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

Analysis of the Molecular Networks in Androgen Dependent and Independent Prostate Cancer Revealed Fragile and Robust Subsystems

Androgen ablation therapy is currently the primary treatment for metastatic prostate cancer. Unfortunately, in nearly all cases, androgen ablation fails to permanently arrest cancer progression. As androgens like testosterone are withdrawn, prostate cancer cells lose their androgen sensitivity and begin to proliferate without hormone growth factors. In this study, we constructed and analyzed a mathematical model of the integration between hormone growth factor signaling, androgen receptor activation, and the expression of cyclin D and Prostate-Specific Antigen in human LNCaP prostate adenocarcinoma cells. The objective of the study was to investigate which signaling systems were important in the loss of androgen dependence. The model was formulated as a set of ordinary differential equations which described 212 species and 384 interactions, including both the mRNA and protein levels for key species. An ensemble approach was chosen to constrain model parameters and to estimate the impact of parametric uncertainty on model predictions. Model parameters were identified using 14 steady-state and dynamic LNCaP data sets taken from literature sources. Alterations in the rate of Prostatic Acid Phosphatase expression was sufficient to capture varying levels of androgen dependence. Analysis of the model provided insight into the importance of network components as a function of androgen dependence. The importance of androgen receptor availability and the MAPK/Akt signaling axes was independent of androgen status. Interestingly, androgen receptor availability was important even in androgen-independent LNCaP cells. Translation became progressively more important in androgen-independent LNCaP cells. Further analysis suggested a positive synergy between the MAPK and Akt signaling axes and the translation of key proliferative markers like cyclin D in androgen-independent cells. Taken together, the results support the targeting of both the Akt and MAPK pathways. Moreover, the analysis suggested that direct targeting of the translational machinery, specifically eIF4E, could be efficacious in androgen-independent prostate cancers

Discriminating between rival biochemical network models: three approaches to optimal experiment design

Background: The success of molecular systems biology hinges on the ability to use computational models to design predictive experiments, and ultimately unravel underlying biological mechanisms. A problem commonly encountered in the computational modelling of biological networks is that alternative, structurally different models of similar complexity fit a set of experimental data equally well. In this case, more than one molecular mechanism can explain available data. In order to rule out the incorrect mechanisms, one needs to invalidate incorrect models. At this point, new experiments maximizing the difference between the measured values of alternative models should be proposed and conducted. Such experiments should be optimally designed to produce data that are most likely to invalidate incorrect model structures. Results: In this paper we develop methodologies for the optimal design of experiments with the aim of discriminating between different mathematical models of the same biological system. The first approach determines the 'best' initial condition that maximizes the L2 (energy) distance between the outputs of the rival models. In the second approach, we maximize the L2-distance of the outputs by designing the optimal external stimulus (input) profile of unit L2-norm. Our third method uses optimized structural changes (corresponding, for example, to parameter value changes reflecting gene knock-outs) to achieve the same goal. The numerical implementation of each method is considered in an example, signal processing in starving Dictyostelium amœbæ. Conclusions: Model-based design of experiments improves both the reliability and the efficiency of biochemical network model discrimination. This opens the way to model invalidation, which can be used to perfect our understanding of biochemical networks. Our general problem formulation together with the three proposed experiment design methods give the practitioner new tools for a systems biology approach to experiment design. </p

Structural Identifiability of Systems Biology Models: A Critical Comparison of Methods

Analysing the properties of a biological system through in silico experimentation requires a satisfactory mathematical representation of the system including accurate values of the model parameters. Fortunately, modern experimental techniques allow obtaining time-series data of appropriate quality which may then be used to estimate unknown parameters. However, in many cases, a subset of those parameters may not be uniquely estimated, independently of the experimental data available or the numerical techniques used for estimation. This lack of identifiability is related to the structure of the model, i.e. the system dynamics plus the observation function. Despite the interest in knowing a priori whether there is any chance of uniquely estimating all model unknown parameters, the structural identifiability analysis for general non-linear dynamic models is still an open question. There is no method amenable to every model, thus at some point we have to face the selection of one of the possibilities. This work presents a critical comparison of the currently available techniques. To this end, we perform the structural identifiability analysis of a collection of biological models. The results reveal that the generating series approach, in combination with identifiability tableaus, offers the most advantageous compromise among range of applicability, computational complexity and information provided

A joint model-based experimental design approach for the identification of kinetic models in continuous flow laboratory reactors

Continuous flow laboratory reactors are typically used for the development of kinetic models for catalytic reactions. Sequential model-based design of experiments (MBDoE) procedures have been proposed in literature where experiments are optimally designed for discriminating amongst candidate models or for improving the estimation of kinetic parameters. However, the effectiveness of these procedures is strongly affected by the initial model uncertainty, leading to suboptimal design solutions and higher number of experiments to be executed. A joint model-based design of experiments (j-MBDoE) technique, based on multi-objective optimization, is proposed in this paper for the simultaneous solution of the dual problem of discriminating among competitive kinetic models and improving the estimation of the model parameters. The effectiveness of the proposed design methodology is tested and discussed through a simulated case study for the identification of kinetic models of methanol oxidation over silver catalyst