Global Sensitivity Analysis Methodology Research Articles

A re-sampling statistics based imprecise moment independent global sensitivity analysis methodology with limited data of uncorrelated and correlated geotechnical properties

Traditional Global Sensitivity Analysis (GSA) is often performed using variance-based Sobol’s GSA, considering statistics of inputs estimated from limited data to be precise. This can lead to inaccuracies in the importance ranking of inputs due to negligence of – i) epistemic uncertainties in their statistics, and ii) role of other moments of outputs in Sensitivity Indices (SIs). This study overcomes these limitations by proposing an imprecise moment independent GSA methodology. The methodology couples re-sampling statistical techniques, i.e., Jackknifing and Bootstrapping with Monte-Carlo Simulations based Borgonovo’s moment independent GSA to estimate distributions of SIs. The re-sampling techniques estimate epistemic uncertainties in the statistics of inputs by generating re-constituted samples. These epistemic uncertainties are then propagated via Borgonovo’s GSA to estimate their imprecise moment independent SIs. The methodology is further coupled with Nataf’s transformation and Moving Least Square-Response Surface Methods to deal with problems of correlated inputs and lack of explicit input-output relationships. The generalized nature of methodology is demonstrated for three real case studies (one tunnel and two slopes), with different correlation structures between inputs, input-outputs relationships (explicit/implicit), and failure mechanisms. The methodology estimated the distributions of SIs of inputs instead of their point estimates, indicating the propagation of epistemic uncertainties truthfully. The Jackknife-GSA was significantly efficient (∼99 %) with negligible differences in statistics of SIs as compared to Bootstrap-GSA. The correlation between inputs significantly affects the statistics of SIs. Further, a reduction in the imprecision of SIs of inputs with their increasing sample sizes was observed, which is consistent with the general understanding.

A Bayesian multi-model inference methodology for imprecise moment-independent global sensitivity analysis of rock structures

Traditional global sensitivity analysis (GSA) neglects the epistemic uncertainties associated with the probabilistic characteristics (i.e. type of distribution type and its parameters) of input rock properties emanating due to the small size of datasets while mapping the relative importance of properties to the model response. This paper proposes an augmented Bayesian multi-model inference (BMMI) coupled with GSA methodology (BMMI-GSA) to address this issue by estimating the imprecision in the moment-independent sensitivity indices of rock structures arising from the small size of input data. The methodology employs BMMI to quantify the epistemic uncertainties associated with model type and parameters of input properties. The estimated uncertainties are propagated in estimating imprecision in moment-independent Borgonovo's indices by employing a reweighting approach on candidate probabilistic models. The proposed methodology is showcased for a rock slope prone to stress-controlled failure in the Himalayan region of India. The proposed methodology was superior to the conventional GSA (neglects all epistemic uncertainties) and Bayesian coupled GSA (B-GSA) (neglects model uncertainty) due to its capability to incorporate the uncertainties in both model type and parameters of properties. Imprecise Borgonovo's indices estimated via proposed methodology provide the confidence intervals of the sensitivity indices instead of their fixed-point estimates, which makes the user more informed in the data collection efforts. Analyses performed with the varying sample sizes suggested that the uncertainties in sensitivity indices reduce significantly with the increasing sample sizes. The accurate importance ranking of properties was only possible via samples of large sizes. Further, the impact of the prior knowledge in terms of prior ranges and distributions was significant; hence, any related assumption should be made carefully.

