Steady state and (bi-) stability evaluation of simple protease signalling networks

Signal transduction networks are complex, as are their mathematical models. Gaining a deeper understanding requires a system analysis. Important aspects are the number, location and stability of steady states. In particular, bistability has been recognised as an important feature to achieve molecular switching. This paper compares different model structures and analysis methods particularly useful for bistability analysis. The biological applications include proteolytic cascades as, for example, encountered in the apoptotic signalling pathway or in the blood clotting system. We compare three model structures containing zero-order, inhibitor and cooperative ultrasensitive reactions, all known to achieve bistability. The combination of phase plane and bifurcation analysis provides an illustrative and comprehensive understanding of how bistability can be achieved and indicates how robust this behaviour is. Experimentally, some so-called “inactive” components were shown to have a residual activity. This has been mostly ignored in mathematical models. Our analysis reveals that bistability is only mildly affected in the case of zero-order or inhibitor ultrasensitivity. However, the case where bistability is achieved by cooperative ultrasensitivity is severely affected by this perturbation

Bridging Time Scales in Cellular Decision Making with a Stochastic Bistable Switch

Cellular transformations which involve a significant phenotypical change of the cell's state use bistable biochemical switches as underlying decision systems. In this work, we aim at linking cellular decisions taking place on a time scale of years to decades with the biochemical dynamics in signal transduction and gene regulation, occuring on a time scale of minutes to hours. We show that a stochastic bistable switch forms a viable biochemical mechanism to implement decision processes on long time scales. As a case study, the mechanism is applied to model the initiation of follicle growth in mammalian ovaries, where the physiological time scale of follicle pool depletion is on the order of the organism's lifespan. We construct a simple mathematical model for this process based on experimental evidence for the involved genetic mechanisms. Despite the underlying stochasticity, the proposed mechanism turns out to yield reliable behavior in large populations of cells subject to the considered decision process. Our model explains how the physiological time constant may emerge from the intrinsic stochasticity of the underlying gene regulatory network. Apart from ovarian follicles, the proposed mechanism may also be of relevance for other physiological systems where cells take binary decisions over a long time scale.Comment: 14 pages, 4 figure

Mechanistic Oral Absorption Modeling and Simulation for Formulation Development and Bioequivalence Evaluation: Report of an FDA Public Workshop

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138394/1/psp412204.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138394/2/psp412204_am.pd

Understanding dynamics using sensitivity analysis: caveat and solution

<p>Abstract</p> <p>Background</p> <p>Parametric sensitivity analysis (PSA) has become one of the most commonly used tools in computational systems biology, in which the sensitivity coefficients are used to study the parametric dependence of biological models. As many of these models describe dynamical behaviour of biological systems, the PSA has subsequently been used to elucidate important cellular processes that regulate this dynamics. However, in this paper, we show that the PSA coefficients are not suitable in inferring the mechanisms by which dynamical behaviour arises and in fact it can even lead to incorrect conclusions.</p> <p>Results</p> <p>A careful interpretation of parametric perturbations used in the PSA is presented here to explain the issue of using this analysis in inferring dynamics. In short, the PSA coefficients quantify the integrated change in the system behaviour due to persistent parametric perturbations, and thus the dynamical information of when a parameter perturbation matters is lost. To get around this issue, we present a new sensitivity analysis based on impulse perturbations on system parameters, which is named impulse parametric sensitivity analysis (iPSA). The inability of PSA and the efficacy of iPSA in revealing mechanistic information of a dynamical system are illustrated using two examples involving switch activation.</p> <p>Conclusions</p> <p>The interpretation of the PSA coefficients of dynamical systems should take into account the persistent nature of parametric perturbations involved in the derivation of this analysis. The application of PSA to identify the controlling mechanism of dynamical behaviour can be misleading. By using impulse perturbations, introduced at different times, the iPSA provides the necessary information to understand how dynamics is achieved, i.e. which parameters are essential and when they become important.</p

Caspase-8 activity has an essential role in CD95/Fas-mediated MAPK activation

Stimulation of CD95/Fas/APO-1 results in the induction of both apoptotic and non-apoptotic signaling pathways. The processes regulating these two opposing pathways have not been thoroughly elucidated to date. In this study, using quantitative immunoblots, imaging, and mathematical modeling, we addressed the dynamics of the DED proteins of the death-inducing signaling complex (DISC), procaspase-8, and cellular FLICE inhibitory proteins (c-FLIPs) to the onset of CD95-mediated ERK1/2 and p38 mitogen-activated protein kinase (MAPK) activation. We found that CD95 DISC-induced caspase-8 activity is important for the initiation of ERK1/2 and p38 MAPK activation. The long c-FLIP isoform, c-FLIPL, and the short c-FLIP isoform, c-FLIPR, inhibited MAPK induction by blocking caspase-8 processing at the DISC. Furthermore, we built a mathematical model describing CD95 DISC-mediated MAPK activation and apoptosis. The model quantitatively defined the dynamics of DED proteins, procaspase-8, and c-FLIP, which lead to caspase-8 activation and induction of apoptotic and non-apoptotic signaling pathways. In conclusion, the combination of biochemical analysis with mathematical modeling provides evidence for an important role of caspase-8 in CD95-mediated activation of MAPKs, while c-FLIP exerts a regulatory function in this process

Systems analysis of apoptosis protein expression allows the case-specific prediction of cell death responsiveness of melanoma cells.

