Dynamical pathway analysis

<p>Abstract</p> <p>Background</p> <p>Although a great deal is known about one gene or protein and its functions under different environmental conditions, little information is available about the complex behaviour of biological networks subject to different environmental perturbations. Observing differential expressions of one or more genes between normal and abnormal cells has been a mainstream method of discovering pertinent genes in diseases and therefore valuable drug targets. However, to date, no such method exists for elucidating and quantifying the differential dynamical behaviour of genetic regulatory networks, which can have greater impact on phenotypes than individual genes.</p> <p>Results</p> <p>We propose to redress the deficiency by formulating the functional study of biological networks as a control problem of dynamical systems. We developed mathematical methods to study the stability, the controllability, and the steady-state behaviour, as well as the transient responses of biological networks under different environmental perturbations. We applied our framework to three real-world datasets: the SOS DNA repair network in <it>E. coli </it>under different dosages of radiation, the GSH redox cycle in mice lung exposed to either poisonous air or normal air, and the MAPK pathway in mammalian cell lines exposed to three types of HIV type I Vpr, a wild type and two mutant types; and we found that the three genetic networks exhibited fundamentally different dynamical properties in normal and abnormal cells.</p> <p>Conclusion</p> <p>Difference in stability, relative stability, degrees of controllability, and transient responses between normal and abnormal cells means considerable difference in dynamical behaviours and different functioning of cells. Therefore differential dynamical properties can be a valuable tool in biomedical research.</p

Phonon-driven ultrafast exciton dissociation at donor-acceptor polymer heterojunctions

A quantum-dynamical analysis of phonon-driven exciton dissociation at polymer heterojunctions is presented, using a hierarchical electron-phonon model parameterized for three electronic states and 24 vibrational modes. Two interfering decay pathways are identified: a direct charge separation, and an indirect pathway via an intermediate bridge state. Both pathways depend critically on the dynamical interplay of high-frequency C=C stretch modes and low-frequency ring-torsional modes. The ultrafast, highly non-equilibrium dynamics is consistent with time-resolved spectroscopic observations

Algebraic Systems Biology: A Case Study for the Wnt Pathway

Steady state analysis of dynamical systems for biological networks give rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We demonstrate this for the shuttle model of the Wnt signaling pathway. Here the variety is described by a polynomial system in 19 unknowns and 36 parameters. Current methods from computational algebraic geometry and combinatorics are applied to analyze this model.Comment: 24 pages, 2 figure

The case of the trapped singularities

A case study in bifurcation and stability analysis is presented, in which reduced dynamical system modelling yields substantial new global and predictive information about the behaviour of a complex system. The first smooth pathway, free of pathological and persistent degenerate singularities, is surveyed through the parameter space of a nonlinear dynamical model for a gradient-driven, turbulence-shear flow energetics in magnetized fusion plasmas. Along the route various obstacles and features are identified and treated appropriately. An organizing centre of low codimension is shown to be robust, several trapped singularities are found and released, and domains of hysteresis, threefold stable equilibria, and limit cycles are mapped. Characterization of this rich dynamical landscape achieves unification of previous disparate models for plasma confinement transitions, supplies valuable intelligence on the big issue of shear flow suppression of turbulence, and suggests targeted experimental design, control and optimization strategies.Comment: 21 pages, 12 figures, 34 postscript figure file

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation, and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.Comment: Submitted to 'Systems Medicine' as a book chapte

Transfer Functions for Protein Signal Transduction: Application to a Model of Striatal Neural Plasticity

We present a novel formulation for biochemical reaction networks in the context of signal transduction. The model consists of input-output transfer functions, which are derived from differential equations, using stable equilibria. We select a set of 'source' species, which receive input signals. Signals are transmitted to all other species in the system (the 'target' species) with a specific delay and transmission strength. The delay is computed as the maximal reaction time until a stable equilibrium for the target species is reached, in the context of all other reactions in the system. The transmission strength is the concentration change of the target species. The computed input-output transfer functions can be stored in a matrix, fitted with parameters, and recalled to build discrete dynamical models. By separating reaction time and concentration we can greatly simplify the model, circumventing typical problems of complex dynamical systems. The transfer function transformation can be applied to mass-action kinetic models of signal transduction. The paper shows that this approach yields significant insight, while remaining an executable dynamical model for signal transduction. In particular we can deconstruct the complex system into local transfer functions between individual species. As an example, we examine modularity and signal integration using a published model of striatal neural plasticity. The modules that emerge correspond to a known biological distinction between calcium-dependent and cAMP-dependent pathways. We also found that overall interconnectedness depends on the magnitude of input, with high connectivity at low input and less connectivity at moderate to high input. This general result, which directly follows from the properties of individual transfer functions, contradicts notions of ubiquitous complexity by showing input-dependent signal transmission inactivation.Comment: 13 pages, 5 tables, 15 figure

Structural Kinetic Modeling of Metabolic Networks

To develop and investigate detailed mathematical models of cellular metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, explicit kinetic modeling based on differential equations is still often severely hampered by inadequate knowledge of the enzyme-kinetic rate laws and their associated parameter values. Here we propose a method that aims to give a detailed and quantitative account of the dynamical capabilities of metabolic systems, without requiring any explicit information about the particular functional form of the rate equations. Our approach is based on constructing a local linear model at each point in parameter space, such that each element of the model is either directly experimentally accessible, or amenable to a straightforward biochemical interpretation. This ensemble of local linear models, encompassing all possible explicit kinetic models, then allows for a systematic statistical exploration of the comprehensive parameter space. The method is applied to two paradigmatic examples: The glycolytic pathway of yeast and a realistic-scale representation of the photosynthetic Calvin cycle.Comment: 14 pages, 8 figures (color

On the Kinetics of Body versus End Evaporation and Addition of Supramolecular Polymers

Although pathway-specific kinetic theories are fundamentally important to describe and understand reversible polymerisation kinetics, they come in principle at a cost of having a large number of system-specific parameters. Here, we construct a dynamical Landau theory to describe the kinetics of activated linear supramolecular self-assembly, which drastically reduces the number of parameters and still describes most of the interesting and generic behavior of the system in hand. This phenomenological approach hinges on the fact that if nucleated, the polymerisation transition resembles a phase transition. We are able to describe hysteresis, overshooting, undershooting and the existence of a lag time before polymerisation takes off, and pinpoint the conditions required for observing these types of phenomenon in the assembly and disassembly kinetics. We argue that the phenomenological kinetic parameter in our theory is a pathway controller, i.e., it controls the relative weights of the molecular pathways through which self-assembly takes place