Global sensitivity analysis based on multi-objective optimization of rural tourism building performance

Morphological design has significant impacts on the performance of rural tourism buildings (RTBs). Multi-objective optimization has been practiced for three prototypes of RTBs in Tianjin, China to explore the RTB design with better energy load, indoor daylighting and thermal comfort performance. However, making decisions from the solution set is still a challenging task for decision-makers. So post-optimization analysis is conducted in this study, and multi-objective optimization solution set of the three RTB types is investigated through global sensitivity analysis (GSA) on the platform of R studio. To begin with, correlation coefficients of the parameters are analyzed by Spearman and partial correlation coefficients methods, and strong correlation relationships are discovered among design parameters of RTBs. Afterwards, Genizi and random forest-based cforest methods are adopted for GSA towards different performance of RTBs, and comprehensive analysis is implemented for the results. Finally, it's found that the depth of frequently used space has significant impacts on annual, cooling and heating load, and daylighting of RTBs. Besides, the height of skylight is discovered to be key important parameter for both cooling and daylighting, and the width as well as the window to wall ratio of the heating space in winter have important influence on winter thermal comfort performance. Overall, the framework and methodology for GSA in post-optimization phase is put forward. The influential mechanism of morphological design parameters on energy load, daylighting and thermal comfort performance of RTBs is explored on basis of the multi-objective optimization solution set. This study not only supplies scientific suggestions for decision-making of RTBs in Tianjin, China, but also offers reference for RTB design and practice in similar regions of the world.

Theoretical modeling and optimal matching on the damping property of mechatronic shock absorber with low speed and heavy load capacity

In this paper, a mechatronic shock absorber based on ball screw pair is designed, which can produce large damping force under the same working conditions, the dynamic model of mechatronic shock absorber is established, in which the damping force is divided into inertial damping force, electromagnetic damping force, and mechanical damping force, respectively. The global sensitivity analysis methodology, named Sobol based on variance, is employed to carry out parameter sensitivity analysis, the parameters of excitation amplitude, frequency, load resistance, motor back electromotive force constant, motor electromagnetic torque constant, lead screw, motor reducer transmission ratio are investigated comprehensively. Results indicate that for the operational conditions, the load resistance has the greatest impact on equivalent damping coefficient; while for the structural parameters, the transmission ratio has the greatest impact on equivalent damping coefficient. Based on the results of parameter sensitivity analysis, aiming at vehicle ride comfort, take a certain type of light truck as an example, the optimal approach of load resistance range under different structural parameters are proposed. Finally, the experimental tests are conducted, and validates the established dynamic model. This work provides a theoretical basis for guiding the future design of the mechatronic shock absorber.

Influence and interactions of input factors in urban flood inundation modeling: An examination with variance-based global sensitivity analysis

Flood risk assessment and management in urbanized area experience an increasing reliance on the supporting information provided by numerical flood modeling as a rapid and efficient tool. Although hydrodynamic modeling based on shallow water equations requires less parameters than hydrologic ones, uncertainties of the input factors describing both the driving forces and the complex urbanized environment still have important influences on the accuracy of the urban flood simulation results once induced into the modeling procedure. The influences of input factors of engineering concern in urban flood hydrodynamic modeling in an intensely urbanized area of 0.58 km2 in the city of Chongqing, China with a mixture of different land-use types are investigated in this study by taking advantage of a variance-based global sensitivity analysis methodology with particular focus upon the interaction between the uncertainties of different input factors describing the external driving force, the underlying urban surface, the drainage loss and the spatial resolution of modeling. The global sensitivity analysis results are examined with regard to maximum values of the flood extent, water depth and discharge and their variation in the course of the urban flood propagation. Influences of the input factors and their interactions are observed to vary for different model outputs. From a spatially-distributed perspective, a dependence of the interactions between input factors is found to be upon the relative location of their acting area associated to the land-use type. Antagonistic effects of the input factors describing the underlying urban surface and the drainage loss for the rainfall-induced flood water accumulations and movements are analyzed with the flood evolution. Main effects of different input factors and their interactions are of a certain consistency with the underlying physical processes of the urban flood propagation from both static and temporal perspective of the global sensitivity analysis results.

