Sensitivity analysis of the penicillin fermentation process model based on LHS-EPRCC

Parameter estimation is a major challenge for mathematical modelling of biological systems. Given the uncertainties associated with model parameters, it is important to understand how sensitive the model output is to variations in parameter values. A local sensitivity analysis determines the model sensitivity to parameter variations over a localised region around the nominal parameter values, whereas a global sensitivity analysis (GSA) investigates the sensitivity over the entire parameter space. Using a T-cell receptor-activated Erk-MAPK signalling pathway model as an example, the authors present a comparative study of a variety of different sensitivity analysis techniques. These techniques include: local sensitivity analysis, existing GSA methods of partial rank correlation coefficient, Sobol's, extended Fourier amplitude sensitivity test, as well as a weighted average of local sensitivities and a new GSA method to extract global parameter sensitivities from a parameter identification routine. Results of this study revealed critical reactions in the signalling pathway and their impact on the signalling dynamics and provided insights into embedded regulatory mechanisms such as feedback loops in the pathway. From this study, a recommendation emerges for a general sensitivity analysis strategy to efficiently and reliably infer quantitative, dynamic as well as topological properties from systems biology models.

Simulation of fate and transport mechanisms in the porous systems from contaminant transport models are affected by uncertainty associated with input model parameters. Sensitivity analysis (SA) provides tools to quantify the sources of uncertainty to the variations in the model output metrics. To quantify the uncertainty associated with physical non-equilibrium contaminant transport model, global SA was conducted for the problem mimicking reactive transport in the saturated soil column conditions. Five global SA methods, namely Morris, RSA (Regionalized Sensitivity Analysis), Sobol, FAST (Fourier Amplitude Sensitivity Test), and PAWN, were tested based on the temporal moments of contaminant concentrations for two output metrics: zeroth temporal moment (ZTM) and mean residence time (MRT). The ranking order of ten input model parameters from global SA methods for two output metrics was compared. Morris SA implied that the ZTM at outlet of the soil column is highly sensitive to sorption distribution coefficient in the mobile and immobile regions and less sensitive to dispersion coefficient and degradation rate constant in the immobile region. The mass-transfer coefficient showed highest non-linear interactions with other flow and transport parameters based on the highest value of standard deviation of elementary effects (EEs) for ZTM output metric. The sorption distribution coefficient in the mobile region and mass-transfer coefficient showed highest sensitivity and non-linear effect toward MRT based on the Morris method. The comparison of global SA methods revealed that the top two sensitive parameters affecting ZTM and MRT were the same from all the considered methods. However, large difference in the ranking order of bottom three sensitive parameters was observed. The sorption distribution coefficient of mobile region and mass-transfer coefficient were observed as the most sensitive parameters affecting ZTM and MRT based on the comparison of all five global SA methods. Overall results suggest that the non-linear contaminant transport model should be examined based on multiple sensitivity output metrics via a multi-model approach. The multi-model global SA approach implemented in this study highlighted its significance in quantifying the interplay of non-linear model parameters.

ABSTRACTPROSAIL is a combination of the leaf optical properties spectra (PROSPECT) model and the scattering by arbitrarily inclined leaves (SAIL) canopy bidirectional reflectance model. When modelling forest canopy reflectance using the PROSAIL radiative transfer model, the sensitivities of parameters can affect the modelling accuracy. Traditionally, sensitivities have been assessed using local sensitivity analysis (LSA); however, drawbacks to this approach include a lack of consideration for coupled effects between different parameters. In this study, parameter sensitivities in the PROSAIL model were calculated using two global sensitivity analysis (GSA) methods (the Extended Fourier Amplitude Sensitivity Test (EFAST) method and the Morris method), field measurements, and Landsat 5 Thematic Mapper (TM) data for a Moso bamboo forest. The results of GSA were compared with those of LSA in order to identify the key parameters impacting the Moso bamboo forest canopy reflectance, and to provide a reference for model optimization and vegetation canopy inversion improvement. The results showed that: (1) the sensitivities of six major input parameters of the PROSAIL model were generally consistent with the sorting orders of the two GSA methods, but were not in accordance with those from the LSA method, especially in the mid-infrared band; (2) coupled effects among parameters acting on reflectance simulation in visible light bands were greater than those in infrared bands; (3) the simulated canopy reflectance was evaluated using Landsat 5 TM data, and the results simulated based on LSA analysis showed higher error than those based on GSA analysis, because the LSA method ignored the influence of some parameters on canopy reflectance, e.g. leaf mesophyll structure (N), average leaf angle (ALA), leaf water content (Cw), and leaf dry matter content (Cm). However, GSA was able to fully consider the coupled effects among parameters, and thus identified the sensitive parameters impacting on reflectance more accurately.

