Evaluating the Use of Global Sensitivity Analysis in Dynamic MFA

Dynamic material flow analysis (MFA) provides information about material usage over time and consequent changes in material stocks and flows. In order to understand the effect of limited data quality and model assumptions on MFA results, the use of sensitivity analysis methods in dynamic MFA studies has been on the increase. So far, sensitivity analysis in dynamic MFA has been conducted by means of a one‐at‐a‐time method, which tests parameter perturbations individually and observes the outcomes on output. In contrast to that, variance‐based global sensitivity analysis decomposes the variance of the model output into fractions caused by the uncertainty or variability of input parameters. The present study investigates interaction and time‐delay effects of uncertain parameters on the output of an archetypal input‐driven dynamic material flow model using variance‐based global sensitivity analysis. The results show that determining the main (first‐order) effects of parameter variations is often sufficient in dynamic MFA because substantial effects attributed to the simultaneous variation of several parameters (higher‐order effects) do not appear for classical setups of dynamic material flow models. For models with time‐varying parameters, time‐delay effects of parameter variation on model outputs need to be considered, potentially boosting the computational cost of global sensitivity analysis. Finally, the implications of exploring the sensitivities of model outputs with respect to parameter variations in the archetypical model are used to derive model‐ and goal‐specific recommendations on choosing appropriate sensitivity analysis methods in dynamic MFA.     

Easy parameter identifiability analysis with COPASI

Background and scope

Differential equation systems modeling biochemical reaction networks can only give quantitative predictions, when they are in accordance with experimental data. However, even if a model can well recapitulate given data, it is often the case that some of its kinetic parameters can be arbitrarily chosen without significantly affecting the simulation results. This indicates a lack of appropriate data to determine those parameters. In this case, the parameter is called to be practically non-identifiable. Well-identified parameters are paramount for reliable quantitative predictions and, therefore, identifiability analysis is an important topic in modeling of biochemical reaction networks. Here, we describe a hidden feature of the free modeling software COPASI, which can be exploited to easily and quickly conduct a parameter identifiability analysis of differential equation systems by calculating likelihood profiles. The proposed combination of an established method for parameter identifiability analysis with the user-friendly features of COPASI offers an easy and rapid access to parameter identifiability analysis even for non-experts.

Availability

COPASI is freely available for academic use at http://www.copasi.org.     

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

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

Interrogating the effect of enzyme kinetics on metabolism using differentiable constraint-based models

Metabolic models are typically characterized by a large number of parameters. Traditionally, metabolic control analysis is applied to differential equation-based models to investigate the sensitivity of predictions to parameters. A corresponding theory for constraint-based models is lacking, due to their formulation as optimization problems. Here, we show that optimal solutions of optimization problems can be efficiently differentiated using constrained optimization duality and implicit differentiation. We use this to calculate the sensitivities of predicted reaction fluxes and enzyme concentrations to turnover numbers in an enzyme-constrained metabolic model of Escherichia coli. The sensitivities quantitatively identify rate limiting enzymes and are mathematically precise, unlike current finite difference based approaches used for sensitivity analysis. Further, efficient differentiation of constraint-based models unlocks the ability to use gradient information for parameter estimation. We demonstrate this by improving, genome-wide, the state-of-the-art turnover number estimates for E. coli. Finally, we show that this technique can be generalized to arbitrarily complex models. By differentiating the optimal solution of a model incorporating both thermodynamic and kinetic rate equations, the effect of metabolite concentrations on biomass growth can be elucidated. We benchmark these metabolite sensitivities against a large experimental gene knockdown study, and find good alignment between the predicted sensitivities and in vivo metabolome changes. In sum, we demonstrate several applications of differentiating optimal solutions of constraint-based metabolic models, and show how it connects to classic metabolic control analysis.     