Development of a Sensitivity Analysis method to highlight key parameters of a dry Anaerobic Digestion reactor model

Global sensitivity analysis enables to identify model parameters that have the most significant impact on model outputs and therefore require an estimation effort. This work demonstrates the reliability of a global sensitivity analysis methodology based on Definitive Screening Design and multiple linear regression analysis that requires a low number of runs. The method is applied to a simplified anaerobic digestion model. The model is firstly used to simulate a case study of a thermophilic dry anaerobic digestion of a potential agricultural waste. Then, the influence of the kinetic and mass transfer parameters of the model on the biogas flowrate, the percentage of methane in the biogas and the pH are estimated and discussed. The sensitivity analysis reveals that the slow hydrolysis constant and the upper pH inhibition limit of the hydrolytic biomass are decisive in correctly describing the biogas flowrate. The methane percentage in the biogas slightly varies with kinetic parameters, between 53 % and 55 %. Moreover, the mass transfer coefficient has significant impact on the pH through CO2 desorption. The method simplicity and reliability make its application easy to any type of model.

A Methodology for Global Sensitivity Analysis of Activated Sludge Models: Case Study with Activated Sludge Model No. 3 (ASM3).

The main objective of this study was to demonstrate a computational approach of global sensitivity analysis (GSA) integrated with functional principal component analysis (fPCA) for activated sludge models through aggregation of time-dependent model response patterns into time-independent coefficients of functional principal components (PCs). This proposed approach addresses the main issue of time-varying character of GSA indices when calculated solely on the time-dependent model outputs. The GSA-fPCA methodology was implemented using the rigorous model Activated Sludge Model No. 3 (ASM3) as case study. The approach transforms the time-dependent model outputs into functional PCs prior to calculation of GSA indices to remove the time-varying character of the calculated GSA indices. This work focused on the evaluation of the following key computational factors that may significantly influence the performance of the GSA-fPCA methodology: (a) model parameter sampling range, (b) model simulation period, (c) basis functions system, and (d) state of the system being modeled-batch or continuous activated sludge process. Results show that first few functional PCs capture up to 100% of the curve patterns in the time-dependent model outputs. The sensitivity indices calculated from the PC scores via Morris' GSA technique elucidated parameter sensitivity patterns inherent to the complex mathematical structure of ASM3. PRACTITIONER POINTS: Functional principal components-mediated GSA technique to remove time-varying character of sensitivity indices derived from time-dependent dynamical models. Technique amenable to improving efficiency of capturing response patterns into few functional principal components through various basis functions. Identifying priority parameters for ASM3 model calibration requires specification of target model outputs to which parameter sensitivities are calculated. GSA-fPCA offers a comprehensive numerical approach to manipulating models depending on the intended applications: simple fast-responding models to complex models.

Uncertainty analysis for seawater intrusion in fractured coastal aquifers: Effects of fracture location, aperture, density and hydrodynamic parameters

In this study we use polynomial chaos expansion (PCE) to perform uncertainty analysis for seawater intrusion (SWI) in fractured coastal aquifers (FCAs) which is simulated using the coupled discrete fracture network (DFN) and variable-density flow (VDF) models. The DFN-VDF model requires detailed discontinuous analysis of the fractures. In real field applications, these characteristics are usually uncertain which may have a major effect on the predictive capability of the model. Thus, we perform global sensitivity analysis (GSA) to provide a preliminary assessment on how these uncertainties can affect the model outputs. As our conceptual model, we consider fractured configurations of the Henry Problem which is widely used to understand SWI processes. A finite element DFN-VDF model is developed in the framework of COMSOL Multiphysics®. We examine the uncertainty of several SWI metrics and salinity distribution due to the incomplete knowledge of fracture characteristics. PCE is used as a surrogate model to reduce the computational burden. A new sparse PCE technique is used to allow for high polynomial orders at low computational cost. The Sobol’ indices (SIs) are used as sensitivity measures to identify the key variables driving the model outputs uncertainties. The proposed GSA methodology based on PCE and SIs is useful for identifying the source of uncertainties on the model outputs with an affordable computational cost and an acceptable accuracy. It shows that fracture hydraulic conductivity is the first source of uncertainty on the salinity distribution. The imperfect knowledge of fracture location and density affects mainly the toe position and the total flux of saltwater entering the aquifer. Marginal effects based on the PCE are used to understand the effects of fracture characteristics on SWI. The findings provide a technical support for monitoring, controlling and preventing SWI in FCAs.

