RankAggreg, an R package for weighted rank aggregation

Background

Determining the parameters of a mathematical model from quantitative measurements is the main bottleneck of modelling biological systems. Parameter values can be estimated from steady-state data or from dynamic data. The nature of suitable data for these two types of estimation is rather different. For instance, estimations of parameter values in pathway models, such as kinetic orders, rate constants, flux control coefficients or elasticities, from steady-state data are generally based on experiments that measure how a biochemical system responds to small perturbations around the steady state. In contrast, parameter estimation from dynamic data requires time series measurements for all dependent variables. Almost no literature has so far discussed the combined use of both steady-state and transient data for estimating parameter values of biochemical systems.

Results

In this study we introduce a constrained optimization method for estimating parameter values of biochemical pathway models using steady-state information and transient measurements. The constraints are derived from the flux connectivity relationships of the system at the steady state. Two case studies demonstrate the estimation results with and without flux connectivity constraints. The unconstrained optimal estimates from dynamic data may fit the experiments well, but they do not necessarily maintain the connectivity relationships. As a consequence, individual fluxes may be misrepresented, which may cause problems in later extrapolations. By contrast, the constrained estimation accounting for flux connectivity information reduces this misrepresentation and thereby yields improved model parameters.

Conclusion

The method combines transient metabolic profiles and steady-state information and leads to the formulation of an inverse parameter estimation task as a constrained optimization problem. Parameter estimation and model selection are simultaneously carried out on the constrained optimization problem and yield realistic model parameters that are more likely to hold up in extrapolations with the model.     

Translating biochemical network models between different kinetic formats

Mechanistic biochemical network models describe the dynamics of intracellular metabolite pools in terms of substance concentrations, stoichiometry and reaction kinetics. Data from stimulus response experiments are currently the most informative source for in-vivo parameter estimation in such models. However, only a part of the parameters of classical enzyme kinetic models can usually be estimated from typical stimulus response data. For this reason, several alternative kinetic formats using different “languages” (e.g. linear, power laws, linlog, generic and convenience) have been proposed to reduce the model complexity. The present contribution takes a rigorous “multi-lingual” approach to data evaluation by translating biochemical network models from one kinetic format into another. For this purpose, a new high-performance algorithm has been developed and tested. Starting with a given model, it replaces as many kinetic terms as possible by alternative expressions while still reproducing the experimental data. Application of the algorithm to a published model for Escherichia coli's sugar metabolism demonstrates the power of the new method. It is shown that model translation is a powerful tool to investigate the information content of stimulus response data and the predictive power of models. Moreover, the local and global approximation capabilities of the models are elucidated and some pitfalls of traditional single model approaches to data evaluation are revealed.     

Simultaneous versus sequential optimal experiment design for the identification of multi-parameter microbial growth kinetics as a function of temperature

Optimal experiment design for parameter estimation (OED/PE) has become a popular tool for efficient and accurate estimation of kinetic model parameters. When the kinetic model under study encloses multiple parameters, different optimization strategies can be constructed. The most straightforward approach is to estimate all parameters simultaneously from one optimal experiment (single OED/PE strategy). However, due to the complexity of the optimization problem or the stringent limitations on the system's dynamics, the experimental information can be limited and parameter estimation convergence problems can arise. As an alternative, we propose to reduce the optimization problem to a series of two-parameter estimation problems, i.e., an optimal experiment is designed for a combination of two parameters while presuming the other parameters known. Two different approaches can be followed: (i) all two-parameter optimal experiments are designed based on identical initial parameter estimates and parameters are estimated simultaneously from all resulting experimental data (global OED/PE strategy), and (ii) optimal experiments are calculated and implemented sequentially whereby the parameter values are updated intermediately (sequential OED/PE strategy).This work exploits OED/PE for the identification of the Cardinal Temperature Model with Inflection (CTMI) (Rosso et al., 1993). This kinetic model describes the effect of temperature on the microbial growth rate and encloses four parameters. The three OED/PE strategies are considered and the impact of the OED/PE design strategy on the accuracy of the CTMI parameter estimation is evaluated. Based on a simulation study, it is observed that the parameter values derived from the sequential approach deviate more from the true parameters than the single and global strategy estimates. The single and global OED/PE strategies are further compared based on experimental data obtained from design implementation in a bioreactor. Comparable estimates are obtained, but global OED/PE estimates are, in general, more accurate and reliable.     