Robustness of post-reconstruction and direct kinetic parameter estimates under rigid head motion in dynamic brain PET imaging

ObjectiveDynamic PET imaging is extensively used in brain imaging to estimate parametric maps. Inter-frame motion can substantially disrupt the voxel-wise time-activity curves (TACs), leading to erroneous maps during kinetic modelling. Therefore, it is important to characterize the robustness of kinetic parameters under various motion and kinetic model related factors.MethodsFully 4D brain simulations ([¹⁵O]H₂O and [¹⁸F]FDG dynamic datasets) were performed using a variety of clinically observed motion patterns. Increasing levels of head motion were investigated as well as varying temporal frames of motion initiation. Kinetic parameter estimation was performed using both post-reconstruction kinetic analysis and direct 4D image reconstruction to assess bias from inter-frame emission blurring and emission/attenuation mismatch.ResultsKinetic parameter bias heavily depends on the time point of motion initiation. Motion initiated towards the end of the scan results in the most biased parameters. For the [¹⁸F]FDG data, k₄ is the more sensitive parameter to positional changes, while K₁ and blood volume were proven to be relatively robust to motion. Direct 4D image reconstruction appeared more sensitive to changes in TACs due to motion, with parameter bias spatially propagating and depending on the level of motion.ConclusionKinetic parameter bias highly depends upon the time frame at which motion occurred, with late frame motion-induced TAC discontinuities resulting in the least accurate parameters. This is of importance during prolonged data acquisition as is often the case in neuro-receptor imaging studies. In the absence of a motion correction, use of TOF information within 4D image reconstruction could limit the error propagation.     

Strategies for dealing with incomplete information in the modeling of molecular interaction networks

Modelers of molecular interaction networks encounter the paradoxical situation that while large amounts of data are available, these are often insufficient for the formulation and analysis of mathematical models describing the network dynamics. In particular, information on the reaction mechanisms and numerical values of kinetic parameters are usually not available for all but a few well-studied model systems. In this article we review two strategies that have been proposed for dealing with incomplete information in the study of molecular interaction networks: parameter sensitivity analysis and model simplification. These strategies are based on the biologically justified intuition that essential properties of the system dynamics are robust against moderate changes in the value of kinetic parameters or even in the rate laws describing the interactions. Although advanced measurement techniques can be expected to relieve the problem of incomplete information to some extent, the strategies discussed in this article will retain their interest as tools providing an initial characterization of essential properties of the network dynamics.     

Process model comparison and transferability across bioreactor scales and modes of operation for a mammalian cell bioprocess

A Monod kinetic model, logistic equation model, and statistical regression model were developed for a Chinese hamster ovary cell bioprocess operated under three different modes of operation (batch, bolus fed‐batch, and continuous fed‐batch) and grown on two different bioreactor scales (3 L bench‐top and 15 L pilot‐scale). The Monod kinetic model was developed for all modes of operation under study and predicted cell density, glucose glutamine, lactate, and ammonia concentrations well for the bioprocess. However, it was computationally demanding due to the large number of parameters necessary to produce a good model fit. The transferability of the Monod kinetic model structure and parameter set across bioreactor scales and modes of operation was investigated and a parameter sensitivity analysis performed. The experimentally determined parameters had the greatest influence on model performance. They changed with scale and mode of operation, but were easily calculated. The remaining parameters, which were fitted using a differential evolutionary algorithm, were not as crucial. Logistic equation and statistical regression models were investigated as alternatives to the Monod kinetic model. They were less computationally intensive to develop due to the absence of a large parameter set. However, modeling of the nutrient and metabolite concentrations proved to be troublesome due to the logistic equation model structure and the inability of both models to incorporate a feed. The complexity, computational load, and effort required for model development has to be balanced with the necessary level of model sophistication when choosing which model type to develop for a particular application. © 2012 American Institute of Chemical Engineers Biotechnol. Prog., 2013     

Identification of unstructured model for subtilin production through Bacillus subtilis using hybrid genetic algorithm