Computational evaluation for effects of feedstock variations on the sensitivities of biochemical mechanism parameters in anaerobic digestion kinetic models

This work demonstrates a computational approach for the exploration of the importance of biochemical mechanism parameters in anaerobic digestion models subjected to concentration variations of digestion feedstock components. The methodology consists of an algorithm integrating global sensitivity analysis (GSA), functional principal component analysis (FPCA), and rank-clustering techniques. The GSA-FPCA integration removes the time-varying character of GSA (Morris’) indices while the rank-clustering step provides a statistical approach to grouping the ranks of parameter sensitivities as affected by feedstock component variations. To substantiate generalizations of findings, two digestion models of differing complexity were used: Case 1 – single-component feedstock digestion model with substrate inhibition, and Case 2 – rigorous model Anaerobic Digestion Model No. 1 (ADM1). Results indicate that 95–99% of the variations in the time-dependent outputs can be captured by the principal components (PCs) after FPCA transformation, and that the first PC is sufficient to represent the model outputs. This capability of the FPCA to capture overall response curve patterns reduces the dimensionality of model response perturbation measures and makes the resulting data projections onto time-independent sensitivity indices intuitive of response curve perturbations. Ranked Morris sensitivity indices calculated from the first PC scores revealed stoichiometric parameters that dominantly affect kinetic responses as well as least sensitive parameters. The GSA-FPCA-Clustering approach elucidates digestion kinetic patterns only obvious under a systematic GSA methodology.

Variance based global sensitivity analysis of physiologically based pharmacokinetic absorption models for BCS I-IV drugs.

Regulatory agencies have a strong interest in sensitivity analysis for the evaluation of physiologically-based pharmacokinetic (PBPK) models used in pharmaceutical research and drug development and regulatory submissions. One of the applications of PBPK is the prediction of fraction absorbed and bioavailability for drugs following oral administration. In this context, we performed a variance based global sensitivity analysis (GSA) on in-house PBPK models for drug absorption, with the aim of identifying key parameters that influence the predictions of the fraction absorbed and the bioavailability for neutral, acidic and basic compounds. This analysis was done for four different classes of drugs, defined according to the Biopharmaceutics Classification System, differentiating compounds by permeability and solubility. For class I compounds (highly permeable, highly soluble), the parameters that mainly influence the fraction absorbed are related to the formulation properties, for class II compounds (highly permeable, lowly soluble) to the dissolution process, for class III (lowly permeable, highly soluble) to both absorption process and formulation properties and for class IV (lowly permeable, lowly soluble) to both absorption and dissolution processes. Considering the bioavailability, the results are similar to those for the fraction absorbed, with the addition that parameters related to gut wall and liver clearance influence as well the predictions. This work aimed to give a demonstration of the GSA methodology and highlight its importance in improving our understanding of PBPK absorption models and in guiding the choice of parameters that can safely be assumed, estimated or require data generation to allow informed model prediction.

An efficient approach for dynamic global sensitivity analysis of stochastic train-track-bridge system

Abstract The parameters in time-varying train-track-bridge system (TTBS) are inevitably subjected to uncertainty, leading to variability in its dynamic responses. This work provides an investigation as to how uncertainty in the parameters influences the dynamic responses of time-varying TTBS, which refers to dynamic sensitivity analysis in the context of stochastic dynamic system. A powerful global sensitivity analysis (GSA), which maintains numerous attractive advantages over local sensitivity analysis (LSA), is proposed to measure the impact of uncertain system parameters on dynamic responses in a quantitative manner, thereby ranking them in order of importance. Furthermore, an analytical Gaussian process model (GPM)-based approach is developed to greatly alleviate the computational cost involved in dynamic GSA of time-varying TTBS. The proposed analytical GPM-based approach possesses the capacity to calculate the sensitivity indices of individual parameters as well as parameter clusters. The effectiveness of the proposed GPM-based dynamic GSA methodology is evaluated by comparison with the brute-force Monte Carlo simulation (MCS) on a mass-spring-damper system. The perfect agreement between the analytical GPM-obtained and MCS-derived time-varying sensitivity indices verifies the feasibility and reliability of the proposed methodology. An illustrative example is further provided to fully demonstrate the application of the developed GPM-based approach to dynamic GSA of time-varying TTBS. The dynamic GSA results enable us to gain insight into the temporal evolution of the global influences of individual parameters and groups of parameters on dynamic responses of TTBS.

