Maria Rodriguez-Fernandez

Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems

BackgroundWe consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness.ResultsWe have developed a new procedure based on the scatter search methodology for nonlinear optimization of dynamic models of arbitrary (or even unknown) structure (i.e. black-box models). In this contribution, we describe and apply this novel metaheuristic, inspired by recent developments in the field of operations research, to a set of complex identification problems and we make a critical comparison with respect to the previous (above mentioned) successful methods.ConclusionRobust and efficient methods for parameter estimation are of key importance in systems biology and related areas. The new metaheuristic presented in this paper aims to ensure the proper solution of these problems by adopting a global optimization approach, while keeping the computational effort under reasonable values. This new metaheuristic was applied to a set of three challenging parameter estimation problems of nonlinear dynamic biological systems, outperforming very significantly all the methods previously used for these benchmark problems.

Monte Carlo evaluation of derivative-based global sensitivity measures

Abstract A novel approach for evaluation of derivative-based global sensitivity measures (DGSM) is presented. It is compared with the Morris and the Sobol’ sensitivity indices methods. It is shown that there is a link between DGSM and Sobol’ sensitivity indices. DGSM are very easy to implement and evaluate numerically. The computational time required for numerical evaluation of DGSM is many orders of magnitude lower than that for estimation of the Sobol’ sensitivity indices. It is also lower than that for the Morris method. Efficiencies of Monte Carlo (MC) and quasi-Monte Carlo (QMC) sampling methods for calculation of DGSM are compared. It is shown that the superiority of QMC over MC depends on the problems effective dimension, which can also be estimated using DGSM.

Modeling cortisol dynamics in the neuro-endocrine axis distinguishes normal, depression, and post-traumatic stress disorder (PTSD) in humans.

Cortisol, secreted in the adrenal cortex in response to stress, is an informative biomarker that distinguishes anxiety disorders such as major depression and post-traumatic stress disorder (PTSD) from normal subjects. Yehuda et al. proposed a hypothesis that, in humans, the hypersensitive hypothalamus-pituitary-adrenal (HPA) axis is responsible for the occurrence of differing levels of cortisol in anxiety disorders. Specifically, PTSD subjects have lower cortisol levels during the late subjective night in comparison to normal subjects, and this was assumed to occur due to strong negative feedback loops in the HPA axis. In the present work, to address this hypothesis, we modeled the cortisol dynamics using nonlinear ordinary differential equations and estimated the kinetic parameters of the model to fit the experimental data of three categories, namely, normal, depressed, and PTSD human subjects. We concatenated the subjects (n = 3) in each category and created a model subject (n = 1) without considering the patient-to-patient variability in each case. The parameters of the model for the three categories were simultaneously obtained through global optimization. Bifurcation analysis carried out with the optimized parameters exhibited two supercritical Hopf points and, for the choice of parameters, the oscillations were found to be circadian in nature. The fitted kinetic parameters indicate that PTSD subjects have a strong negative feedback loop and, as a result, the predicted oscillating cortisol levels are extremely low at the nadir in contrast to normal subjects, albeit within the endocrinologic range. We also simulated the phenotypes for each of the categories and, as observed in the clinical data of PTSD patients, the simulated cortisol levels are consistently low at the nadir, and correspondingly the negative feedback was found to be extremely strong. These results from the model support the hypothesis that high stress intensity and strong negative feedback loop may cause hypersensitive neuro-endocrine axis that results in hypocortisolemia in PTSD.

SensSB: a software toolbox for the development and sensitivity analysis of systems biology models

SUMMARY SensSB (Sensitivity Analysis for Systems Biology) is an easy to use, MATLAB-based software toolbox, which integrates several local and global sensitivity methods that can be applied to a wide variety of biological models. In addition to addressing the sensitivity analysis problem, SensSB aims to cover all the steps involved during the modeling process. The main features of SensSB are: (i) derivative and variance-based global sensitivity analysis, (ii) pseudo-global identifiability analysis, (iii) optimal experimental design (OED) based on global sensitivities, (iv) robust parameter estimation, (v) local sensitivity and identifiability analysis, (vi) confidence intervals of the estimated parameters and (vii) OED based on the Fisher Information Matrix (FIM). SensSB is also able to import models in the Systems Biology Mark-up Language (SBML) format. Several examples from simple analytical functions to more complex biological pathways have been implemented and can be downloaded together with the toolbox. The importance of using sensitivity analysis techniques for identifying unessential parameters and designing new experiments is quantified by increased identifiability metrics of the models and decreased confidence intervals of the estimated parameters. AVAILABILITY SensSB is a software toolbox freely downloadable from http://www.iim.csic.es/ approximately gingproc/SensSB.html. The web site also contains several examples and an extensive documentation. CONTACT mrodriguez@iim.csic.es SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.

