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Metabolism results from enzymatic- and non-enzymatic interactions of several molecules, is easily parameterized with the dissociation constant and occurs via biochemical networks. The dissociation constant is an empirically determined parameter and cannot be used directly to investigate in silico models of biochemical networks. Here, we develop and present an algorithm to define, compute and assess the relevance of the probable dissociation constant for every reaction of a biochemical network. The reactants and reactions of this network are modelled by a stoichiometry number matrix. The algorithm computes the null space and then serially generates subspaces by combinatorially summing the spanning vectors that are non-trivial and unique. This is done until the terms of each row either monotonically diverge or form an alternating sequence whose terms can be partitioned into subsets with almost the same number of oppositely signed terms. For a selected null space-generated subspace the algorithm utilizes several statistical and mathematical descriptors to select and bin terms from each row into distinct outcome-specific subsets. The terms of each subset are summed, mapped to the real-valued open interval 0 , ∞ and used to populate a reaction-specific outcome vector. The p1-norm for this vector is then the probable dissociation constant for this reaction. These steps are continued until every reaction of a modelled network is unambiguously annotated. The assertions presented are complemented by computational studies of a biochemical network for aerobic glycolysis. The fundamental premise of this work is that every row of a null space-generated subspace is a valid reaction and can therefore, be modelled as a reaction-specific sequence vector with a dimension that corresponds to the cardinality of the subspace after excluding all trivial- and redundant-vectors. A major finding of this study is that the row-wise sum or the sum of the terms contained in each reaction-specific sequence vector is mapped unambiguously to a positive real number. This means that the probable dissociation constants, for all reactions, can be directly computed from the stoichiometry number matrix and are suitable indicators of outcome for every reaction of the modelled biochemical network. Additionally, we find that the unambiguous annotation for a biochemical network will require a minimum number of iterations and will determine computational complexity. [ABSTRACT FROM AUTHOR]

We present an adaptation of the Approximate Bayesian Computation method to estimate the satisfaction probability function of a temporal logic property for Markov Population Models. In this paper, we tackle the problem of estimating the satisfaction probability function of a temporal logic property w.r.t. a parametric Markovian model of Chemical Reaction Network. We want to assess the probability with which the trajectories generated by a parametric Markov Population Model (MPM) satisfy a logical formula over the whole parameter space. In the first step of the work, we formally define a distance between a trajectory of an MPM and a logical property. If the distance is 0, the trajectory satisfies the property. The larger the distance is, further the trajectory is from satisfying the property. In the second step, we adapt the Approximate Bayesian Computation method using the distance defined in the first step. This adaptation yields a new algorithm, called automaton-ABC, whose output is a density function that directly leads to the estimation of the desired satisfaction probability function. We apply our methodology to several examples and models, and we compare it to state-of-the-art techniques. We show that the sequential version of our algorithm relying on ABC-SMC leads to an efficient exploration of the parameter space with respect to the formula and gives good approximations of the satisfaction probability function at a reduced computational cost. • We develop the notion of satisfiability distance for the path of a Markov Population Model from an MITL property. • We detail how Linear Hybrid Automata computes such satisfiability distances. • We develop a new method called automaton-ABC that estimates the satisfaction probability function of a parametric MPM. • We test it on several models of biochemical networks to show the efficiency of the method. [ABSTRACT FROM AUTHOR]

The development of mechanistic models of biological systems is a central part of Systems Biology. One major challenge in developing these models is the accurate inference of model parameters. In recent years, nested sampling methods have gained increased attention in the Systems Biology community due to the fact that they are parallelizable and provide error estimates with no additional computations. One drawback that severely limits the usability of these methods, however, is that they require the likelihood function to be available, and thus cannot be applied to systems with intractable likelihoods, such as stochastic models. Here we present a likelihood-free nested sampling method for parameter inference which overcomes these drawbacks. This method gives an unbiased estimator of the Bayesian evidence as well as samples from the posterior. We derive a lower bound on the estimators variance which we use to formulate a novel termination criterion for nested sampling. The presented method enables not only the reliable inference of the posterior of parameters for stochastic systems of a size and complexity that is challenging for traditional methods, but it also provides an estimate of the obtained variance. We illustrate our approach by applying it to several realistically sized models with simulated data as well as recently published biological data. We also compare our developed method with the two most popular other likeliood-free approaches: pMCMC and ABC-SMC. The C++ code of the proposed methods, together with test data, is available at the github web page https://github.com/Mijan/LFNS_paper. Author summary: The behaviour of mathematical models of biochemical reactions is governed by model parameters encoding for various reaction rates, molecule concentrations and other biochemical quantities. As the general purpose of these models is to reproduce and predict the true biological response to different stimuli, the inference of these parameters, given experimental observations, is a crucial part of Systems Biology. While plenty of methods have been published for the inference of model parameters, most of them require the availability of the likelihood function and thus cannot be applied to models that do not allow for the computation of the likelihood. Further, most established methods do not provide an estimate of the variance of the obtained estimator. In this paper, we present a novel inference method that accurately approximates the posterior distribution of parameters and does not require the evaluation of the likelihood function. Our method is based on the nested sampling algorithm and approximates the likelihood with a particle filter. We show that the resulting posterior estimates are unbiased and provide a way to estimate not just the posterior distribution, but also an error estimate of the final estimator. We illustrate our method on several stochastic models with simulated data as well as one model of transcription with real biological data. [ABSTRACT FROM AUTHOR]