Subtilin production is favorable when Bacillus subtilis 168 is subjected to stress condition such as nutrient scarcity. A mathematical model underlying such growth process has immense applicability in determining the optimal operating conditions at industrial scale. We present this work with multiple objectives of a) selection of a substrate for creating the minimal nutrient media for B. subtilis thereby enhancing subtilin production, b) experimental study of the growth along with morphological characteristics of B. subtilis and product profile in nutrient scarcity condition and c) identification of an optimal unstructured model for subtilin production using a computational framework. First, we show that subtilin can be produced while B. subtilis is grown using galactose and B. subtilis undergoes morphological changes and takes filamentous shape. We then constructed a series of plausible models and used a hybrid method combining Genetic Algorithm and gradient based search methodologies, for model selection. The estimated kinetic parameters and the stoichiometric analysis indicate that the B. subtilis growth/death, product profile and respiratory mechanism undergo specific modifications in galactose as an adaptive response. Current study provides an inexpensive platform to produce subtilin and the predictive framework presented here has potential applications for large scale production of subtilin.     

The importance of assessing parameter sensitivity when using biophysical models: a case study using plethodontid salamanders

Landscapes are continually changing due to numerous assaults, including habitat alteration, anthropogenic disturbances, and climate change. Understanding how species will respond to these changes is of critical importance for conservation and management. Mechanistic models, such as biophysical models (BPMs), are an increasingly popular tool to predict how local population dynamics or species’ distributions may be altered in response to environmental and climate changes. By mechanistically modeling relationships between environmental conditions, physiology and behavior, it is possible to make accurate predictions about how species may respond. However, BPMs are often difficult to implement due to lack of appropriate, species-specific data that is biologically realistic or relevant. In this study, we present a BPM for the salamander Plethodon jordani and assess how adding more biological realism has potential to alter model predictions about annual energy budgets. Additionally, we conducted local and global sensitivity analyses to evaluate the importance of accurately specifying model parameter values and functional relationships. We found that the addition of biological realism resulted in greater model complexity as well as substantially different estimates of energy balance. Correct parameterization of biophysical models is also critical, as small changes in parameter values can result in disproportionately large changes in downstream model estimates. Our model highlights the overall importance of using ecologically relevant and specific data for input parameters, as well as careful assessment of parameter sensitivity. We encourage researchers to be aware of the data they are using to parameterize BPMs, and urge the collection of system-specific data that is relevant in spatial and temporal scale. We also recommend greater and more transparent use of sensitivity analyses to provide a better understanding of the model, as well as greater confidence in model predictions.     

The uncertainty in simulations by a Global Biome Model (BIOME3) to alternative parameter values

The sensitivity of a global biome model (BIOME3) to uncertainty in parameter values was investigated by testing the model's sensitivity to minimum and maximum parameter values obtained from an extensive literature search. Simulations were conducted replacing the default parameter value by each of the maximum and minimum values determined from the literature. In doing so, the aim was to identify those parameters where the use of an alternate (observed) value leads to a significant change in the simulation of plant functional types at a global scale, in order to identify those which are functionally important to the model. BIOME3 was found to be insensitive to changes in the majority of its parameters, providing a generally sound foundation for confidence in model simulations. However, there was considerable sensitivity shown to over a quarter of the parameters. Three main types of parameters led to a change in plant functional types distribution relative to the control simulation: (i) parameters affecting the photosynthesis parameterization; (ii) parameters affecting the evapotranspiration parameterization; and (iii) root distribution which affected both parts of the model. The main causes of sensitivity were changes in the photosynthesis parameters leading to differential changes in plant functional type's net primary productivity. This caused a shift in the competitive balance between specific plant functional types or between C3 and C4 plant types, and a consequent change in their global distribution. Changes to the evapotranspiration parameters and root distribution similarly affected net primary productivity and soil moisture, and often led to shifts in the competitive balance between grass and trees. Changes in the value for several poorly known parameters produced substantial changes in the distribution of plant functional types, and reduced the κ‐statistic to a large degree, indicating areas of potential uncertainty in the model. This suggests that great care must be taken in prescribing values to these parameters and provides guidance on which parameters need further attention in observational work.     

