accounting for main microenvironment signals and signalling pathways in EMT. Here, we address this issue through a systems approach using the logical modelling framework to generate new testable predictions for the field.(...)"Instituto Gulbenkian de Ciência (FCG-IGC

A dynamics based analysis of allosteric modulation in heat shock proteins

The 70 kDa and 90 kDa heat shock proteins (Hsp70 and Hsp90) are molecular chaperones that play central roles in maintaining cellular homeostasis in all organisms of life with the exception of archaea. In addition to their general chaperone function in protein quality control, Hsp70 and Hsp90 cooperate in the regulation and activity of some 200 known natively folded protein clients which include protein kinases, transcription factors and receptors, many of which are implicated as key regulators of essential signal transduction pathways. Both chaperones are considered to be large multi-domain proteins that rely on ATPase activity and co-chaperone interactions to regulate their conformational cycles for peptide binding and release. The unique positioning of Hsp90 at the crossroads of several fundamental cellular pathways coupled with its known association with diverse oncogenic peptide clients has brought the molecular chaperone under increasing interest as a potential anti-cancer target that is crucially implicated with all eight hallmarks of the disease. Current orthosteric drug discovery efforts aimed at the inhibition of the ATPase domain of Hsp90 have been limited due to high levels of associated toxicity. In an effort to circumnavigate this, the combined focus of research efforts is shifting toward alternative approaches such as interference with co-chaperone binding and the allosteric inhibition/activation of the molecular chaperone. The overriding aim of this thesis was to demonstrate how the computational technique of Perturbation response scanning (PRS) coupled with all-atom molecular dynamics simulations (MD) and dynamic residue interaction network (DRN) analysis can be used as a viable strategy to efficiently scan and accurately identify allosteric control element capable of modulating the functional dynamics of a protein. In pursuit of this goal, this thesis also contributes to the current understanding of the nucleotide dependent allosteric mechanisms at play in cellular functionality of both Hsp70 and Hsp90. All-atom MD simulations of E. coli DnaK provided evidence of nucleotide driven modulation of conformational dynamics in both the catalytically active and inactive states. PRS analysis employed on these trajectories demonstrated sensitivity toward bound nucleotide and peptide substrate, and provided evidence of a putative allosterically active intermediate state between the ATPase active and inactive conformational states. Simultaneous binding of ATP and peptide substrate was found to allosterically prime the chaperone for interstate conversion regardless of the transition direction. Detailed analysis of these allosterically primed states revealed select residue sites capable of selecting a coordinate shift towards the opposite conformational state. In an effort to validate these results, the predicted allosteric hot spot sites were cross-validated with known experimental works and found to overlap with functional sites implicated in allosteric signal propagation and ATPase activation in Hsp70. This study presented for the first time, the application of PRS as a suitable diagnostic tool for the elucidation and quantification of the allosteric potential of select residues to effect functionally relevant global conformational rearrangements. The PRS methodology described in this study was packaged within the Python programming environment in the MD-TASK software suite for command-line ease of use and made freely available. Homology modelling techniques were used to address the lack of experimental structural data for the human cytosolic isoform of Hsp90 and for the first time provided accurate full-length structural models of human Hsp90α in fully-closed and partially-open conformations. Long-range all-atom MD simulations of these structures revealed nucleotide driven modulation of conformational dynamics in Hsp90. Subsequent DRN and PRS analysis of these MD trajectories allowed for the quantification and elucidation of nucleotide driven allosteric modulation in the molecular chaperone. A detailed PRS analysis revealed allosteric inter-domain coupling between the extreme terminals of the chaperone in response to external force perturbations at either domain. Furthermore PRS also identified several individual residue sites that are capable of selecting conformational rearrangements towards functionally relevant states which may be considered to be putative allosteric target sites for future drug discovery efforts Molecular docking techniques were employed to investigate the modulation of conformational dynamics of human Hsp90α in response to ligand binding interactions at two identified allosteric sites at the C-terminal. High throughput screening of a small library of natural compounds indigenous to South Africa revealed three hit compounds at these sites: Cephalostatin 17, 20(29)-Lupene-3β isoferulate and 3'-Bromorubrolide F. All-atom MD simulations on these protein-ligand complexes coupled with DRN analysis and several advanced trajectory based analysis techniques provided evidence of selective allosteric modulation of Hsp90α conformational dynamics in response to the identity and location of the bound ligands. Ligands bound at the four-helix bundle presented as putative allosteric inhibitors of Hsp90α, driving conformational dynamics in favour of dimer opening and possibly dimer separation. Meanwhile, ligand interactions at an adjacent sub-pocket located near the interface between the middle and C-terminal domains demonstrated allosteric activation of the chaperone, modulating conformational dynamics in favour of the fully-closed catalytically active conformational state. Taken together, the data presented in this thesis contributes to the understanding of allosteric modulation of conformational dynamics in Hsp70 and Hsp90, and provides a suitable platform for future biochemical and drug discovery studies. Furthermore, the molecular docking and computational identification of allosteric compounds with suitable binding affinity for allosteric sites at the CTD of human Hsp90α provide for the first time “proof-of-principle” for the use of PRS in conjunction with MD simulations and DRN analysis as a suitable method for the rapid identification of allosteric sites in proteins that can be probed by small molecule interaction. The data presented in this section could pave the way for future allosteric drug discovery studies for the treatment of Hsp90 associated pathologies

