Parametric sensitivity analysis for biochemical reaction networks based on pathwise information theory.

BackgroundStochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state space dimension of these equations, numerical simulations are computationally expensive. This is a particular problem for analysis tasks requiring repeated simulations for different parameter values. Such tasks are computationally expensive to the point of infeasibility with the chemical master equation.ResultsIn this article, we apply parametric model order reduction techniques in order to construct accurate low-dimensional parametric models of the chemical master equation. These surrogate models can be used in various parametric analysis task such as identifiability analysis, parameter estimation, or sensitivity analysis. As biological examples, we consider two models for gene regulation networks, a bistable switch and a network displaying stochastic oscillations.ConclusionsThe results show that the parametric model reduction yields efficient models of stochastic biochemical reaction networks, and that these models can be useful for systems biology applications involving parametric analysis problems such as parameter exploration, optimization, estimation or sensitivity analysis.

Sensitivity analysis of urban flood model parameters is important for urban flood simulation. Efficient and accurate acquisition of sensitive parameters is the key to real-time model calibration. In order to quickly obtain the sensitive runoff parameters of the urban flood simulation model, this study proposes an artificial neural network-based identification method for sensitive parameters. Artificial neural network (ANN) models were constructed with the binary classification and multi-classification methods, and used environmental indicators that affect the parameter sensitivity of different hydrological response units as the input, with the sensitivity parameters of the Storm water management model (SWMM) being the output. The optimization of the ANN was realized by adjusting the number of nodes in the hidden layer and the maximum number of iterations. An example application was conducted in Zhengzhou, China. The results show that the binary classification ANN quickly identified sensitive parameters, and the prediction accuracy of all parameters exceeded 96%. Convergence can be achieved when the number of nodes in the hidden layer does not exceed twice the number of input nodes, and the maximum number of iterations does not exceed 200. Rapid and accurate identification of the sensitive runoff parameters of the urban flood simulation model was achieved, which reduced the time required for parameter sensitivity analysis.

Parameter sensitivity analysis can determine the influence of the input parameters on the model output. Identification and calibration of critical parameters are the crucial points of the process model optimization. Based on the Extended Fourier Amplitude Sensitivity Test (EFAST) and the Morris method, this paper analyzes and compares the parameter sensitivity of the annual mean net primary productivity (NPP) of Larix olgensis Henry forests in Jilin Province simulated by the Lund–Potsdam–Jena dynamic global vegetation model (LPJ model) in 2009–2014 and 2000–2019, and deeply examines the sensitivity and influence of the two methods to each parameter and their respective influence on the model’s output. Moreover, it optimizes some selected parameters and re-simulates the NPP of Larix olgensis forests in Jilin Province from 2010 to 2019. The conclusions are the following: (1) For the LPJ model, the sensitive and non-influential parameters could be identified, which could guide the optimization order of the model and was valuable for model area applications. (2) The results of the two methods were similar but not identical. The sensitivity parameters were significantly correlated (p < 0.05); parameter krp was the most sensitive parameter, followed by parameters αm, αa and gm. These sensitive parameters were mainly found in the photosynthesis, water balance, and allometric growth modules. (3) The EFAST method had a higher precision than the Morris method, which could calculate quantitatively the contribution rate of each parameter to the variances of the model results; however, the Morris method involved fewer model running times and higher efficiency. (4) The mean relative error (MRE) and mean absolute error (MAE) of the simulated value of LPJ model after parameter optimization decreases. The optimized annual mean value of NPP from 2010 to 2019 was 580 g C m−2 a−1, with a mean annual growth rate of 2.13%, exhibiting a fluctuating growth trend. The MAE of the simulated value of LPJ model after parameter optimization decreases.