An adaptive least-squares global sensitivity method and application to a plasma-coupled combustion prediction with parametric correlation

We introduce an efficient non-intrusive surrogate-based methodology for global sensitivity analysis and uncertainty quantification. Modified covariance-based sensitivity indices (mCov-SI) are defined for outputs that reflect correlated effects. The overall approach is applied to simulations of a complex plasma-coupled combustion system with disparate uncertain parameters in sub-models for chemical kinetics and a laser-induced breakdown ignition seed. The surrogate is based on an Analysis of Variance (ANOVA) expansion, such as widely used in statistics, with orthogonal polynomials representing the ANOVA subspaces and a polynomial dimensional decomposition (PDD) representing its multi-dimensional components. The coefficients of the PDD expansion are obtained using a least-squares regression, which both avoids the direct computation of high-dimensional integrals and affords an attractive flexibility in choosing sampling points. This facilitates importance sampling using a Bayesian calibrated posterior distribution, which is fast and thus particularly advantageous in common practical cases, such as our large-scale demonstration, for which the asymptotic convergence properties of polynomial expansions cannot be realized due to computation expense. Effort, instead, is focused on efficient finite-resolution sampling. Standard covariance-based sensitivity indices (Cov-SI) are employed to account for correlation of the uncertain parameters. Magnitude of Cov-SI is unfortunately unbounded, which can produce extremely large indices that limit their utility. Alternatively, mCov-SI are then proposed in order to bound this magnitude ∈[0,1]. The polynomial expansion is coupled with an adaptive ANOVA strategy to provide an accurate surrogate as the union of several low-dimensional spaces, avoiding the typical computational cost of a high-dimensional expansion. It is also adaptively simplified according to the relative contribution of the different polynomials to the total variance. The approach is demonstrated for a laser-induced turbulent combustion simulation model, which includes parameters with correlated effects.

Global sensitivity analysis of load distribution and displacement in multi-bolt composite joints

Abstract This paper presents the development of a novel methodology for global sensitivity analysis of multi-bolt composite joints. Two sources of uncertainty were considered, i.e., the mechanical properties of composite plies and the bolt-hole clearance which comes from assembly phase. The uncertainty propagation in the composite plate was derived through the classical laminate theory, while the load distribution within bolts and the joint displacement were determined by an analytical spring-based method. A kind of Monte Carlo simulation was used to calculate the variance-based sensitivity indices. Furthermore, the proposed methodology was applied to a generic single-lap composite joint, which can also be extended to represent double-lap joints, to identify the significant input random variables with respect to structural responses of the joint. Useful conclusions for the design of multi-bolt composite joints were obtained from the computational results and discussions.

Methodology for Global Sensitivity Analysis of Flexible Pavements in a Bayesian Back-Analysis Framework

AbstractProbabilistic sensitivity analysis is a crucial tool in the uncertainty analysis of systems, which allows the understanding of how the uncertainty in the output response can be apportioned to different sources of uncertainty in the input parameters. Sobol’s method is a widely accepted global sensitivity analysis (GSA) technique that has been applied to rank the input design parameters, based on their respective impact on the response randomness. Although this variance-based technique is highly efficient when the design parameters are independent, the estimation of Sobol indices in the presence of correlation has not been sufficiently documented. This paper addresses this shortcoming through the development of a generalized method for GSA in the Bayesian back-analysis framework, in which the Kullback-Leibler (K-L) entropy measure serves as the measure of sensitivity. The methodology has been explored in the context of design of flexible pavements in the mechanistic-empirical (M-E) framework, in whi...