Computational Techniques for Stochastic Reachability

As automated control systems grow in prevalence and complexity, there is an increasing demand for verification and controller synthesis methods to ensure these systems perform safely and to desired specifications. In addition, uncertain or stochastic behaviors are often exhibited (such as wind affecting the motion of an aircraft), making probabilistic verification desirable. Stochastic reachability analysis provides a formal means of generating the set of initial states that meets a given objective (such as safety or reachability) with a desired level of probability, known as the reachable (or safe) set, depending on the objective. However, the applicability of reachability analysis is limited in the scope and size of system it can address. First, generating stochastic reachable or viable sets is computationally intensive, and most existing methods rely on an optimal control formulation that requires solving a dynamic program, and which scales exponentially in the dimension of the state space. Second, almost no results exist for extending stochastic reachability analysis to systems with incomplete information, such that the controller does not have access to the full state of the system. This thesis addresses both of the above limitations, and introduces novel computational methods for generating stochastic reachable sets for both perfectly and partially observable systems. We initially consider a linear system with additive Gaussian noise, and introduce two methods for computing stochastic reachable sets that do not require dynamic programming. The first method uses a particle approximation to formulate a deterministic mixed integer linear program that produces an estimate to reachability probabilities. The second method uses a convex chance-constrained optimization problem to generate an under-approximation to the reachable set. Using these methods we are able to generate stochastic reachable sets for a four-dimensional spacecraft docking example in far less time than it would take had we used a dynamic program. We then focus on discrete time stochastic hybrid systems, which provide a flexible modeling framework for systems that exhibit mode-dependent behavior, and whose state space has both discrete and continuous components. We incorporate a stochastic observation process into the hybrid system model, and derive both theoretical and computational results for generating stochastic reachable sets subject to an observation process. The derivation of an information state allows us to recast the problem as one of perfect information, and we prove that solving a dynamic program over the information state is equivalent to solving the original problem. We then demonstrate that the dynamic program to solve the reachability problem for a partially observable stochastic hybrid system shares the same properties as for a partially observable Markov decision process (POMDP) with an additive cost function, and so we can exploit approximation strategies designed for POMDPs to solve the reachability problem. To do so, however, we first generate approximate representations of the information state and value function as either vectors or Gaussian mixtures, through a finite state approximation to the hybrid system or using a Gaussian mixture approximation to an indicator function defined over a convex region. For a system with linear dynamics and Gaussian measurement noise, we show that it exhibits special properties that do not require an approximation of the information state, which enables much more efficient computation of the reachable set. In all cases we provide convergence results and numerical examples