An interactive graphical interface tool for parameter calibration, sensitivity analysis, uncertainty analysis, and visualization for the Soil and Water Assessment Tool

Stochastic chemical reaction networks (CRNs) are complex systems that combine the features of concurrent transformation of multiple variables in each elementary reaction event and nonlinear relations between states and their rates of change. Most general results concerning CRNs are limited to restricted cases where a topological characteristic known as deficiency takes a value 0 or 1, implying uniqueness and positivity of steady states and surprising, low-information forms for their associated probability distributions. Here we derive equations of motion for fluctuation moments at all orders for stochastic CRNs at general deficiency. We show, for the standard base case of proportional sampling without replacement (which underlies the mass-action rate law), that the generator of the stochastic process acts on the hierarchy of factorial moments with a finite representation. Whereas simulation of high-order moments for many-particle systems is costly, this representation reduces the solution of moment hierarchies to a complexity comparable to solving a heat equation. At steady states, moment hierarchies for finite CRNs interpolate between low-order and high-order scaling regimes, which may be approximated separately by distributions similar to those for deficiency-zero networks and connected through matched asymptotic expansions. In CRNs with multiple stable or metastable steady states, boundedness of high-order moments provides the starting condition for recursive solution downward to low-order moments, reversing the order usually used to solve moment hierarchies. A basis for a subset of network flows defined by having the same mean-regressing property as the flows in deficiency-zero networks gives the leading contribution to low-order moments in CRNs at general deficiency, in a 1/n expansion in large particle numbers. Our results give a physical picture of the different informational roles of mean-regressing and non-mean-regressing flows and clarify the dynamical meaning of deficiency not only for first-moment conditions but for all orders in fluctuations.

We consider the problem of estimating parameter sensitivity for Markovian models of reaction networks. Sensitivity values measure the responsiveness of an output with respect to the model parameters. They help in analysing the network, understanding its robustness properties and identifying the important reactions for a specific output. Sensitivity values are commonly estimated using methods that perform finite-difference computations along with Monte Carlo simulations of the reaction dynamics. These methods are computationally efficient and easy to implement, but they produce a biased estimate which can be unreliable for certain applications. Moreover, the size of the bias is generally unknown and hence the accuracy of these methods cannot be easily determined. There also exist unbiased schemes for sensitivity estimation but these schemes can be computationally infeasible, even for very simple networks. Our goal in this paper is to present a new method for sensitivity estimation, which combines the computational efficiency of finite-difference methods with the accuracy of unbiased schemes. Our method is easy to implement and it relies on an exact representation of parameter sensitivity that we recently proved elsewhere. Through examples, we demonstrate that the proposed method can outperform the existing methods, both biased and unbiased, in many situations.

This paper used both methods of single parameter and Multi-parameter combination sensitivity analysis in groundwater numerical model parameter sensitivity analysis. With the examples of Jiaozuo, Henan province, choosing coefficient of permeability, porosity and longitudinal dispersion degree as factor, the paper analysis the main controlling factors of contaminant migration of Hexavalent chromium in groundwater. Single parameter sensitivity analysis results show that the permeability coefficient gives largest impact to the migration of hexavalent chromium. It is positively correlates with groundwater numerical model. The rest of the parameters assume the inverse correlation. Multi-parameter combination sensitivity analysis results show that the permeability coefficient has absolute advantage among various parameter combinations. Another conclusion is that longitudinal dispersion degree affects smaller on the process of hexavalent chromium pollutants migration, but the impact on the final density is bigger.

Stochastic models for chemical reaction networks have become very popular in recent years. For such models, the estimation of parameter sensitivities is an important and challenging problem. Sensitivity values help in analyzing the network, understanding its robustness properties and also in identifying the key reactions for a given outcome. Most of the methods that exist in the literature for the estimation of parameter sensitivities, rely on Monte Carlo simulations using Gillespie's stochastic simulation algorithm or its variants. It is well-known that such simulation methods can be prohibitively expensive when the network contains reactions firing at different time-scales, which is a feature of many important biochemical networks. For such networks, it is often possible to exploit the time-scale separation and approximately capture the original dynamics by simulating a model, which is obtained by eliminating the fast reactions in a certain way. The aim of this paper is to tie these model reduction techniques with sensitivity analysis. We prove that under some conditions, the sensitivity values for the reduced model can be used to approximately recover the sensitivity values for the original model. Through an example we illustrate how our result can help in sharply reducing the computational costs for the estimation of parameter sensitivities for reaction networks with multiple time-scales. To prove our result, we use coupling arguments based on the random time change representation of Kurtz. We also exploit certain connections between the distributions of the occupation times of Markov chains and multi-dimensional wave equations.