Assessing the potential impact of Salmonella vaccines in an endemically infected dairy herd

Salmonella spp. in cattle contribute to bacterial foodborne disease for humans. Reduction of Salmonella prevalence in herds is important to prevent human Salmonella infections. Typical control measures are culling of infectious animals, vaccination, and improved hygiene management. Vaccines have been developed for controlling Salmonella transmission in dairy herds; however, these vaccines are imperfect and a variety of vaccine effects on susceptibility, infectiousness, Salmonella shedding level, and duration of infectious period were reported. To assess the potential impact of imperfect Salmonella vaccines on prevalence over time and the eradication criterion, we developed a deterministic compartmental model with both replacement (cohort) and lifetime (continuous) vaccination strategies, and applied it to a Salmonella Cerro infection in a dairy farm. To understand the uncertainty of prevalence and identify key model parameters, global parameter uncertainty and sensitivity analyses were performed. The results show that imperfect Salmonella vaccines reduce the prevalence of Salmonella Cerro. Among three vaccine effects that were being considered, decreasing the length of the infectious period is most effective in reducing the endemic prevalence. Analyses of contour lines of prevalence or the critical reproduction ratio illustrate that, reducing prevalence to a certain level or zero can be achieved by choosing vaccines that have either a single vaccine effect at relatively high effectiveness, or two or more vaccine effects at relatively low effectiveness. Parameter sensitivity analysis suggests that effective control measures through applying Salmonella vaccines should be adjusted at different stages of infection. In addition, lifetime (continuous) vaccination is more effective than replacement (cohort) vaccination. The potential application of the developed vaccination model to other Salmonella serotypes related to foodborne diseases was also discussed. The presented study may be used as a tool for guiding the development of Salmonella vaccines.     

基于BIOME-BGC模型的长白落叶松林净初级生产力模拟参数敏感性

基于植被生理生态过程的模型包含较多参数,合理的参数取值能够极大地提高模型的模拟能力.参数敏感性分析可以全面分析模型参数对模拟结果的影响程度,在筛选模型敏感参数过程中起到重要作用.本研究以模拟吉林省汪清林业局长白落叶松林净初级生产力（NPP）为例,分析了BIOME-BGC模型的参数敏感性.首先利用样地实测NPP数据与模拟值进行对比分析,检验模型对长白落叶松林NPP的模拟能力;然后利用Morris法和EFAST法筛选出BIOME-BGC模型中对长白落叶松林NPP影响较大的敏感参数.在此基础上,通过EFAST法对所有筛选出的参数进行定量的敏感性分析,计算了敏感参数的全局敏感性指数、一阶敏感性指数和二阶敏感性指数.结果表明： BIOME-BGC模型能够较好地模拟研究区内长白落叶松林NPP的变化趋势;Morris法可以在样本量较少的情况下实现对BIOME-BGC模型敏感参数的筛选,而EFAST法可以定量分析BIOME-BGC模型中单个参数以及不同参数之间交互作用对模拟结果的影响程度;BIOME-BGC模型中对长白落叶松林NPP影响较大的敏感参数为新生茎与叶片的碳分配比和叶片碳氮比,且二者之间的交互作用明显大于其他参数之间的交互作用.     

Sensitivity analysis to identify key parameters influencing Salmonella infection dynamics in a pig batch

In the context of managed herds, epidemiological models usually take into account relatively complex interactions involving a high number of parameters. Some parameters may be uncertain and/or highly variable, especially epidemiological parameters. Their impact on the model outputs must then be assessed by a sensitivity analysis, allowing to identify key parameters. The prevalence over time is an output of particular interest in epidemiological models, so sensitivity analysis methods adapted to such dynamic output are needed.In this paper, such a sensitivity analysis method, based on a principal component analysis and on analysis of variance, is presented. It allows to compute a generalised sensitivity index for each parameter of a model representing Salmonella spread within a pig batch. The model is a stochastic discrete-time model describing the batch dynamics and movements between rearing rooms, from birth to slaughterhouse delivery. Four health states were introduced: Salmonella-free, seronegative shedder, seropositive shedder and seropositive carrier. The indirect transmission was modelled via an infection probability function depending on the quantity of Salmonella in the rearing room.Simulations were run according to a fractional factorial design enabling the estimation of main effects and two-factor interactions. For each of the 18 epidemiological parameters, four values were chosen, leading to 4096 scenarios. For each scenario, 15 replications were performed, leading to 61 440 simulations. The sensitivity analysis was then conducted on the seroprevalence output.The parameters governing the infection probability function and residual room contaminations were identified as key parameters. To control the Salmonella seroprevalence, efficient measures should therefore aim at these parameters. Moreover, the shedding rate and maternal protective factor also had a major impact. Therefore, further investigation on the protective effect of maternal or post-infection antibodies would be needed.     