Many cancer entities and their associated cell line models are highly heterogeneous in their responsiveness to apoptosis inducers and, despite a detailed understanding of the underlying signaling networks, cell death susceptibility currently cannot be predicted reliably from protein expression profiles. Here, we demonstrate that an integration of quantitative apoptosis protein expression data with pathway knowledge can predict the cell death responsiveness of melanoma cell lines. By a total of 612 measurements, we determined the absolute expression (nM) of 17 core apoptosis regulators in a panel of 11 melanoma cell lines, and enriched these data with systems-level information on apoptosis pathway topology. By applying multivariate statistical analysis and multi-dimensional pattern recognition algorithms, the responsiveness of individual cell lines to tumor necrosis factor-related apoptosis-inducing ligand (TRAIL) or dacarbazine (DTIC) could be predicted with very high accuracy (91 and 82% correct predictions), and the most effective treatment option for individual cell lines could be pre-determined in silico. In contrast, cell death responsiveness was poorly predicted when not taking knowledge on protein-protein interactions into account (55 and 36% correct predictions). We also generated mathematical predictions on whether anti-apoptotic Bcl-2 family members or x-linked inhibitor of apoptosis protein (XIAP) can be targeted to enhance TRAIL responsiveness in individual cell lines. Subsequent experiments, making use of pharmacological Bcl-2/Bcl-xL inhibition or siRNA-based XIAP depletion, confirmed the accuracy of these predictions. We therefore demonstrate that cell death responsiveness to TRAIL or DTIC can be predicted reliably in a large number of melanoma cell lines when investigating expression patterns of apoptosis regulators in the context of their network-level interplay. The capacity to predict responsiveness at the cellular level may contribute to personalizing anti-cancer treatments in the future

Mathematical analysis of the Escherichia coli chemotaxis signalling pathway

We undertake a detailed mathematical analysis of a recent nonlinear ordinary differential equation (ODE) model describing the chemotactic signalling cascade within an {\it Escherichia coli} cell. The model includes a detailed description of the cell signalling cascade and an average approximation of the receptor activity. A steady-state stability analysis reveals the system exhibits one positive real steady-state which is shown to be asymptotically stable. Given the occurrence of a negative feedback between phosphorylated CheB (CheB-P) and the receptor state, we ask under what conditions, the system may exhibit oscillatory type behaviour. A detailed analysis of parameter space reveals that whilst variation in kinetic rate parameters within known biological limits is unlikely to lead to such behaviour, changes in the total concentration of the signalling proteins does. We postulate that experimentally observed overshoot behaviour can actually be described by damped oscillatory dynamics and consider the relationship between overshoot amplitude, total cell protein concentration and the magnitude of the external ligand stimulus. Model reductions of the full ODE model allow us to understand the link between phosphorylation events and the negative feedback between CheB-P and receptor methylation, as well as elucidate why some mathematical models exhibit overshoot and others do not. Our manuscript closes by discussing intercell variability of total protein concentration as means of ensuring the overall survival of a population as cells are subjected to different environments

Global Analysis of Dynamical Decision-Making Models through Local Computation around the Hidden Saddle

Bistable dynamical switches are frequently encountered in mathematical modeling of biological systems because binary decisions are at the core of many cellular processes. Bistable switches present two stable steady-states, each of them corresponding to a distinct decision. In response to a transient signal, the system can flip back and forth between these two stable steady-states, switching between both decisions. Understanding which parameters and states affect this switch between stable states may shed light on the mechanisms underlying the decision-making process. Yet, answering such a question involves analyzing the global dynamical (i.e., transient) behavior of a nonlinear, possibly high dimensional model. In this paper, we show how a local analysis at a particular equilibrium point of bistable systems is highly relevant to understand the global properties of the switching system. The local analysis is performed at the saddle point, an often disregarded equilibrium point of bistable models but which is shown to be a key ruler of the decision-making process. Results are illustrated on three previously published models of biological switches: two models of apoptosis, the programmed cell death and one model of long-term potentiation, a phenomenon underlying synaptic plasticity

Bcl-2 inhibits apoptosis by increasing the time-to-death and intrinsic cell-to-cell variations in the mitochondrial pathway of cell death

BH3 mimetics have been proposed as new anticancer therapeutics. They target anti-apoptotic Bcl-2 proteins, up-regulation of which has been implicated in the resistance of many cancer cells, particularly leukemia and lymphoma cells, to apoptosis. Using probabilistic computational modeling of the mitochondrial pathway of apoptosis, verified by single-cell experimental observations, we develop a model of Bcl-2 inhibition of apoptosis. Our results clarify how Bcl-2 imparts its anti-apoptotic role by increasing the time-to-death and cell-to-cell variability. We also show that although the commitment to death is highly impacted by differences in protein levels at the time of stimulation, inherent stochastic fluctuations in apoptotic signaling are sufficient to induce cell-to-cell variability and to allow single cells to escape death. This study suggests that intrinsic cell-to-cell stochastic variability in apoptotic signaling is sufficient to cause fractional killing of cancer cells after exposure to BH3 mimetics. This is an unanticipated facet of cancer chemoresistance.Comment: 11 pages, In pres

Exact model reduction of combinatorial reaction networks

Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models