Mathematical model to assess the impacts of aflatoxin contamination in crops, livestock and humans

Community-acquired pneumonia (CAP) is a common respiratory infection that happens outside of hospitals, and it is caused by bacteria, viruses, or fungus. It remains a serious threat to the world, particularly affecting children, the elderly, and immunocompromised individuals. The fractional-order pneumonia model has been developed in this study to determine the disease dynamics in the system. The model stability is proved for the existing equilibrium points. Global sensitivity analysis was carried out utilizing Latin hypercube sampling (LHS) and partial rank correlation coefficient (PRCC) to find the key parameters influencing disease transmission. Control analysis is considered as an effective strategy for preventing the spread of the disease pneumonia. It is often necessary to combine timely treatment, immunization, and boosting immunity. However, eliminating this disease in the population will be challenging if control strategies aren’t given at the appropriate time and in sufficient quantity. We conduct a cost-effectiveness analysis of four optimal control strategies utilizing numerical methods. Our findings indicate that vaccination is the most cost-effective and efficient control intervention among the strategies compared.

In physiologically based pharmacokinetic (PBPK) modelling, the large number of input parameters, limited amount of available data and the structural model complexity generally hinder simultaneous estimation of uncertain and/or unknown parameters. These parameters are generally subject to estimation. However, the approaches taken for parameter estimation vary widely. Global sensitivity analyses are proposed as a method to systematically determine the most influential parameters that can be subject to estimation. Herein, a global sensitivity analysis was conducted to identify the key drug and physiological parameters influencing drug disposition in PBPK models and to potentially reduce the PBPK model dimensionality. The impact of these parameters was evaluated on the tissue-to-unbound plasma partition coefficients (Kpus) predicted by the Rodgers and Rowland model using Latin hypercube sampling combined to partial rank correlation coefficients (PRCC). For most drug classes, PRCC showed that LogP and fraction unbound in plasma (fup) were generally the most influential parameters for Kpu predictions. For strong bases, blood:plasma partitioning was one of the most influential parameter. Uncertainty in tissue composition parameters had a large impact on Kpu and Vss predictions for all classes. Among tissue composition parameters, changes in Kpu outputs were especially attributed to changes in tissue acidic phospholipid concentrations and extracellular protein tissue:plasma ratio values. In conclusion, this work demonstrates that for parameter estimation involving PBPK models and dimensionality reduction purposes, less influential parameters might be assigned fixed values depending on the parameter space, while influential parameters could be subject to parameters estimation.