Mechanical performance of endodontic restorations with prefabricated posts: sensitivity analysis of parameters with a 3D finite element model

Many studies have investigated the effect of different parameters of the endodontically restored tooth on its final strength, using in vitro tests and model simulations. However, the differences in the experimental set-up or modelling conditions and the limited number of parameters studied in each case prevent us from obtaining clear conclusions about the relative importance of each parameter. In this study, a validated 3D biomechanical model of the restored tooth was used for an exhaustive sensitivity analysis. The individual influence of 20 different parameters on the mechanical performance of an endodontic restoration with prefabricated posts was studied. The results bring up the remarkable importance of the loading angle on the final restoration strength. Flexural loads are more critical than compressive or tensile loads. Young's modulus of the post and its length and diameter are the most influential parameters for strength, whereas other parameters such as ferrule geometry or core and crown characteristics are less significant.     

Novel image cytometric method for detection of physiological and metabolic changes in Saccharomyces cerevisiae

The studying and monitoring of physiological and metabolic changes in Saccharomyces cerevisiae (S. cerevisiae) has been a key research area for the brewing, baking, and biofuels industries, which rely on these economically important yeasts to produce their products. Specifically for breweries, physiological and metabolic parameters such as viability, vitality, glycogen, neutral lipid, and trehalose content can be measured to better understand the status of S. cerevisiae during fermentation. Traditionally, these physiological and metabolic changes can be qualitatively observed using fluorescence microscopy or flow cytometry for quantitative fluorescence analysis of fluorescently labeled cellular components associated with each parameter. However, both methods pose known challenges to the end-users. Specifically, conventional fluorescent microscopes lack automation and fluorescence analysis capabilities to quantitatively analyze large numbers of cells. Although flow cytometry is suitable for quantitative analysis of tens of thousands of fluorescently labeled cells, the instruments require a considerable amount of maintenance, highly trained technicians, and the system is relatively expensive to both purchase and maintain. In this work, we demonstrate the first use of Cellometer Vision for the kinetic detection and analysis of vitality, glycogen, neutral lipid, and trehalose content of S. cerevisiae. This method provides an important research tool for large and small breweries to study and monitor these physiological behaviors during production, which can improve fermentation conditions to produce consistent and higher-quality products.     

Evaluation of habitat suitability index models by global sensitivity and uncertainty analyses: a case study for submerged aquatic vegetation

Habitat suitability index (HSI) models are commonly used to predict habitat quality and species distributions and are used to develop biological surveys, assess reserve and management priorities, and anticipate possible change under different management or climate change scenarios. Important management decisions may be based on model results, often without a clear understanding of the level of uncertainty associated with model outputs. We present an integrated methodology to assess the propagation of uncertainty from both inputs and structure of the HSI models on model outputs (uncertainty analysis: UA) and relative importance of uncertain model inputs and their interactions on the model output uncertainty (global sensitivity analysis: GSA). We illustrate the GSA/UA framework using simulated hydrology input data from a hydrodynamic model representing sea level changes and HSI models for two species of submerged aquatic vegetation (SAV) in southwest Everglades National Park: Vallisneria americana (tape grass) and Halodule wrightii (shoal grass). We found considerable spatial variation in uncertainty for both species, but distributions of HSI scores still allowed discrimination of sites with good versus poor conditions. Ranking of input parameter sensitivities also varied spatially for both species, with high habitat quality sites showing higher sensitivity to different parameters than low‐quality sites. HSI models may be especially useful when species distribution data are unavailable, providing means of exploiting widely available environmental datasets to model past, current, and future habitat conditions. The GSA/UA approach provides a general method for better understanding HSI model dynamics, the spatial and temporal variation in uncertainties, and the parameters that contribute most to model uncertainty. Including an uncertainty and sensitivity analysis in modeling efforts as part of the decision‐making framework will result in better‐informed, more robust decisions.     