Global Sensitivity Analysis for Repeated Measures Studies With Informative Dropout: A Fully Parametric Approach

We present a global sensitivity analysis methodology for drawing inference about the mean at the final scheduled visit in a repeated measures study with informative dropout. We review and critique the sensitivity frameworks developed by Rotnitzky et al. and Daniels and Hogan. We identify strengths and weaknesses of these approaches and propose an alternative. We illustrate our approach via a comprehensive analysis of the RIS-INT-3 trial.

Methodology for global sensitivity analysis of consequence models

A methodology is presented for global sensitivity analysis of consequence models used in process safety applications. It involves running a consequence model around a hundred times and using the results to construct a statistical emulator, which is essentially a sophisticated curve fit to the data. The emulator is then used to undertake the sensitivity analysis and identify which input parameters (e.g. operating temperature and pressure, wind speed) have a significant effect on the chosen output (e.g. vapour cloud size). Performing the sensitivity analysis using the emulator rather than the consequence model itself leads to significant savings in computing time.To demonstrate the methodology, a global sensitivity analysis is performed on the Phast consequence model for discharge and dispersion. The scenarios studied consist of above-ground, horizontal, steady-state discharges of dense-phase carbon dioxide (CO2), with orifices ranging in diameter from ½ to 2 inch and the liquid CO2 stagnation conditions maintained at between 100 and 150 bar. These scenarios are relevant in scale to leaks from large diameter above-ground pipes or vessels.Seven model input parameters are varied: the vessel temperature and pressure, orifice size, wind speed, humidity, ground surface roughness and height of the release. The input parameters that have a dominant effect on the dispersion distance of the CO2 cloud are identified, both in terms of their direct effect on the dispersion distance and their indirect effect, through interactions with other varying input parameters.The analysis, including the Phast simulations, runs on a standard office laptop computer in less than 30 min. Tests are performed to confirm that a hundred Phast runs are sufficient to produce an emulator with an acceptable degree of accuracy. Increasing the number of Phast runs is shown to have no effect on the conclusions of the sensitivity analysis.The study demonstrates that Bayesian analysis of model sensitivity can be conducted rapidly and easily on consequence models such as Phast. There is the potential for this to become a routine part of consequence modelling.

Global Sensitivity Analysis of Jointed Plain Concrete Pavement Mechanistic–Empirical Performance Predictions

The new AASHTO Mechanistic-Empirical Pavement Design Guide (MEPDG) provides pavement analysis and performance predictions for various what-if scenarios. MEPDG performance predictions for anticipated climatic and traffic conditions will depend on the values of the input parameters that characterize pavement materials, layers, design features, and condition. A comprehensive global sensitivity analysis methodology is proposed for evaluating performance predictions for jointed plain concrete pavement to MEPDG inputs for five climatic conditions and three traffic levels. MEPDG inputs evaluated in the analysis include traffic volume, layer thicknesses, material properties, groundwater depth, and geometric parameters. Correlations between MEPDG inputs were considered as appropriate. The global sensitivity analysis varied all inputs simultaneously across the problem domain for each of the 15 base cases (five climates x three traffic levels). Two response surface modeling approaches, multivariate linear regressions and artificial neural networks, were developed for evaluation of MEPDG input sensitivities across the problem domain. The response surface modeling approaches based on artificial neural networks not only provided robust and accurate representations of the complex relationships between MEPDG inputs and distress outputs but also captured the variation in sensitivity across the problem domain. The normalized sensitivity index for the design limit proposed in the study provides practical interpretation of sensitivity by relating a given percentage change in an MEPDG design input to the corresponding percentage change in predicted distress relative to its design limit value.