Simultaneous model discrimination and parameter estimation in dynamic models of cellular systems

BackgroundModel development is a key task in systems biology, which typically starts from an initial model candidate and, involving an iterative cycle of hypotheses-driven model modifications, leads to new experimentation and subsequent model identification steps. The final product of this cycle is a satisfactory refined model of the biological phenomena under study. During such iterative model development, researchers frequently propose a set of model candidates from which the best alternative must be selected. Here we consider this problem of model selection and formulate it as a simultaneous model selection and parameter identification problem. More precisely, we consider a general mixed-integer nonlinear programming (MINLP) formulation for model selection and identification, with emphasis on dynamic models consisting of sets of either ODEs (ordinary differential equations) or DAEs (differential algebraic equations).ResultsWe solved the MINLP formulation for model selection and identification using an algorithm based on Scatter Search (SS). We illustrate the capabilities and efficiency of the proposed strategy with a case study considering the KdpD/KdpE system regulating potassium homeostasis in Escherichia coli. The proposed approach resulted in a final model that presents a better fit to the in silico generated experimental data.ConclusionsThe presented MINLP-based optimization approach for nested-model selection and identification is a powerful methodology for model development in systems biology. This strategy can be used to perform model selection and parameter estimation in one single step, thus greatly reducing the number of experiments and computations of traditional modeling approaches.

Quantity and accessibility for specific targeting of receptors in tumours.

Synaphic (ligand-directed) targeting of drugs is an important potential new approach to drug delivery, particularly in oncology. Considerable success with this approach has been achieved in the treatment of blood-borne cancers, but the advances with solid tumours have been modest. Here, we have studied the number and availability for ligand binding of the receptors for two targeting ligands. The results show that both paucity of total receptors and their poor availability are major bottlenecks in drug targeting. A tumour-penetrating peptide greatly increases the availability of receptors by promoting transport of the drug to the extravascular tumour tissue, but the number of available receptors still remains low, severely limiting the utility of the approach. Our results emphasize the importance of using drugs with high specific activity to avoid exceeding receptor capacity because any excess drug conjugate would lose the targeting advantage. The mathematical models we describe make it possible to focus on those aspects of the targeting mechanism that are most likely to have a substantial effect on the overall efficacy of the targeting.

Detailed kinetic model describing new oligosaccharides synthesis using different β-galactosidases

The production of prebiotic galactooligosaccharides (GOS) from lactose has been widely studied whereas the synthesis of new prebiotic oligosaccharides with improved properties as those derived from lactulose is receiving an increasing interest. Understanding the mechanism of enzymatic oligosaccharides synthesis from lactulose would help to improve the quality of the products in a rational way as well as to increase the production efficiency by optimally selecting the operating conditions. A detailed kinetic model describing the enzymatic transgalactosylation reaction during lactulose hydrolysis is presented here for the first time. The model was calibrated with the experimental data obtained in batch assays with two different β-galactosidases at various temperatures and concentrations of substrate. A complete system identification loop, including model selection, robust estimation of the parameters by means of a global optimization method and computation of confidence intervals was performed. The kinetic model showed a good agreement between experimental data and predictions for lactulose conversion and provided important insights into the mechanism of formation of new oligosaccharides with potential prebiotic properties.

Modeling the Intra- and Extracellular Cytokine Signaling Pathway under Heat Stroke in the Liver