Deterministic global optimization algorithm based on outer approximation for the parameter estima- tion of nonlinear dynamic biological systems

ABSTRACT: BACKGROUND: The estimation of parameter values for mathematical models of biological systems is an optimization problem that is particularly challenging due to the nonlinearities involved. One major difficulty is the existence of multiple minima in which standard optimization methods may fall during the search. Deterministic global optimization methods overcome this limitation, ensuring convergence to the global optimum within a desired tolerance. Global optimization techniques are typically classified into stochastic and deterministic. The former typically lead to lower CPU times but offer no guarantee of convergence to the global minimum in a finite number of iterations. In contrast, deterministic methods provide solutions of a given quality (i.e., optimality gap), but tend to lead to large computational burdens. RESULTS: This work presents a deterministic outer approximation-based algorithm for the global optimization of dynamic problems arising in the parameter estimation of models of biological systems. Our approach, which offers a theoretical guarantee of convergence to the global minimum, reformulating the set of ordinary differential equations into an equivalent set of algebraic equations through the use of orthogonal collocation methods, giving rise to a nonconvex nonlinear programming (NLP) problem. This nonconvex NLP is decomposed into two hierarchical levels: a master mixed-integer linear programming problem (MILP) that provides a rigorous lower bound on the optimal solution, and a reduced-space slave NLP that yields an upper bound. The algorithm iterates between these two levels until a termination criterion is satisfied. CONCLUSION: The capabilities of our approach were tested in two benchmark problems, in which the performance of our algorithm was compared with that of the commercial global optimization package BARON. The proposed strategy produced near optimal solutions (i.e., within a desired tolerance) in a fraction of the CPU time required by BARON.     

Identification of sparse neural functional connectivity using penalized likelihood estimation and basis functions

One key problem in computational neuroscience and neural engineering is the identification and modeling of functional connectivity in the brain using spike train data. To reduce model complexity, alleviate overfitting, and thus facilitate model interpretation, sparse representation and estimation of functional connectivity is needed. Sparsities include global sparsity, which captures the sparse connectivities between neurons, and local sparsity, which reflects the active temporal ranges of the input-output dynamical interactions. In this paper, we formulate a generalized functional additive model (GFAM) and develop the associated penalized likelihood estimation methods for such a modeling problem. A GFAM consists of a set of basis functions convolving the input signals, and a link function generating the firing probability of the output neuron from the summation of the convolutions weighted by the sought model coefficients. Model sparsities are achieved by using various penalized likelihood estimations and basis functions. Specifically, we introduce two variations of the GFAM using a global basis (e.g., Laguerre basis) and group LASSO estimation, and a local basis (e.g., B-spline basis) and group bridge estimation, respectively. We further develop an optimization method based on quadratic approximation of the likelihood function for the estimation of these models. Simulation and experimental results show that both group-LASSO-Laguerre and group-bridge-B-spline can capture faithfully the global sparsities, while the latter can replicate accurately and simultaneously both global and local sparsities. The sparse models outperform the full models estimated with the standard maximum likelihood method in out-of-sample predictions.     

Optimal sampling time selection for parameter estimation in dynamic pathway modeling

Systems Biology is an emerging research area, which considers mathematical representations of inter- and intra-cellular dynamics. Among the many research problems that have been addressed, dynamic modeling of signal transduction pathways has received increasing attention. The usual approach to represent intra-cellular dynamics are nonlinear, usually ordinary, differential equations. The purpose of the models is to test and generate hypothesis of specific pathways and it is therefore required to estimate model parameters from experimental data. The experiments to generate data are complex and expensive, as a consequence of which the time series available are usually rather short, with few if any replicates. Almost certainly, not all variables one would like to include in a model can be measured. Parameter estimation is therefore an important research problem in Systems Biology and the focus of this paper. In particular, we are interested in optimizing the sampling time selection in order to minimize the variance of the parameter estimation error. With few sampling time points feasible, their selection is of practical importance in experimental design. Finally, the theoretical results are supported with an application.     