BackgroundThe potential impact of pre-exposure chemoprophylaxis (PrEP) on heterosexual transmission of HIV-1 infection in resource-limited settings is uncertain.Methodology/Principle FindingsA deterministic mathematical model was used to simulate the effects of antiretroviral PrEP on an HIV-1 epidemic in sub-Saharan Africa under different scenarios (optimistic, neutral and pessimistic) both with and without sexual disinhibition. Sensitivity analyses were used to evaluate the effect of uncertainty in input parameters on model output and included calculation of partial rank correlations and standardized rank regressions. In the scenario without sexual disinhibition after PrEP initiation, key parameters influencing infections prevented were effectiveness of PrEP (partial rank correlation coefficient (PRCC) = 0.94), PrEP discontinuation rate (PRCC = −0.94), level of coverage (PRCC = 0.92), and time to achieve target coverage (PRCC = −0.82). In the scenario with sexual disinhibition, PrEP effectiveness and the extent of sexual disinhibition had the greatest impact on prevention. An optimistic scenario of PrEP with 90% effectiveness and 75% coverage of the general population predicted a 74% decline in cumulative HIV-1 infections after 10 years, and a 28.8% decline with PrEP targeted to the highest risk groups (16% of the population). Even with a 100% increase in at-risk behavior from sexual disinhibition, a beneficial effect (23.4%–62.7% decrease in infections) was seen with 90% effective PrEP across a broad range of coverage (25%–75%). Similar disinhibition led to a rise in infections with lower effectiveness of PrEP (≤50%).Conclusions/SignificanceMathematical modeling supports the potential public health benefit of PrEP. Approximately 2.7 to 3.2 million new HIV-1 infections could be averted in southern sub-Saharan Africa over 10 years by targeting PrEP (having 90% effectiveness) to those at highest behavioral risk and by preventing sexual disinhibition. This benefit could be lost, however, by sexual disinhibition and by high PrEP discontinuation, especially with lower PrEP effectiveness (≤50%).

The uncertainty of parameters will have a significant impact on slope stability, where sensitivity analysis is a commonly used method in uncertainty research. However, traditional sensitivity analysis method costs much computation time. When calculating the sensitivity index of one parameter, all other parameters are taken as fixed values, and the uncertainty of all parameters cannot be considered simultaneously. Therefore, the variance-based and the moment-independent global sensitivity analysis (GSA) methods are both introduced to determine the influence of geotechnical parameters on slope stability in this study. To solve the importance index of GSA, the least angle regression algorithm, the kernel density estimation, and orthogonal polynomial estimation methods are developed to obtain variance-based importance index and the moment-independent importance index, respectively. The proposed methods allow all variables to change simultaneously within their variation range and have high computational efficiency. The results are in good at with those obtained by the variance-based Monte Carlo simulation method, which is considered as the exact solution forobtaining the importance index. The influence of the correlation between the shear strength parameters (c and φ) on the importance index is also studied, which indicates that the negative correlation will have a great impact on the importance index, which in turn affects the safety assessment of slope. Three engineering cases have been studied for engineering application, and the compared results indicate that the impact of the geotechnical parameters uncertainty on the safety factor (Fs) and failure probability (pf) are different. Therefore, the approaches based on GSA which can integrate the Fs with pf will be a promising approach for slope stability evaluation.

Local and global sensitivity analysis (SA) methods were compared to demonstrate how the choice of SA method leads to differences in the quantification of the relative importance of model parameters in driving canopy reflectance variability. The global SA method used was the Extended Fourier Amplitude Sensitivity Test (EFAST), while a series of basecase simulations were defined for the local SA, and model parameters were perturbed sequentially. Canopy reflectance was simulated using the ProGOSAIL model. Some pronounced differences were found between the two methods in terms of the magnitude of the importance, the rank importance, and the wavelengths at which model parameters are most important in explaining reflectance variability.

Copula-based methods for global sensitivity analysis with correlated random variables and stochastic processes under incomplete probability information

Uncertainty and sensitivity analysis of cooling and heating loads for building energy planning