Hierarchical multivariate regression-based sensitivity analysis reveals complex parameter interaction patterns in dynamic models

Dynamic models of biological systems often possess complex and multivariate mappings between input parameters and output state variables, posing challenges for comprehensive sensitivity analysis across the biologically relevant parameter space. In particular, more efficient and robust ways to obtain a solid understanding of how the sensitivity to each parameter depends on the values of the other parameters are sorely needed.We report a new methodology for global sensitivity analysis based on Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR)-based approximations (metamodelling) of the input–output mappings of dynamic models, which we expect to be generic, efficient and robust, even for systems with highly nonlinear input–output relationships. The two-step HC-PLSR metamodelling automatically separates the observations (here corresponding to different combinations of input parameter values) into groups based on the dynamic model behaviour, then analyses each group separately with Partial Least Squares Regression (PLSR). This produces one global regression model comprising all observations, as well as regional regression models within each group, where the regression coefficients can be used as sensitivity measures. Thereby a more accurate description of complex interactions between inputs to the dynamic model can be revealed through analysis of how a certain level of one input parameter affects the model sensitivity to other inputs. We illustrate the usefulness of the HC-PLSR approach on a dynamic model of a mouse heart muscle cell, and demonstrate how it reveals interaction patterns of probable biological significance not easily identifiable by a global regression-based sensitivity analysis alone.Applied for sensitivity analysis of a complex, high-dimensional dynamic model of the mouse heart muscle cell, several interactions between input parameters were identified by the two-step HC-PLSR analysis that could not be detected in the single-step global analysis. Hence, our approach has the potential to reveal new biological insight through the identification of complex parameter interaction patterns. The HC-PLSR metamodel complexity can be adjusted according to the nonlinear complexity of the input–output mapping of the analysed dynamic model through adjustment of the number of regional regression models included. This facilitates sensitivity analysis of dynamic models of varying complexities.

Inactivating ion channels augment robustness of subthreshold intrinsic response dynamics to parametric variability in hippocampal model neurons

Voltage-gated ion channels play a critical role in regulating neuronal intrinsic response dynamics (IRD). Here, we computationally analysed the roles of the two inactivating subthreshold conductances (A and T), individually and in various combinations with the non-inactivating h conductance, in regulating several physiological IRD measurements in the theta frequency range. We found that the independent presence of a T conductance, unlike that of an h conductance, was unable to sustain an inductive phase lead in the theta frequency range, despite its ability to mediate theta frequency resonance. The A conductance, on the other hand, when expressed independently, acted in a manner similar to a leak conductance with reference to most IRD measurements. Next, analysing the impact of pair-wise coexpression of these channels, we found that the coexpression of the h and T conductances augmented the range of parameters over which they sustained resonance and inductive phase lead. Additionally, coexpression of the A conductance with the h or the T conductance elicited changes in IRD measurements that were similar to those obtained with the expression of a leak conductance with a resonating conductance. Finally, to understand the global sensitivity of IRD measurements to all parameters associated with models expressing all three channels, we generated 100,000 neuronal models, each built with a unique set of parametric values. We categorized valid models among these by matching their IRD measurements with experimental counterparts, and found that functionally similar models could be achieved even when underlying parameters displayed tremendous variability and exhibited weak pair-wise correlations. Our results suggest that the three prominent subthreshold conductances contribute differently to intrinsic excitability and to phase coding. We postulate that the differential expression and activity-dependent plasticity of these conductances contribute to robustness of subthreshold IRD, whereby response homeostasis is achieved by recruiting several non-unique combinations of these channel parameters.

A methodology for global-sensitivity analysis of time-dependent outputs in systems biology modelling

One of the main challenges in the development of mathematical and computational models of biological systems is the precise estimation of parameter values. Understanding the effects of uncertainties in parameter values on model behaviour is crucial to the successful use of these models. Global sensitivity analysis (SA) can be used to quantify the variability in model predictions resulting from the uncertainty in multiple parameters and to shed light on the biological mechanisms driving system behaviour. We present a new methodology for global SA in systems biology which is computationally efficient and can be used to identify the key parameters and their interactions which drive the dynamic behaviour of a complex biological model. The approach combines functional principal component analysis with established global SA techniques. The methodology is applied to a model of the insulin signalling pathway, defects of which are a major cause of type 2 diabetes and a number of key features of the system are identified.