Quantitative Redox Biology: An Approach to Understand the Role of Reactive Species in Defining the Cellular Redox Environment

Systems biology is now recognized as a needed approach to understand the dynamics of inter- and intra-cellular processes. Redox processes are at the foundation of nearly all aspects of biology. Free radicals, related oxidants, and antioxidants are central to the basic functioning of cells and tissues. They set the cellular redox environment and, therefore, are the key to regulation of biochemical pathways and networks, thereby influencing organism health. To understand how short-lived, quasi-stable species, such as superoxide, hydrogen peroxide, and nitric oxide, connect to the metabolome, proteome, lipidome, and genome we need absolute quantitative information on all redox active compounds as well as thermodynamic and kinetic information on their reactions, i.e., knowledge of the complete redoxome. Central to the state of the redoxome are the interactive details of the superoxide/peroxide formation and removal systems. Quantitative information is essential to establish the dynamic mathematical models needed to reveal the temporal evolution of biochemical pathways and networks. This new field of Quantitative Redox Biology will allow researchers to identify new targets for intervention to advance our efforts to achieve optimal human health.     

Rich parameterization improves RNA structure prediction

Current approaches to RNA structure prediction range from physics-based methods, which rely on thousands of experimentally measured thermodynamic parameters, to machine-learning (ML) techniques. While the methods for parameter estimation are successfully shifting toward ML-based approaches, the model parameterizations so far remained fairly constant. We study the potential contribution of increasing the amount of information utilized by RNA folding prediction models to the improvement of their prediction quality. This is achieved by proposing novel models, which refine previous ones by examining more types of structural elements, and larger sequential contexts for these elements. Our proposed fine-grained models are made practical thanks to the availability of large training sets, advances in machine-learning, and recent accelerations to RNA folding algorithms. We show that the application of more detailed models indeed improves prediction quality, while the corresponding running time of the folding algorithm remains fast. An additional important outcome of this experiment is a new RNA folding prediction model (coupled with a freely available implementation), which results in a significantly higher prediction quality than that of previous models. This final model has about 70,000 free parameters, several orders of magnitude more than previous models. Being trained and tested over the same comprehensive data sets, our model achieves a score of 84% according to the F?-measure over correctly-predicted base-pairs (i.e., 16% error rate), compared to the previously best reported score of 70% (i.e., 30% error rate). That is, the new model yields an error reduction of about 50%. Trained models and source code are available at www.cs.bgu.ac.il/?negevcb/contextfold.     

Practical identifiability of biokinetic parameters of a model describing two-step nitrification in biofilms

Parameter estimation and model calibration are key problems in the application of biofilm models in engineering practice, where a large number of model parameters need to be determined usually based on experimental data with only limited information content. In this article, identifiability of biokinetic parameters of a biofilm model describing two-step nitrification was evaluated based solely on bulk phase measurements of ammonium, nitrite, and nitrate. In addition to evaluating the impact of experimental conditions and available measurements, the influence of mass transport limitation within the biofilm and the initial parameter values on identifiability of biokinetic parameters was evaluated. Selection of parameters for identifiability analysis was based on global mean sensitivities while parameter identifiability was analyzed using local sensitivity functions. At most, four of the six most sensitive biokinetic parameters were identifiable from results of batch experiments at bulk phase dissolved oxygen concentrations of 0.8 or 5 mg O(2)/L. High linear dependences between the parameters of the subsets (KO2,AOB,muAOB) and (KO2,NOB,muNOB) resulted in reduced identifiability. Mass transport limitation within the biofilm did not influence the number of identifiable parameters but, in fact, decreased collinearity between parameters, especially for parameters that are otherwise correlated (e.g., muAOB) and KO2,AOB, or muNOB and KO2,NOB). The choice of the initial parameter values had a significant impact on the identifiability of two parameter subsets, both including the parameters muAOB and KO2,AOB. Parameter subsets that did not include the subsets muAOB and KO2,AOB or muNOB and KO2,NOB were clearly identifiable independently of the choice of the initial parameter values.     

Extended Kalman Filter for Estimation of Parameters in Nonlinear State-Space Models of Biochemical Networks

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.     

A new approach of fitting biomass dynamics models to data

A non-traditional approach of fitting dynamic resource biomass models to data is developed in this paper. A variational adjoint technique is used for dynamic parameter estimation. In the variational formulation, a cost function measuring the distance between the model solution and the observations is minimized. The data assimilation method provides a novel and computationally efficient procedure for combining all available information, i.e., the data and the model in the analysis of a resource system. This technique will be used to analyze data for the North-east Arctic cod stock. Two alternative population growth models: the logistic and the Gompertz model are used for estimating parameters of simple bioeconomic models by the method of constrained least squares. Estimates of the parameters of the models dynamics are reasonable and can be accepted. The main inference from the work is that the average fishing mortality is found to be significantly above the maximum sustainable yield value.     