To infer the parameters of mechanistic models with intractable likelihoods, techniques such as approximate Bayesian computation (ABC) are increasingly being adopted. One of the main disadvantages of ABC in practical situations, however, is that parameter inference must generally rely on summary statistics of the data. This is particularly the case for problems involving high-dimensional data, such as biological imaging experiments. However, some summary statistics contain more information about parameters of interest than others, and it is not always clear how to weight their contributions within the ABC framework. We address this problem by developing an automatic, adaptive algorithm that chooses weights for each summary statistic. Our algorithm aims to maximize the distance between the prior and the approximate posterior by automatically adapting the weights within the ABC distance function. Computationally, we use a nearest neighbour estimator of the distance between distributions. We justify the algorithm theoretically based on properties of the nearest neighbour distance estimator. To demonstrate the effectiveness of our algorithm, we apply it to a variety of test problems, including several stochastic models of biochemical reaction networks, and a spatial model of diffusion, and compare our results with existing algorithms. [ABSTRACT FROM AUTHOR]

Parameter estimation for models of biochemical systems is computationally expensive due to the nonlinearity and high dimensionality of the coupled systems of ordinary differential equations underlying the models. Hence, it is important to apply novel methods to the problem and evaluate their performance. We consider the Bat algorithm (BA) and the Firefly algorithm (FA) with respect to parameter estimation of S-system models. Using three S-systems of increasing complexity from the MADMan benchmarking framework, we assess and compare the relative performance of the two algorithms relative to various data sets, initial conditions, and noise levels. Simulation results show that both algorithms can be effectively used in estimating parameters of the S-system models. In particular, in all three S-systems used, the FA performed better than the BA based on the final cost function values and relative estimate errors. The introduction of noise to data significantly affected the convergence of both algorithms. [ABSTRACT FROM AUTHOR]

A persistent obstacle for constructing kinetic models of metabolism is uncertainty in the kinetic properties of enzymes. Currently, available methods for building kinetic models can cope indirectly with uncertainties by integrating data from different biological levels and origins into models. In this study, we use the recently proposed computational approach iSCHRUNK (n ilico Approach to aracterization and eduction of certainty in the inetic Models), which combines Monte Carlo parameter sampling methods and machine learning techniques, in the context of Bayesian inference. Monte Carlo parameter sampling methods allow us to exploit synergies between different data sources and generate a population of kinetic models that are consistent with the available data and physicochemical laws. The machine learning allows us to data-mine the a priori generated kinetic parameters together with the integrated datasets and derive posterior distributions of kinetic parameters consistent with the observed physiology. In this work, we used iSCHRUNK to address a design question: can we identify which are the kinetic parameters and what are their values that give rise to a desired metabolic behavior? Such information is important for a wide variety of studies ranging from biotechnology to medicine. To illustrate the proposed methodology, we performed Metabolic Control Analysis, computed the flux control coefficients of the xylose uptake (XTR), and identified parameters that ensure a rate improvement of XTR in a glucose-xylose co-utilizing S. cerevisiae strain. Our results indicate that only three kinetic parameters need to be accurately characterized to describe the studied physiology, and ultimately to design and control the desired responses of the metabolism. This framework paves the way for a new generation of methods that will systematically integrate the wealth of available omics data and efficiently extract the information necessary for metabolic engineering and synthetic biology decisions. [ABSTRACT FROM AUTHOR]

Protein structure alignment is an important tool for studying evolutionary biology and protein modeling. A tool which intensively searches for the globally optimal non-sequential alignments is rarely found. We propose ALIGN-CSA which shows improvement in scores, such as DALI-score, SP-score, SO-score and TM-score over the benchmark set including 286 cases. We performed benchmarking of existing popular alignment scoring functions, where the dependence of the search algorithm was effectively eliminated by using ALIGN-CSA. For the benchmarking, we set the minimum block size to 4 to prevent much fragmented alignments where the biological relevance of small alignment blocks is hard to interpret. With this condition, globally optimal alignments were searched by ALIGN-CSA using the four scoring functions listed above, and TM-score is found to be the most effective in generating alignments with longer match lengths and smaller RMSD values. However, DALI-score is the most effective in generating alignments similar to the manually curated reference alignments, which implies that DALI-score is more biologically relevant score. Due to the high demand on computational resources of ALIGN-CSA, we also propose a relatively fast local refinement method, which can control the minimum block size and whether to allow the reverse alignment. ALIGN-CSA can be used to obtain much improved alignment at the cost of relatively more extensive computation. For faster alignment, we propose a refinement protocol that improves the score of a given alignment obtained by various external tools. All programs are available from . [ABSTRACT FROM AUTHOR]

