Insights into the behaviour of systems biology models from dynamic sensitivity and identifiability analysis: a case study of an NF-kB signaling pathway

Mathematical modelling offers a variety of useful techniques to help in understanding the intrinsic behaviour of complex signal transduction networks. From the system engineering point of view, the dynamics of metabolic and signal transduction models can always be described by nonlinear ordinary differential equations (ODEs) following mass balance principles. Based on the state-space formulation, many methods from the area of automatic control can conveniently be applied to the modelling, analysis and design of cell networks. In the present study, dynamic sensitivity analysis is performed on a model of the IB-NF-B signal pathway system. Univariate analysis of the Euclidean-form overall sensitivities shows that only 8 out of the 64 parameters in the model have major influence on the nuclear NF-B oscillations. The sensitivity matrix is then used to address correlation analysis, identifiability assessment and measurement set selection within the framework of least squares estimation and multivariate analysis. It is shown that certain pairs of parameters are exactly or highly correlated to each other in terms of their effects on the measured variables. The experimental design strategy provides guidance on which proteins should best be considered for measurement such that the unknown parameters can be estimated with the best statistical precision. The whole analysis scheme we describe provides efficient parameter estimation techniques for complex cell networks

The sloppy model universality class and the Vandermonde matrix

In a variety of contexts, physicists study complex, nonlinear models with many unknown or tunable parameters to explain experimental data. We explain why such systems so often are sloppy; the system behavior depends only on a few `stiff' combinations of the parameters and is unchanged as other `sloppy' parameter combinations vary by orders of magnitude. We contrast examples of sloppy models (from systems biology, variational quantum Monte Carlo, and common data fitting) with systems which are not sloppy (multidimensional linear regression, random matrix ensembles). We observe that the eigenvalue spectra for the sensitivity of sloppy models have a striking, characteristic form, with a density of logarithms of eigenvalues which is roughly constant over a large range. We suggest that the common features of sloppy models indicate that they may belong to a common universality class. In particular, we motivate focusing on a Vandermonde ensemble of multiparameter nonlinear models and show in one limit that they exhibit the universal features of sloppy models.Comment: New content adde

Methodologies for quantitative systems pharmacology (QSP) models : Design and estimation

With the increased interest in the application of quantitative systems pharmacology (QSP) models within medicine research and development, there is an increasing need to formalize model development and verification aspects. In February 2016, a workshop was held at Roche Pharma Research and Early Development to focus discussions on two critical methodological aspects of QSP model development: optimal structural granularity and parameter estimation. We here report in a perspective article a summary of presentations and discussions

Global parameter estimation methods for stochastic biochemical systems

<p>Abstract</p> <p>Background</p> <p>The importance of stochasticity in cellular processes having low number of molecules has resulted in the development of stochastic models such as chemical master equation. As in other modelling frameworks, the accompanying rate constants are important for the end-applications like analyzing system properties (e.g. robustness) or predicting the effects of genetic perturbations. Prior knowledge of kinetic constants is usually limited and the model identification routine typically includes parameter estimation from experimental data. Although the subject of parameter estimation is well-established for deterministic models, it is not yet routine for the chemical master equation. In addition, recent advances in measurement technology have made the quantification of genetic substrates possible to single molecular levels. Thus, the purpose of this work is to develop practical and effective methods for estimating kinetic model parameters in the chemical master equation and other stochastic models from single cell and cell population experimental data.</p> <p>Results</p> <p>Three parameter estimation methods are proposed based on the maximum likelihood and density function distance, including probability and cumulative density functions. Since stochastic models such as chemical master equations are typically solved using a Monte Carlo approach in which only a finite number of Monte Carlo realizations are computationally practical, specific considerations are given to account for the effect of finite sampling in the histogram binning of the state density functions. Applications to three practical case studies showed that while maximum likelihood method can effectively handle low replicate measurements, the density function distance methods, particularly the cumulative density function distance estimation, are more robust in estimating the parameters with consistently higher accuracy, even for systems showing multimodality.</p> <p>Conclusions</p> <p>The parameter estimation methodologies described in this work have provided an effective and practical approach in the estimation of kinetic parameters of stochastic systems from either sparse or dense cell population data. Nevertheless, similar to kinetic parameter estimation in other modelling frameworks, not all parameters can be estimated accurately, which is a common problem arising from the lack of complete parameter identifiability from the available data.</p

The Influence of Different Stresses on Glomalin Levels in an Arbuscular Mycorrhizal Fungus—Salinity Increases Glomalin Content

Glomalin is a glycoprotein produced by arbuscular mycorrhizal (AM) fungi, and the soil fraction containing glomalin is correlated with soil aggregation. Thus, factors potentially influencing glomalin production could be of relevance for this ecosystem process and for understanding AM fungal physiology. Previous work indicated that glomalin production in AM fungi may be a stress response, or related to suboptimal mycelium growth. We show here that environmental stress can enhance glomalin production in the mycelium of the AM fungus Glomus intraradices. We applied NaCl and glycerol in different intensities to the medium in which the fungus was grown in vitro, causing salinity stress and osmotic stress, respectively. As a third stress type, we simulated grazing on the extraradical hyphae of the fungus by mechanically injuring the mycelium by clipping. NaCl caused a strong increase, while the clipping treatment led to a marginally significant increase in glomalin production. Even though salinity stress includes osmotic stress, we found substantially different responses in glomalin production due to the NaCl and the glycerol treatment, as glycerol addition did not cause any response. Thus, our results indicate that glomalin is involved in inducible stress responses in AM fungi for salinity, and possibly grazing stress