Stimulus design for model selection and validation in cell signaling

Mechanism-based chemical kinetic models are increasingly being used to describe biological signaling. Such models serve to encapsulate current understanding of pathways and to enable insight into complex biological processes. One challenge in model development is that, with limited experimental data, multiple models can be consistent with known mechanisms and existing data. Here, we address the problem of model ambiguity by providing a method for designing dynamic stimuli that, in stimulus–response experiments, distinguish among parameterized models with different topologies, i.e., reaction mechanisms, in which only some of the species can be measured. We develop the approach by presenting two formulations of a model-based controller that is used to design the dynamic stimulus. In both formulations, an input signal is designed for each candidate model and parameterization so as to drive the model outputs through a target trajectory. The quality of a model is then assessed by the ability of the corresponding controller, informed by that model, to drive the experimental system. We evaluated our method on models of antibody–ligand binding, mitogen-activated protein kinase (MAPK) phosphorylation and de-phosphorylation, and larger models of the epidermal growth factor receptor (EGFR) pathway. For each of these systems, the controller informed by the correct model is the most successful at designing a stimulus to produce the desired behavior. Using these stimuli we were able to distinguish between models with subtle mechanistic differences or where input and outputs were multiple reactions removed from the model differences. An advantage of this method of model discrimination is that it does not require novel reagents, or altered measurement techniques; the only change to the experiment is the time course of stimulation. Taken together, these results provide a strong basis for using designed input stimuli as a tool for the development of cell signaling models.     

陆地植被净初级生产力计算模型研究进展

植被净初级生产力(NPP)研究是全球变化与陆地生态系统的核心内容之一。在回顾NPP模型研究的基础上,综合分析了气候模型、生态生理过程模型、光能利用率模型各自的优缺点,并对NPP模型研究做出展望。生态生理过程模型是当前陆地NPP估算研究的主要手段,而区域尺度转换则是它所面临的关键问题。近年来光能利用率模型已成为NPP估算的一种全新手段,它利用遥感所获得的全覆盖数据,使区域及全球尺度的NPP估算成为可能,但其生态学机理还有待于进一步研究。已有研究表明,“生态一遥感耦合模型”将是陆地NPP估算的主要发展方向,它融合了生态生理过程模型和光能利用率模型的优点,增强了NPP模型估算的可靠性和可操作性。     

SBML-PET: a Systems Biology Markup Language-based parameter estimation tool

The estimation of model parameters from experimental data remains a bottleneck for a major breakthrough in systems biology. We present a Systems Biology Markup Language (SBML) based Parameter Estimation Tool (SBML-PET). The tool is designed to enable parameter estimation for biological models including signaling pathways, gene regulation networks and metabolic pathways. SBML-PET supports import and export of the models in the SBML format. It can estimate the parameters by fitting a variety of experimental data from different experimental conditions. SBML-PET has a unique feature of supporting event definition in the SMBL model. SBML models can also be simulated in SBML-PET. Stochastic Ranking Evolution Strategy (SRES) is incorporated in SBML-PET for parameter estimation jobs. A classic ODE Solver called ODEPACK is used to solve the Ordinary Differential Equation (ODE) system. AVAILABILITY: http://sysbio.molgen.mpg.de/SBML-PET/. The website also contains detailed documentation for SBML-PET.     

A decompositional approach to parameter estimation in pathway modeling: a case study of the Akt and MAPK pathways and their crosstalk

Parameter estimation is a critical problem in modeling biological pathways. It is difficult because of the large number of parameters to be estimated and the limited experimental data available. In this paper, we propose a decompositional approach to parameter estimation. It exploits the structure of a large pathway model to break it into smaller components, whose parameters can then be estimated independently. This leads to significant improvements in computational efficiency. We present our approach in the context of Hybrid Functional Petri Net modeling and evolutionary search for parameter value estimation. However, the approach can be easily extended to other modeling frameworks and is independent of the search method used. We have tested our approach on a detailed model of the Akt and MAPK pathways with two known and one hypothesized crosstalk mechanisms. The entire model contains 84 unknown parameters. Our simulation results exhibit good correlation with experimental data, and they yield positive evidence in support of the hypothesized crosstalk between the two pathways.     