This paper answers an open question of Chen et al. (DNA 2012: proceedings of the 18th international meeting on DNA computing and molecular programming, vol 7433 of lecture notes in computer science. Springer, Berlin, pp 25–42, 2012), who showed that a function $$f:\mathbb {N}^k\rightarrow \mathbb {N}^l$$ is deterministically computable by a stochastic chemical reaction network (CRN) if and only if the graph of $$f$$ is a semilinear subset of $$\mathbb {N}^{k+l}$$ . That construction crucially used “leaders”: the ability to start in an initial configuration with constant but non-zero counts of species other than the $$k$$ species $$X_1,\ldots ,X_k$$ representing the input to the function $$f$$ . The authors asked whether deterministic CRNs without a leader retain the same power. We answer this question affirmatively, showing that every semilinear function is deterministically computable by a CRN whose initial configuration contains only the input species $$X_1,\ldots ,X_k$$ , and zero counts of every other species, so long as $$f({\bf 0})={\bf 0}$$ . We show that this CRN completes in expected time $$O(n)$$ , where $$n$$ is the total number of input molecules. This time bound is slower than the $$O(\log ^5 n)$$ achieved in Chen et al. (2012), but faster than the $$O(n \log n)$$ achieved by the direct construction of Chen et al. (2012).

Parametric sensitivity analysis (SA) is an essential tool in optical data analysis aiming to quantify the relative importance of optical model parameters and identify those with a low influence which should remain fixed during analysis in order to simplify a model. Typically, such sensitivity studies are performed using a local sensitivity analysis, also referred to as “one-at-a-time” analysis, which estimates parameter sensitivity by evaluating the changes in model output while perturbing one parameter at a time and holding all other parameters fixed. All the pitfalls of the local sensitivity approach are quite obvious and well known; however, local SA is still prevailing in the area of data analysis for spectroscopic ellipsometry. In this study, we discuss applications of a global qualitative analysis introduced by Morris in 1991 which determines an overall significance for each model parameter and describes its nonlinear effect on model’s output and/or interactions with other parameters. The Morris method allows effective separation of the model parameters into different groups such as parameters with negligible effects, parameters with large linear effects without interactions, and parameters with large nonlinear and/or interaction effects. Here, we carried out the Morris sensitivity analysis to reveal the model parameter significance ranking in a test case of the B-spline model for titanium nitride (TiN). Such a screening approach can be considered as a practical tool for the initial global SA strategy prior to true “all-at-a-time” global sensitivity analysis.

Ecosystem models are useful tools for understanding ecological processes and for sustainable management of resources. In biogeochemical field, numerical models have been widely used for investigating carbon dynamics under global changes from site to regional and global scales. However, it is still challenging to optimize parameters and estimate parameterization uncertainty for complex process‐based models such as the Erosion Deposition Carbon Model (EDCM), a modified version of CENTURY, that consider carbon, water, and nutrient cycles of ecosystems. This study was designed to conduct the parameter identifiability, optimization, sensitivity, and uncertainty analysis of EDCM using our developed EDCM‐Auto, which incorporated a comprehensive R package—Flexible Modeling Framework (FME) and the Shuffled Complex Evolution (SCE) algorithm. Using a forest flux tower site as a case study, we implemented a comprehensive modeling analysis involving nine parameters and four target variables (carbon and water fluxes) with their corresponding measurements based on the eddy covariance technique. The local sensitivity analysis shows that the plant production‐related parameters (e.g., PPDF1 and PRDX) are most sensitive to the model cost function. Both SCE and FME are comparable and performed well in deriving the optimal parameter set with satisfactory simulations of target variables. Global sensitivity and uncertainty analysis indicate that the parameter uncertainty and the resulting output uncertainty can be quantified, and that the magnitude of parameter‐uncertainty effects depends on variables and seasons. This study also demonstrates that using the cutting‐edge R functions such as FME can be feasible and attractive for conducting comprehensive parameter analysis for ecosystem modeling.