COVID-19 is a world pandemic that has affected and continues to affect the social lives of people. Due to its social and economic impact, different countries imposed preventive measures that are aimed at reducing the transmission of the disease. Such control measures include physical distancing, quarantine, hand-washing, travel and boarder restrictions, lockdown, and the use of hand sanitizers. Quarantine, out of the aforementioned control measures, is considered to be more stressful for people to manage. When people are stressed, their body immunity becomes weak, which leads to multiplying of coronavirus within the body. Therefore, a mathematical model consisting of six compartments, Susceptible-Exposed-Quarantine-Infectious-Hospitalized-Recovered (SEQIHR) was developed, aimed at showing the impact of stress on the transmission of COVID-19 disease. From the model formulated, the positivity, bounded region, existence, uniqueness of the solution, the model existence of free and endemic equilibrium points, and local and global stability were theoretically proved. The basic reproduction number (R0) was derived by using the next-generation matrix method, which shows that, when R0 < 1, the disease-free equilibrium is globally asymptotically stable whereas when R0 > 1 the endemic equilibrium is globally asymptotically stable. Moreover, the Partial Rank Correlation Coefficient (PRCC) method was used to study the correlation between model parameters and R0. Numerically, the SEQIHR model was solved by using the Rung-Kutta fourth-order method, while the least square method was used for parameter identifiability. Furthermore, graphical presentation revealed that when the mental health of an individual is good, the body immunity becomes strong and hence minimizes the infection. Conclusively, the control parameters have a significant impact in reducing the transmission of COVID-19.

Ranking non-pharmaceutical interventions against Covid-19 global pandemic using global sensitivity analysis—Effect on number of deaths

Intelligent sensitivity analysis framework based on machine learning for spacecraft thermal design