A Test of Highly Optimized Tolerance Reveals Fragile Cell-Cycle Mechanisms Are Molecular Targets in Clinical Cancer Trials

Robustness, a long-recognized property of living systems, allows function in the face of uncertainty while fragility, i.e., extreme sensitivity, can potentially lead to catastrophic failure following seemingly innocuous perturbations. Carlson and Doyle hypothesized that highly-evolved networks, e.g., those involved in cell-cycle regulation, can be resistant to some perturbations while highly sensitive to others. The “robust yet fragile” duality of networks has been termed Highly Optimized Tolerance (HOT) and has been the basis of new lines of inquiry in computational and experimental biology. In this study, we tested the working hypothesis that cell-cycle control architectures obey the HOT paradigm. Three cell-cycle models were analyzed using monte-carlo sensitivity analysis. Overall state sensitivity coefficients, which quantify the robustness or fragility of a given mechanism, were calculated using a monte-carlo strategy with three different numerical techniques along with multiple parameter perturbation strategies to control for possible numerical and sampling artifacts. Approximately 65% of the mechanisms in the G1/S restriction point were responsible for 95% of the sensitivity, conversely, the G2-DNA damage checkpoint showed a much stronger dependence on a few mechanisms; ∼32% or 13 of 40 mechanisms accounted for 95% of the sensitivity. Our analysis predicted that CDC25 and cyclin E mechanisms were strongly implicated in G1/S malfunctions, while fragility in the G2/M checkpoint was predicted to be associated with the regulation of the cyclin B-CDK1 complex. Analysis of a third model containing both G1/S and G2/M checkpoint logic, predicted in addition to mechanisms already mentioned, that translation and programmed proteolysis were also key fragile subsystems. Comparison of the predicted fragile mechanisms with literature and current preclinical and clinical trials suggested a strong correlation between efficacy and fragility. Thus, when taken together, these results support the working hypothesis that cell-cycle control architectures are HOT networks and establish the mathematical estimation and subsequent therapeutic exploitation of fragile mechanisms as a novel strategy for anti-cancer lead generation

Incorporation of enzyme concentrations into FBA and identification of optimal metabolic pathways

<p>Abstract</p> <p>Background</p> <p>In the present article, we propose a method for determining optimal metabolic pathways in terms of the level of concentration of the enzymes catalyzing various reactions in the entire metabolic network. The method, first of all, generates data on reaction fluxes in a pathway based on steady state condition. A set of constraints is formulated incorporating weighting coefficients corresponding to concentration of enzymes catalyzing reactions in the pathway. Finally, the rate of yield of the target metabolite, starting with a given substrate, is maximized in order to identify an optimal pathway through these weighting coefficients.</p> <p>Results</p> <p>The effectiveness of the present method is demonstrated on two synthetic systems existing in the literature, two pentose phosphate, two glycolytic pathways, core carbon metabolism and a large network of carotenoid biosynthesis pathway of various organisms belonging to different phylogeny. A comparative study with the existing extreme pathway analysis also forms a part of this investigation. Biological relevance and validation of the results are provided. Finally, the impact of the method on metabolic engineering is explained with a few examples.</p> <p>Conclusions</p> <p>The method may be viewed as determining an optimal set of enzymes that is required to get an optimal metabolic pathway. Although it is a simple one, it has been able to identify a carotenoid biosynthesis pathway and the optimal pathway of core carbon metabolic network that is closer to some earlier investigations than that obtained by the extreme pathway analysis. Moreover, the present method has identified correctly optimal pathways for pentose phosphate and glycolytic pathways. It has been mentioned using some examples how the method can suitably be used in the context of metabolic engineering.</p

Optimization in computational systems biology

Optimization aims to make a system or design as effective or functional as possible. Mathematical optimization methods are widely used in engineering, economics and science. This commentary is focused on applications of mathematical optimization in computational systems biology. Examples are given where optimization methods are used for topics ranging from model building and optimal experimental design to metabolic engineering and synthetic biology. Finally, several perspectives for future research are outlined

An iterative identification procedure for dynamic modeling of biochemical networks

<p>Abstract</p> <p>Background</p> <p>Mathematical models provide abstract representations of the information gained from experimental observations on the structure and function of a particular biological system. Conferring a predictive character on a given mathematical formulation often relies on determining a number of non-measurable parameters that largely condition the model's response. These parameters can be identified by fitting the model to experimental data. However, this fit can only be accomplished when identifiability can be guaranteed.</p> <p>Results</p> <p>We propose a novel iterative identification procedure for detecting and dealing with the lack of identifiability. The procedure involves the following steps: 1) performing a structural identifiability analysis to detect identifiable parameters; 2) globally ranking the parameters to assist in the selection of the most relevant parameters; 3) calibrating the model using global optimization methods; 4) conducting a practical identifiability analysis consisting of two (<it>a priori </it>and <it>a posteriori</it>) phases aimed at evaluating the quality of given experimental designs and of the parameter estimates, respectively and 5) optimal experimental design so as to compute the scheme of experiments that maximizes the quality and quantity of information for fitting the model.</p> <p>Conclusions</p> <p>The presented procedure was used to iteratively identify a mathematical model that describes the NF-<it>κ</it>B regulatory module involving several unknown parameters. We demonstrated the lack of identifiability of the model under typical experimental conditions and computed optimal dynamic experiments that largely improved identifiability properties.</p