Background: Magnesium ion, as important cation in the human body, involved in various enzymatic reactions, glucose transport and insulin release. Now diabetes mellitus and diabetic complications have become important public health problems around the world.Objective: This paper explores the association between concentration levels of serum magnesium and common complications and comorbidities of diabetes mellitus and other biochemical indexes.Methods: There are 1217 eligible patients selected from 14,317 cases of diabetic hospitalization patients from January 2010 to December 2011. Random forest algorithm was applied to assess the importance of various biochemical indexes and to perform diabetic complications prediction.Results: The research results showed that low concentration of serum magnesium and four common diabetic complications - diabetic retinopathy, diabetic nephropathy, diabetic neuropathy and diabetic macroangiopathy - exists association, but no obvious correlation with other comorbidities like hypertension.Conclusions: The specific factors of four common diabetic complications were selected from the biochemical indexes to provide a reference direction for further research. [ABSTRACT FROM AUTHOR]

Mechanistic mathematical modeling of biochemical reaction networks using ordinary differential equation (ODE) models has improved our understanding of small- and medium-scale biological processes. While the same should in principle hold for large- and genome-scale processes, the computational methods for the analysis of ODE models which describe hundreds or thousands of biochemical species and reactions are missing so far. While individual simulations are feasible, the inference of the model parameters from experimental data is computationally too intensive. In this manuscript, we evaluate adjoint sensitivity analysis for parameter estimation in large scale biochemical reaction networks. We present the approach for time-discrete measurement and compare it to state-of-the-art methods used in systems and computational biology. Our comparison reveals a significantly improved computational efficiency and a superior scalability of adjoint sensitivity analysis. The computational complexity is effectively independent of the number of parameters, enabling the analysis of large- and genome-scale models. Our study of a comprehensive kinetic model of ErbB signaling shows that parameter estimation using adjoint sensitivity analysis requires a fraction of the computation time of established methods. The proposed method will facilitate mechanistic modeling of genome-scale cellular processes, as required in the age of omics. [ABSTRACT FROM AUTHOR]

Iron is a trace metal, key for the development of living organisms. Its absorption process is complex and highly regulated at the transcriptional, translational and systemic levels. Recently, the internalization of the DMT1 transporter has been proposed as an additional regulatory mechanism at the intestinal level, associated to the mucosal block phenomenon. The short-term effect of iron exposure in apical uptake and initial absorption rates was studied in Caco-2 cells at different apical iron concentrations, using both an experimental approach and a mathematical modeling framework. This is the first report of short-term studies for this system. A non-linear behavior in the apical uptake dynamics was observed, which does not follow the classic saturation dynamics of traditional biochemical models. We propose a method for developing mathematical models for complex systems, based on a genetic programming algorithm. The algorithm is aimed at obtaining models with a high predictive capacity, and considers an additional parameter fitting stage and an additional Jackknife stage for estimating the generalization error. We developed a model for the iron uptake system with a higher predictive capacity than classic biochemical models. This was observed both with the apical uptake dataset used for generating the model and with an independent initial rates dataset used to test the predictive capacity of the model. The model obtained is a function of time and the initial apical iron concentration, with a linear component that captures the global tendency of the system, and a non-linear component that can be associated to the movement of DMT1 transporters. The model presented in this paper allows the detailed analysis, interpretation of experimental data, and identification of key relevant components for this complex biological process. This general method holds great potential for application to the elucidation of biological mechanisms and their key components in other complex systems. [ABSTRACT FROM AUTHOR]

We present StochSS: Stochastic Simulation as a Service, an integrated development environment for modeling and simulation of both deterministic and discrete stochastic biochemical systems in up to three dimensions. An easy to use graphical user interface enables researchers to quickly develop and simulate a biological model on a desktop or laptop, which can then be expanded to incorporate increasing levels of complexity. StochSS features state-of-the-art simulation engines. As the demand for computational power increases, StochSS can seamlessly scale computing resources in the cloud. In addition, StochSS can be deployed as a multi-user software environment where collaborators share computational resources and exchange models via a public model repository. We demonstrate the capabilities and ease of use of StochSS with an example of model development and simulation at increasing levels of complexity. [ABSTRACT FROM AUTHOR]

