The stochastic quasi-steady-state assumption: reducing the model but not the noise.
Ontology highlight
ABSTRACT:
SUBMITTER: Srivastava R
PROVIDER: S-EPMC3094464 | biostudies-other | 2011 Apr
REPOSITORIES: biostudies-other
Similar Datasets
Project description:In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady-state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by nonelementary reaction-rate functions (e.g., Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the nonelementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of nonelementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the nonelementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in nonelementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the prefactor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when nonelementary reaction functions are obtained using the total QSSA. Our work provides an apparently novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales.
| S-EPMC4129492 | biostudies-literature
Project description:Large gene regulatory networks (GRN) are often modeled with quasi-steady-state approximation (QSSA) to reduce the huge computational time required for intrinsic noise quantification using Gillespie stochastic simulation algorithm (SSA). However, the question still remains whether the stochastic QSSA model measures the intrinsic noise as accurately as the SSA performed for a detailed mechanistic model or not? To address this issue, we have constructed mechanistic and QSSA models for few frequently observed GRNs exhibiting switching behavior and performed stochastic simulations with them. Our results strongly suggest that the performance of a stochastic QSSA model in comparison to SSA performed for a mechanistic model critically relies on the absolute values of the mRNA and protein half-lives involved in the corresponding GRN. The extent of accuracy level achieved by the stochastic QSSA model calculations will depend on the level of bursting frequency generated due to the absolute value of the half-life of either mRNA or protein or for both the species. For the GRNs considered, the stochastic QSSA quantifies the intrinsic noise at the protein level with greater accuracy and for larger combinations of half-life values of mRNA and protein, whereas in case of mRNA the satisfactory accuracy level can only be reached for limited combinations of absolute values of half-lives. Further, we have clearly demonstrated that the abundance levels of mRNA and protein hardly matter for such comparison between QSSA and mechanistic models. Based on our findings, we conclude that QSSA model can be a good choice for evaluating intrinsic noise for other GRNs as well, provided we make a rational choice based on experimental half-life values available in literature.
| S-EPMC4556639 | biostudies-literature
Project description:Many biochemical networks have complex multidimensional dynamics and there is a long history of methods that have been used for dimensionality reduction for such reaction networks. Usually a deterministic mass action approach is used; however, in small volumes, there are significant fluctuations from the mean which the mass action approach cannot capture. In such cases stochastic simulation methods should be used. In this paper, we evaluate the applicability of one such dimensionality reduction method, the quasi-steady state approximation (QSSA) [L. Menten and M. Michaelis, "Die kinetik der invertinwirkung," Biochem. Z 49, 333369 (1913)] for dimensionality reduction in case of stochastic dynamics. First, the applicability of QSSA approach is evaluated for a canonical system of enzyme reactions. Application of QSSA to such a reaction system in a deterministic setting leads to Michaelis-Menten reduced kinetics which can be used to derive the equilibrium concentrations of the reaction species. In the case of stochastic simulations, however, the steady state is characterized by fluctuations around the mean equilibrium concentration. Our analysis shows that a QSSA based approach for dimensionality reduction captures well the mean of the distribution as obtained from a full dimensional simulation but fails to accurately capture the distribution around that mean. Moreover, the QSSA approximation is not unique. We have then extended the analysis to a simple bistable biochemical network model proposed to account for the stability of synaptic efficacies; the substrate of learning and memory [J. E. Lisman, "A mechanism of memory storage insensitive to molecular turnover: A bistable autophosphorylating kinase," Proc. Natl. Acad. Sci. U.S.A. 82, 3055-3057 (1985)]. Our analysis shows that a QSSA based dimensionality reduction method results in errors as big as two orders of magnitude in predicting the residence times in the two stable states.
| S-EPMC3416873 | biostudies-other
Project description:Using the (slow-scale) linear noise approximation, we give parameter-independent bounds to the substrate and product intrinsic noise variance for the stochastic Michaelis-Menten approximation at steady state.
| S-EPMC3829885 | biostudies-other
Project description:PurposeOscillating steady-state imaging (OSSI) is an SNR-efficient steady-state sequence with T2∗ sensitivity suitable for FMRI. Due to the frequency sensitivity of the signal, respiration- and drift-induced field changes can create unwanted signal fluctuations. This study aims to address this issue by developing retrospective signal correction methods that utilize OSSI signal properties to denoise task-based OSSI FMRI experiments.MethodsA retrospective denoising approach was developed that leverages the unique signal properties of OSSI to perform denoising without a manually specified noise region of interest and works with both voxel timecourses (oscillating steady-state correction [OSSCOR]) or FID timecourses (F-OSSCOR). Simulations were performed to estimate the number of principal components optimal for denoising. In vivo experiments at 3 T field strength were conducted to compare the performance of proposed methods against a standard principal component analysis-based method, measured using mean t score within an region of interest, number of activations, and mean temporal SNR.ResultsCorrection using OSSCOR was significantly better than the standard method in all metrics. Correction using F-OSSCOR was not significantly different from the standard method using an equal number of principal components. Increasing the number of OSSCOR principal components decreased activation strength and increased the number of suspected false positives. However, increasing the number of principal components in F-OSSCOR increased activation strength with little to no increase in false activation.ConclusionBoth OSSCOR and F-OSSCOR substantially reduce physiological noise components and increase temporal SNR, improving the functional results of task-based OSSI functional experiments. F-OSSCOR demonstrates a proof of concept utilization of coil-localized FID signal information for physiological noise correction.