Heat stroke (HS) is a life-threatening illness induced by prolonged exposure to a hot environment that causes central nervous system abnormalities and severe hyperthermia. Current data suggest that the pathophysiological responses to heat stroke may not only be due to the immediate effects of heat exposure per se but also the result of a systemic inflammatory response syndrome (SIRS). The observation that pro- (e.g., IL-1) and anti-inflammatory (e.g., IL-10) cytokines are elevated concomitantly during recovery suggests a complex network of interactions involved in the manifestation of heat-induced SIRS. In this study, we measured a set of circulating cytokine/soluble cytokine receptor proteins and liver cytokine and receptor mRNA accumulation in wild-type and tumor necrosis factor (TNF) receptor knockout mice to assess the effect of neutralization of TNF signaling on the SIRS following HS. Using a systems approach, we developed a computational model describing dynamic changes (intra- and extracellular events) in the cytokine signaling pathways in response to HS that was fitted to novel genomic (liver mRNA accumulation) and proteomic (circulating cytokines and receptors) data using global optimization. The model allows integration of relevant biological knowledge and formulation of new hypotheses regarding the molecular mechanisms behind the complex etiology of HS that may serve as future therapeutic targets. Moreover, using our unique modeling framework, we explored cytokine signaling pathways with three in silico experiments (e.g. by simulating different heat insult scenarios and responses in cytokine knockout strains in silico).

Attenuated thermoregulatory, metabolic, and liver acute phase protein response to heat stroke in TNF receptor knockout mice

Tumor necrosis factor (TNF) is considered an adverse mediator of heat stroke (HS) based on clinical studies showing high serum levels. However, soluble TNF receptors (sTNFR; TNF antagonists) were higher in survivors than nonsurvivors, and TNFR knockout (KO) mice showed a trend toward increased mortality, suggesting TNF has protective actions for recovery. We delineated TNF actions in HS by comparing thermoregulatory, metabolic, and inflammatory responses between B6129F2 (wild type, WT) and TNFR KO mice. Before heat exposure, TNFR KO mice showed ~0.4°C lower core temperature (T(c); radiotelemetry), ~10% lower metabolic rate (M(r); indirect calorimetry), and reduced plasma interleukin (IL)-1α and sIL-1RI than WT mice. KO mice selected warmer temperatures than WT mice in a gradient but remained hypothermic. In the calorimeter, both genotypes showed a similar heating rate, but TNFR KO maintained lower T(c) and M(r) than WT mice for a given heat exposure duration and required ~30 min longer to reach maximum T(c) (42.4°C). Plasma IL-6 increased at ~3 h of recovery in both genotypes, but KO mice showed a more robust sIL-6R response. Higher sIL-6R in the KO mice was associated with delayed liver p-STAT3 protein expression and attenuated serum amyloid A3 (SAA3) gene expression, suggesting the acute phase response (APR) was attenuated in these mice. Our data suggest that the absence of TNF signaling induced a regulated hypothermic state in the KO mice, TNF-IL-1 interactions may modulate T(c) and M(r) during homeostatic conditions, and TNF modulates the APR during HS recovery through interactions with the liver IL-6-STAT3 pathway of SAA3 regulation.

A Detailed Modular Analysis of Heat-Shock Protein Dynamics under Acute and Chronic Stress and Its Implication in Anxiety Disorders

Physiological and psychological stresses cause anxiety disorders such as depression and post-traumatic stress disorder (PTSD) and induce drastic changes at a molecular level in the brain. To counteract this stress, the heat-shock protein (HSP) network plays a vital role in restoring the homeostasis of the system. To study the stress-induced dynamics of heat-shock network, we analyzed three modules of the HSP90 network—namely trimerization reactions, phosphorylation–dephosphorylation reactions, and the conversion of HSP90 from an open to a closed conformation—and constructed a corresponding nonlinear differential equation model based on mass action kinetics laws. The kinetic parameters of the model were obtained through global optimization, and sensitivity analyses revealed that the most sensitive parameters are the kinase and phosphatase that drive the phosphorylation–dephosphorylation reactions. Bifurcation analysis carried out with the estimated kinetic parameters of the model with stress as bifurcation parameter revealed the occurrence of “mushroom”, a type of complex dynamics in which S-shaped and Z-shaped hysteretic bistable forms are present together. We mapped the molecular events responsible for generating the mushroom dynamics under stress and interpreted the occurrence of the S-shaped hysteresis to a normal level of stress, and the Z-shaped hysteresis to the HSP90 variations under acute and chronic stress in the fear conditioned system, and further, we hypothesized that this can be extended to stress-related disorders such as depression and PTSD in humans. Finally, we studied the effect of parameter variations on the mushroom dynamics to get insight about the role of phosphorylation–dephosphorylation parameters in HSP90 network in bringing about complex dynamics such as isolas, where the stable steady states in a bistable system are isolated and separated from each other and not connected by an unstable steady state.