Causal conclusions from observational studies may be sensitive to unmeasured confounding. In such cases, a sensitivity analysis is often conducted, which tries to infer the minimum amount of hidden biases or the minimum strength of unmeasured confounding needed in order to explain away the observed association between treatment and outcome. If the needed bias is large, then the treatment is likely to have significant effects. The Rosenbaum sensitivity analysis is a modern approach for conducting sensitivity analysis in matched observational studies. It investigates what magnitude the maximum of hidden biases from all matched sets needs to be in order to explain away the observed association. However, such a sensitivity analysis can be overly conservative and pessimistic, especially when investigators suspect that some matched sets may have exceptionally large hidden biases. In this article, we generalize Rosenbaum’s framework to conduct sensitivity analysis on quantiles of hidden biases from all matched sets, which are more robust than the maximum. Moreover, the proposed sensitivity analysis is simultaneously valid across all quantiles of hidden biases and is thus a free lunch added to the conventional sensitivity analysis. The proposed approach works for general outcomes, general matched studies and general test statistics. In addition, we demonstrate that the proposed sensitivity analysis also works for bounded null hypotheses when the test statistic satisfies certain properties. An R package implementing the proposed approach is available online. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Switch like responses appear as common strategies in the regulation of cellular systems. Here we present a method to characterize bistable regimes in biochemical reaction networks that can be of use to both direct and reverse engineering of biological switches. In the design of a synthetic biological switch, it is important to study the capability for bistability of the underlying biochemical network structure. Chemical Reaction Network Theory (CRNT) may help at this level to decide whether a given network has the capacity for multiple positive equilibria, based on their structural properties. However, in order to build a working switch, we also need to ensure that the bistability property is robust, by studying the conditions leading to the existence of two different steady states. In the reverse engineering of biological switches, knowledge collected about the bistable regimes of the underlying potential model structures can contribute at the model identification stage to a drastic reduction of the feasible region in the parameter space of search. In this work, we make use and extend previous results of the CRNT, aiming not only to discriminate whether a biochemical reaction network can exhibit multiple steady states, but also to determine the regions within the whole space of parameters capable of producing multistationarity. To that purpose we present and justify a condition on the parameters of biochemical networks for the appearance of multistationarity, and propose an efficient and reliable computational method to check its satisfaction through the parameter space.

CFD simulation of the Sabatier process in a shell-and-tube reactor under local thermal non-equilibrium conditions: Parameter sensitivity and reaction mechanism analysis

Dynamical system models of complex biochemical reaction networks are high-dimensional, nonlinear, and contain many unknown parameters.The capacity for multiple equilibria in such systems plays a key rolein important biochemical processes. Examples show that there is a verydelicate relationship between the structure of a reaction network andits capacity to give rise to several positive equilibria. In thispaper we focus on networks of reactions governed by mass-actionkinetics. As is almost always the case in practice, we assume that noreaction involves the collision of three or more molecules at the sameplace and time, which implies that the associated mass-actiondifferential equations contain only linear and quadratic terms. Wedescribe a general injectivity criterion for quadratic functions ofseveral variables, and relate this criterion to a network's capacityfor multiple equilibria. In order to take advantage of this criterionwe look for explicit general conditions that imply non-vanishing ofpolynomial functions on the positive orthant.In particular, we investigate in detail the case of polynomials withonly one negative monomial, and we fully characterize the case ofaffinely independent exponents.We describe several examples, including an example that shows howthese methods may be used for designing multistable chemical systemsin synthetic biology.