| S-EPMC7722173 | biostudies-literature
Project description:In metabolic networks, metabolites are usually present in great excess over the enzymes that catalyze their interconversion, and describing the rates of these reactions by using the Michaelis-Menten rate law is perfectly valid. This rate law assumes that the concentration of enzyme-substrate complex (C) is much less than the free substrate concentration (S0). However, in protein interaction networks, the enzymes and substrates are all proteins in comparable concentrations, and neglecting C with respect to S0 is not valid. Borghans, DeBoer, and Segel developed an alternative description of enzyme kinetics that is valid when C is comparable to S0. We extend this description, which Borghans et al. call the total quasi-steady state approximation, to networks of coupled enzymatic reactions. First, we analyze an isolated Goldbeter-Koshland switch when enzymes and substrates are present in comparable concentrations. Then, on the basis of a real example of the molecular network governing cell cycle progression, we couple two and three Goldbeter-Koshland switches together to study the effects of feedback in networks of protein kinases and phosphatases. Our analysis shows that the total quasi-steady state approximation provides an excellent kinetic formalism for protein interaction networks, because (1) it unveils the modular structure of the enzymatic reactions, (2) it suggests a simple algorithm to formulate correct kinetic equations, and (3) contrary to classical Michaelis-Menten kinetics, it succeeds in faithfully reproducing the dynamics of the network both qualitatively and quantitatively.
| S-EPMC1828705 | biostudies-literature
Project description:A computer program is developed for the derivation of the rate equation for enzyme reactions on the basis of the pseudo-steady-state assumption and the combination of the pseudo-steady-state and the rapid-equilibrium assumptions. The program not only has an easy input method, but also can obtain a complete rate equation in itself on only one run. The usefulness of the program is demonstrated by deriving the rate equations for some typical enzyme reactions. Details of the program have been deposited as Supplementary Publication SUP 50141 (42 pages) at the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7QB, U.K., from whom copies may be obtained as indicated in Biochem. J. (1988), 249, 5.
| S-EPMC1148980 | biostudies-other
Project description:Microphysiological systems (MPS), consisting of tissue constructs, biomaterials, and culture media, aim to recapitulate relevant organ functions in vitro. MPS components are housed in fluidic hardware with operational protocols, such as periodic complete media replacement. Such batch-like operations provide relevant nutrients and remove waste products but also reset cell-secreted mediators (e.g. cytokines, hormones) and potentially limit exposure to drugs (and metabolites). While each component plays an essential role for tissue functionality, MPS-specific nutrient needs are not yet well-characterized nor utilized to operate MPSs at more physiologically-relevant conditions. MPS-specific nutrient needs for gut (immortalized cancer cells), liver (human primary hepatocytes) and cardiac (iPSC-derived cardiomyocytes) MPSs were experimentally quantified. In a long-term study of the gut MPS (10 days), this knowledge was used to design operational protocols to maintain glucose and lactate at desired levels. This quasi-steady state operation was experimentally validated by monitoring glucose and lactate as well as MPS functionality. In a theoretical study, nutrient needs of an integrated multi-MPS platform (gut, liver, cardiac MPSs) were computationally simulated to identify long-term quasi-steady state operations. This integrative experimental and computational approach demonstrates the utilization of quantitative multi-scale characterization of MPSs and incorporating MPS-specific information to establish more physiologically-relevant experimental operations.
| S-EPMC5964119 | biostudies-literature
Project description:Aerodynamic performance and agility during flapping flight are determined by the combination of wing shape and kinematics. The degree of morphological and kinematic optimisation is unknown and depends upon a large parameter space. Aimed at providing an accurate and computationally inexpensive modelling tool for flapping-wing aerodynamics, we propose a novel CFD (computational fluid dynamics)-informed quasi-steady model (CIQSM), which assumes that the aerodynamic forces on a flapping wing can be decomposed into the quasi-steady forces and parameterised based on CFD results. Using least-squares fitting, we determine a set of proportional coefficients for the quasi-steady model relating wing kinematics to instantaneous aerodynamic force and torque; we calculate power with the product of quasi-steady torques and angular velocity. With the quasi-steady model fully and independently parameterised on the basis of high-fidelity CFD modelling, it is capable of predicting flapping-wing aerodynamic forces and power more accurately than the conventional blade element model (BEM) does. The improvement can be attributed to, for instance, taking into account the effects of the induced downwash and the wing tip vortex on the force generation and power consumption. Our model is validated by comparing the aerodynamics of a CFD model and the present quasi-steady model using the example case of a hovering hawkmoth. It demonstrates that the CIQSM outperforms the conventional BEM while remaining computationally cheap, and hence can be an effective tool for revealing the mechanisms of optimization and control of kinematics and morphology in flapping-wing flight for both bio-flyers and unmanned air systems.
| S-EPMC4918218 | biostudies-other
Project description:C4 plants play a key role in world agriculture. For example, C4 crops such as maize and sorghum are major contributors to both first and third world food production and the C4 grasses sugarcane, miscanthus and switchgrass are major plant sources of bioenergy. In the challenge to manipulate and enhance C4 photosynthesis, steady state models of leaf photosynthesis provide an important tool for gas exchange analysis and thought experiments that can explore photosynthetic pathway changes. Here the C4 photosynthetic model by von Caemmerer and Furbank (1999) has been updated with new kinetic parameterisation and temperature dependencies added. The parameterisation was derived from experiments on the C4 monocot, Setaria viridis, which for the first time provides a cohesive parametrisation. Mesophyll conductance and its temperature dependence have also been included, as this is an important step in the quantitative correlation between the initial slope of the CO2 response curve of CO2 assimilation and in vitro PEP carboxylase activity. Furthermore, the equations for chloroplast electron transport have been updated to include cyclic electron transport flow and equations have been added to calculate electron transport rate from measured CO2 assimilation rates.
| S-EPMC8411607 | biostudies-literature