Event Abstract Back to Event Statistical uncertainty and sensitivity analysis of intracellular signaling models - through approximate Bayesian computation and variance based global sensitivity analysis Olivia Eriksson1, 2*, Alexandra Jauhiainen1, 3, Sara Maad Sasane4, Anu G Nair5, Carolina Sartorius4 and Jeanette Hellgren Kotaleski2, 5, 6 1 Contributed equally to this work, Sweden 2 Stockholm University, Department of Numerical Analysis and Computer Science, Sweden 3 AstraZeneca AB R&D, Early Clinical Biometrics, Sweden 4 Lund University, Centre for Mathematical Sciences, Sweden 5 KTH Royal Institute of Technology, School of Computer Science and Communication, Sweden 6 Karolinska Institute, Department of Neuroscience, Sweden Computational dynamical models describing intracellular signaling pathways of nerve cells are increasing in size and complexity as more information is obtained from experiments. Models describing protein interactions within neurons can contain over hundred protein reactions [1, 2]. These models are built from knowledge about the interaction topology, inferred from e.g. gene knock-out experiments, as well as from experimental quantitative data describing the input-output relationship of the observed system. The quantitative data are often sparse as compared to the size of the system, and translating the experimental information into dynamical models often results in large uncertainties in the parameter (e.g reaction rates) values. This uncertainty is partly due to the sparseness in experimental time series data (practical unidentifiability), but it is also an intrinsic feature of the modeled system (structural unidentifiability) and could reflect the possibility for biological variation [3]; in many biological systems the same function can be achieved in partly different ways due to degeneracy and redundancy. Here we investigate the extent of this parameter uncertainty, in a model describing calcium (Ca)-dependent activation of Calmodulin (CaM), Protein phosphatase 2B (PP2B) and Ca/CaM-dependent protein kinase II (CamKII) [4], which is an intracellular pathway of importance to synaptic plasticity. We presume that the structure of the model is correct and then characterize the uncertainty in the parameters based on data. This is done by sampling the subspace of parameter values which has an equally good fit to data (corresponding to the “viable space” in [5]), through a statistical approach known as Approximate Bayesian Computation (ABC) with Markov Chain Monte Carlo (MCMC) [6]. ABC has been proposed for parameter estimation in system biology models previously, albeit in slightly different settings, e.g. [7, 8], and can be applied to a wide range of problems. In order to characterize the viable space efficiently with several experimental datasets, we employ multivariate probability distributions called copulas as a part of the ABC sampling. The result is a multivariate posterior distribution for the parameters, which represents how much they are constrained by the data (i.e. the uncertainty) as illustrated in Figure 1 (pairwise plots of viable space for four parameters indicating constraints and dependencies before and after calibration to data). The next step is to look into how the parameter uncertainty is translated to uncertainty of the predictions made from the model. We also investigate the role and importance of different parameters, with respect to different model outputs including the predictions, by means of global sensitivity analysis [9]. Figure 2 illustrates the sensitivity of one of the outputs calculated by a method based on the decomposition of the variance [10, 11, 12], showing different types of sensitivity measures. Finally, we explore how the sensitivity of different subsets of parameters change as different parts of the viable space are investigated, which is shown in Figure 3, where sensitivity profiles are clustered into groups with different sensitivity characteristics. Figure 1 Figure 2 Figure 3 Acknowledgements This research was supported by funding from the Swedish e-Science Research Centre and the Human Brain Project References [1] Gutierrez-Arenas O, Eriksson O, Hellgren Kotaleski J (2014) Segregation and Crosstalk of D1 Receptor-Mediated Activation of ERK in Striatal Medium Spiny Neurons upon Acute Administration of Psychostimulants. PLoS Comput Biol 10, e1003445. [2] Nair AG, Gutierrez-Arenas O, Eriksson O, Vincent P, and Hellgren Kotaleski J (2015) Sensing Positive versus Negative Reward Signals through Adenylyl Cyclase-Coupled GPCRs in Direct and Indirect Pathway Striatal Medium Spiny Neurons. J. Neuroscience 35, 14017-14030. [3] Marder E, Goeritz ML, Otopalik AG (2015) Robust circuit rhythms in small circuits arise from variable circuit components and mechanisms. Curr Opin Neurobiol 31, 156-163. [4] Nair AG, Gutierrez-Arenas O, Eriksson O, Jauhiainen A, Blackwell KT and Kotaleski, JH (2014). Modeling intracellular signaling underlying striatal function in health and disease. Progress in molecular biology and translational science, 123, 277 [5] Zamora-Sillero E, Hafner M, Ibig A, Stelling J, and Wagner, A. (2011). Efficient characterization of high-dimensional parameter spaces for systems biology. BMC systems biology 5, 142. [6] Marjoram P, Molitor J, Plagnol V, and Tavare S (2003) Markov chain Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. U.S.A. 100, 15324–15328. [7] Toni T, Welch D, Strelkowa N, Ipsen A, and Stumpf MP. Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J R Soc Interface, 6, 187–202. [8] Liepe J, Kirk P, Filippi S, Toni T, Barnes CP, and Stumpf MP. A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation. Nat Protoc, 9, 439–456. [9] Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S Global sensitivity analysis: the primer. In Wiley 2008 New York, NY:Wiley. [10] Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Math. Comput. Simul. 55, 271–280. [11] Saltelli A (2002) Making best use of model evaluations to compute sensitivity indices. Comp Phys Comm 145, 280 – 297. [12] Halnes G, Ulfhielm E Ljunggren EE, Kotaleski JH and Rospars JP (2009) Modelling and sensitivity analysis of the reactions involving receptor, G-protein and effector in vertebrate olfactory receptor neurons. Journal of computational neuroscience 27, 471-491. Keywords: sensitivity analysis, Approximate Bayesian Computation, copulas, intracellular signalling, Dynamical Modeling, global sensitivity analysis, Markov chain Monte Carlo, variance decomposition Conference: Neuroinformatics 2016, Reading, United Kingdom, 3 Sep - 4 Sep, 2016. Presentation Type: Investigator presentations Topic: Computational neuroscience Citation: Eriksson O, Jauhiainen A, Maad Sasane S, Nair A, Sartorius C and Hellgren Kotaleski J (2016). Statistical uncertainty and sensitivity analysis of intracellular signaling models - through approximate Bayesian computation and variance based global sensitivity analysis. Front. Neuroinform. Conference Abstract: Neuroinformatics 2016. doi: 10.3389/conf.fninf.2016.20.00014 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 31 May 2016; Published Online: 18 Jul 2016. * Correspondence: PhD. Olivia Eriksson, Contributed equally to this work, Stockholm, Sweden, olivia@kth.se Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski Google Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski Google Scholar Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski PubMed Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.