MMT--a pathway modeling tool for data from rapid sampling experiments

The identification of metabolic regulation is a major concern in metabolic engineering. Metabolic regulation phenomena depend on intracellular compounds such as enzymes, metabolites and cofactors. A complete understanding of metabolic regulation requires quantitative information about these compounds under in vivo conditions. This quantitative knowledge in combination with the known network of metabolic pathways allows the construction of mathematical models that describe the dynamic changes in metabolite concentrations over time. Rapid sampling combined with pulse experiments is a useful tool for the identification of metabolic regulation owing to the transient data they provide. Enzymatic tests in combination with ESI-LC-MS (Electrospray Ionization Liquid Chromatographic Tandem Mass Spectrometry) and HPLC measurements have been used to identify up to 30 metabolites and nucleotides from rapid sampling experiments. A metabolic modeling tool (MMT) that is built on a relational database was developed specifically for analysis of rapid sampling experiments. The tool allows to construct complex pathway models with information stored in the relational database. Parameter fitting and simulation algorithms for the resulting system of Ordinary Differential Equations (ODEs) are part of MMT. Additionally explicit sensitivity functions are calculated. The integration of all necessary algorithms in one tool allows fast model analysis and comparison. Complex models have been developed to describe the central metabolic pathways of Escherichia coli during a glucose pulse experiment.     

Global stability and optimisation of a general impulsive biological control model

An impulsive model of augmentative biological control consisting of a general continuous predator-prey model in ordinary differential equations, i.e. a meta-model, augmented by a discrete part describing periodic introductions of predators is considered. The existence of an invariant periodic solution that corresponds to prey eradication is shown and a condition ensuring its global asymptotic stability is given. An optimisation problem related to the preemptive use of augmentative biological control is then considered. It is assumed that the per time unit budget of biological control (i.e. the number of predators to be released) is fixed and the best deployment of this budget is sought in terms of release frequency. The cost function to be minimised is the time needed to reduce an unforeseen prey (pest) invasion occurring at a worst time instant under some harmless level. The analysis shows that the optimisation problem admits a countable infinite number of solutions. An argumentation considering the required robustness of the optimisation result with respect to the invasive prey population level and to the model parameters is then conducted. It is shown that the cost function is decreasing in the predator release frequency so that the best deployment of the biocontrol agents is to carry out as frequent introductions as possible.     

Quantifying Burial,the Transport of Matter from the Lake Biosphere to the Geosphere

Burial is one of the most fundamental processes in contexts of massbalance calculations for substances (such as nutrients, organics, metals and radionuclides) in lakes. Substances can leave a lake by two processes, outflow, i.e., the transport to a downstream system, and burial, i.e., the transport by sedimentation from the lake biosphere to the geosphere. This work gives for the first time, to there best of the author's knowledge, a review on the factors and processes regulating burial and presents a general model for burial. This approach accounts for bottom dynamic conditions (i.e., where areas of fine sediment erosion, transport and accumulation prevail), sedimentation, bioturbation, mineralisation, and the depth and age of the bioactive sediment layer. This approach has been critically tested with very good results for radiocesium, radiostrontium, many metals, calcium from liming and phosphorus, but it has not been presented before in a comprehensive way. This model for burial is meant to be used in massbalance models based on ordinary differential equations (i.e., box models) in contexts where burial is not a target y‐variable but a necessary model variable (an x‐variable). This means that there are also specific demands on this approach, e.g., it must be based on readily accessible driving variables so that it is not too difficult to use the model in practice within the context of an overall lake model. The factors influencing burial, e.g., the deposition of materials and the depth of the bioactive sediment layer, are also needed in calculations of sediment concentrations and to determine amounts of substances or pollutants in sediments. To carry out such calculations, one also needs information on sediment bulk density, water content and organic content. This paper also presents new empirical models for such calculations to be used in the new model for burial.     

Globally optimised parameters for a model of mitotic control in frog egg extracts

DNA synthesis and nuclear division in the developing frog egg are controlled by fluctuations in the activity of M-phase promoting factor (MPF). The biochemical mechanism of MPF regulation is most easily studied in cytoplasmic extracts of frog eggs, for which careful experimental studies of the kinetics of phosphorylation and dephosphorylation of MPF and its regulators have been made. In 1998 Marlovits et al. used these data sets to estimate the kinetic rate constants in a mathematical model of the control system originally proposed by Novak & Tyson. In a recent publication, we showed that a gradient-based optimisation algorithm finds a locally optimal parameter set quite close to the 'Marlovits' estimates. In this paper, we combine global and local optimisation strategies to show that the 'refined Marlovits' parameter set, with one minor but significant modification to the Novak & Tyson equations, is the unique, best-fitting solution to the parameter estimation problem.