Dynamical analysis of the calcium signaling pathway in cardiac myocytes based on logarithmic sensitivity analysis

Many cellular functions are regulated by the Ca(2+) signal which contains specific information in the form of frequency, amplitude, and duration of the oscillatory dynamics. Any alterations or dysfunctions of components in the calcium signaling pathway of cardiac myocytes may lead to a diverse range of cardiac diseases including hypertrophy and heart failure. In this study, we have investigated the hidden dynamics of the intracellular Ca(2+) signaling and the functional roles of its regulatory mechanism through in silico simulations and parameter sensitivity analysis based on an experimentally verified mathematical model. It was revealed that the Ca(2+) dynamics of cardiac myocytes are determined by the balance among various system parameters. Moreover, it was found through the parameter sensitivity analysis that the self-oscillatory Ca(2+) dynamics are most sensitive to the Ca(2+) leakage rate of the sarcolemmal membrane and the maximum rate of NCX, suggesting that these two components have dominant effects on circulating the cytosolic Ca(2+).     

Model parameter uncertainties in a dual-species biofilm competition model affect ecological output parameters much stronger than morphological ones

Bacterial biofilms are complex microbial depositions on immersed interfaces that form wherever the environmental conditions sustain microbial growth. Despite their name, biofilms can develop in highly irregular structures. Recently several mathematical concepts have been introduced to model these spatially structured microbial populations. Regardless of the type of model, they all have, even for microbially relatively simple systems, many parameters which generally are known at most approximately. We investigate the effect of uncertainties in model parameters on four morphological and four ecological output parameters using a nonlinear diffusion model for a biofilm in which two species compete for a shared nutrient. To this end we conduct an extensive computer simulation experiment for two different levels of data uncertainty, three different hydrodynamic conditions, and two different scenarios of bulk substrate availability. Our results indicate that input model parameter uncertainties have a much larger effect on ecological than on morphological output parameters.     

Mathematical identification of critical reactions in the interlocked feedback model

Dynamic simulations are necessary for understanding the mechanism of how biochemical networks generate robust properties to environmental stresses or genetic changes. Sensitivity analysis allows the linking of robustness to network structure. However, it yields only local properties regarding a particular choice of plausible parameter values, because it is hard to know the exact parameter values in vivo. Global and firm results are needed that do not depend on particular parameter values. We propose mathematical analysis for robustness (MAR) that consists of the novel evolutionary search that explores all possible solution vectors of kinetic parameters satisfying the target dynamics and robustness analysis. New criteria, parameter spectrum width and the variability of solution vectors for parameters, are introduced to determine whether the search is exhaustive. In robustness analysis, in addition to single parameter sensitivity analysis, robustness to multiple parameter perturbation is defined. Combining the sensitivity analysis and the robustness analysis to multiple parameter perturbation enables identifying critical reactions. Use of MAR clearly identified the critical reactions responsible for determining the circadian cycle in the Drosophila interlocked circadian clock model. In highly robust models, while the parameter vectors are greatly varied, the critical reactions with a high sensitivity are uniquely determined. Interestingly, not only the per-tim loop but also the dclk-cyc loop strongly affect the period of PER, although the dclk-cyc loop hardly changes its amplitude and it is not potentially influential. In conclusion, MAR is a powerful method to explore wide parameter space without human-biases and to link a robust property to network architectures without knowing the exact parameter values. MAR identifies the reactions critically responsible for determining the period and amplitude in the interlocked feedback model and suggests that the circadian clock intensively evolves or designs the kinetic parameters so that it creates a highly robust cycle.