We consider a class of systems of differential equations with quadratic nonlinearities. This class describes important biochemical models. We show that systems of this class can realize any structurally stable dynamics. Given a low dimensional dynamics, we describe algorithms that allow to realize this dynamics by a large biochemical network. Some concrete biochemical examples are studied. Moreover, we show how a big system with random kinetic rates can simulate a number of low dimensional ones. The proposed method is applied on Calcium oscillations, extracellular signal-regulated kinase (ERK) signaling pathway and multistationary Mitogen-activated protein kinase cascade system (MAPK) models from biochemistry. [ABSTRACT FROM AUTHOR]

The use of a biomechanical model for human grasp modelling is presented. A previously validated biomechanical model of the hand has been used. The equilibrium of the grasped object was added to the model through the consideration of a soft contact model. A grasping posture generation algorithm was also incorporated into the model. All the geometry was represented using a spherical extension of polytopes (s-topes) for efficient collision detection. The model was used to simulate an experiment in which a subject was asked to grasp two cylinders of different diameters and weights. Different objective functions were checked to solve the indeterminate problem. The normal finger forces estimated by the model were compared to those experimentally measured. The popular objective function sum of the squared muscle stresses was shown not suitable for the grasping simulation, requiring at least being complemented by task-dependent grasp quality measures. [ABSTRACT FROM AUTHOR]

Parameter optimization or "data fitting" is a computational process that identifies a set of parameter values that best describe an experimental data set. Parameter optimization is commonly carried out using a computer program utilizing a non-linear least squares (NLLS) algorithm. These algorithms work by continuously refining a user supplied initial guess resulting in a systematic increase in the goodness of fit. A well-understood problem with this class of algorithms is that in the case of models with correlated parameters the optimized output parameters are initial guess dependent. This dependency can potentially introduce user bias into the resultant analysis. While many optimization programs exist, few address this dilemma. Here we present a data analysis tool, MENOTR, that is capable of overcoming the initial guess dependence in parameter optimization. Several case studies with published experimental data are presented to demonstrate the capabilities of this tool. The results presented here demonstrate how to effectively overcome the initial guess dependence of NLLS leading to greater confidence that the resultant optimized parameters are the best possible set of parameters to describe an experimental data set. While the optimization strategies implemented within MENOTR are not entirely novel, the application of these strategies to optimize parameters in kinetic and thermodynamic biochemical models is uncommon. MENOTR was designed to require minimal modification to accommodate a new model making it immediately accessible to researchers with a limited programming background. We anticipate that this toolbox can be used in a wide variety of data analysis applications. Prototype versions of this toolbox have been used in a number of published investigations already, as well as ongoing work with chemical-quenched flow, stopped-flow, and molecular tweezers data sets. Non-linear least squares (NLLS) is a common form of parameter optimization in biochemistry kinetic and thermodynamic investigations These algorithms are used to fit experimental data sets and report corresponding parameter values. The algorithms are fast and able to provide good quality solutions for models involving few parameters. However, initial guess dependence is a well-known drawback of this optimization strategy that can introduce user bias. An alternative method of parameter optimization are genetic algorithms (GA). Genetic algorithms do not have an initial guess dependence but are slow at arriving at the best set of fit parameters. Here, we present MENOTR, a parameter optimization toolbox utilizing a hybrid GA/NLLS algorithm. The toolbox maximizes the strength of each strategy while minimizing the inherent drawbacks. [Display omitted] • MENOTR combines the strengths of non-linear least squares and genetic algorithms. • The routine solves the initial guess dependence of the optimized parameters. • MENOTR capitalizes on parallel processing to accelerate the analysis process. • The routine requires minimal user intervention. [ABSTRACT FROM AUTHOR]

A group test gives a positive (negative) outcome if it contains at least u (at most l) positive items, and an arbitrary outcome if the number of positive items is between thresholds l and u. This problem introduced by Damaschke is called threshold group testing. It is a generalization of classical group testing. Chen and Fu extended this problem to the error-tolerant version and first proposed efficient nonadaptive algorithms. In this article, we extend threshold group testing to the k-inhibitors model in which a test has a positive outcome if it contains at least u positives and at most k−1 inhibitors. By using ( d + k − l, u; 2 e + 1]-disjunct matrix we provide nonadaptive algorithms for the threshold group testing model with k-inhibitors and at most e-erroneous outcomes. The decoding complexity is O( nu+ k log n) for fixed parameters ( d, u, l, k, e). [ABSTRACT FROM AUTHOR]

The article discusses efforts of biology researchers who tend to build ever increasing computational models in the wake of the complex mechanisms underlying biochemical processes systems. It informs that researchers have developed a strategy based on Computational Singular Perturbation (CSP) method which can be used to perform a "biochemically-driven" model reduction of even large and complex kinetic ODE systems. It informs on usefulness of method for model simplification purposes.