scholarly journals Accurate parametric sensitivity of stochastic biochemical systems

2021 ◽  
Author(s):  
Farid Gassoumov

Computational and Systems Biology are experiencing a rapid development in recent years. Mathematical and computational modelling are critical tools for studying cellular dynamics. Molecular interactions in a cell may display significant random fluctuations when some key species have low amounts (RNA, DNA), making the traditional model of the deterministic reaction rate equations insufficient. Consequently, stochastic models are required to accurately represent the biochemical system behaviour. Nonetheless, stochastic models are more challenging to simulate and analyse than the deterministic ones. Parametric sensitivity is a powerful tool for exploring the system behaviour, such as system robustness with respect to perturbations in its parameters. We present an accurate method for estimating parametric sensitivities for stochastic discrete models of biochemical systems using a high order Coupled Finite Difference scheme and illustrate its advantages compared to the existing techniques

2021 ◽  
Author(s):  
Farid Gassoumov

Computational and Systems Biology are experiencing a rapid development in recent years. Mathematical and computational modelling are critical tools for studying cellular dynamics. Molecular interactions in a cell may display significant random fluctuations when some key species have low amounts (RNA, DNA), making the traditional model of the deterministic reaction rate equations insufficient. Consequently, stochastic models are required to accurately represent the biochemical system behaviour. Nonetheless, stochastic models are more challenging to simulate and analyse than the deterministic ones. Parametric sensitivity is a powerful tool for exploring the system behaviour, such as system robustness with respect to perturbations in its parameters. We present an accurate method for estimating parametric sensitivities for stochastic discrete models of biochemical systems using a high order Coupled Finite Difference scheme and illustrate its advantages compared to the existing techniques


2021 ◽  
Author(s):  
Alexandra Teslya

Computational and Systems Biology are recently experiencing a rapid development. Mathematical modeling is a key tool in analyzing critical biological processes in cells and living organisms. In particular, stochastic models are essential to accurately describe the biochemical processes in the cell. However, stochastic models are computationally much more challenging than the traditional deterministic models. Also, the sheer scale of biological processes makes efficiency of the simulation a key issue. In this thesis we study the numerical solution of a continuous stochastic model of biochemical systems, the Chemical Langevin Equation. We propose an adaptive step-size method for the Euler-Maruyama scheme applied to small noise problems. The adaptive technique is p-mean convergent and computes simultaneously all the trajectories, using the same time-step on all trajectories. Our adaptive algorithm is tested on several examples arising in applications and shown to perform much better than the fixed step-size schemes.


2021 ◽  
Author(s):  
Alexandra Teslya

Computational and Systems Biology are recently experiencing a rapid development. Mathematical modeling is a key tool in analyzing critical biological processes in cells and living organisms. In particular, stochastic models are essential to accurately describe the biochemical processes in the cell. However, stochastic models are computationally much more challenging than the traditional deterministic models. Also, the sheer scale of biological processes makes efficiency of the simulation a key issue. In this thesis we study the numerical solution of a continuous stochastic model of biochemical systems, the Chemical Langevin Equation. We propose an adaptive step-size method for the Euler-Maruyama scheme applied to small noise problems. The adaptive technique is p-mean convergent and computes simultaneously all the trajectories, using the same time-step on all trajectories. Our adaptive algorithm is tested on several examples arising in applications and shown to perform much better than the fixed step-size schemes.


2020 ◽  
Vol 11 (1) ◽  
pp. 55-71
Author(s):  
Luca Meacci ◽  
Gustavo C. Buscaglia ◽  
Fernando Mut ◽  
Roberto F. Ausas ◽  
Mario Primicerio

Abstract This work consists in the presentation of a computational modelling approach to study normal and pathological behavior of red blood cells in slow transient processes that can not be accompanied by pure particle methods (which require very small time steps). The basic model, inspired by the best models currently available, considers the cytoskeleton as a discrete non-linear elastic structure. The novelty of the proposed work is to couple this skeleton with continuum models instead of the more common discrete models (molecular dynamics, particle methods) of the lipid bilayer. The interaction of the solid cytoskeleton with the bilayer, which is a two-dimensional fluid, will be done through adhesion forces adapting e cient solid-solid adhesion algorithms. The continuous treatment of the fluid parts is well justified by scale arguments and leads to much more stable and precise numerical problems when, as is the case, the size of the molecules (0.3 nm) is much smaller than the overall size (≃ 8000 nm). In this paper we display some numerical simulations that show how our approach can describe the interaction of an RBC with an exogenous body as well as the relaxation of the shape of an RBC toward its equilibrium configuration in absence of external forces.


2018 ◽  
Author(s):  
Yasmin Z. Paterson ◽  
David Shorthouse ◽  
Markus W. Pleijzier ◽  
Nir Piterman ◽  
Claus Bendtsen ◽  
...  

ABSTRACTIn an age where the volume of data regarding biological systems exceeds our ability to analyse it, many researchers are looking towards systems biology and computational modelling to help unravel the complexities of gene and protein regulatory networks. In particular, the use of discrete modelling allows generation of signalling networks in the absence of full quantitative descriptions of systems, which are necessary for ordinary differential equation (ODE) models. In order to make such techniques more accessible to mainstream researchers, tools such as the BioModelAnalyzer (BMA) have been developed to provide a user-friendly graphical interface for discrete modelling of biological systems. Here we use the BMA to build a library of discrete target functions of known canonical molecular interactions, translated from ordinary differential equations (ODEs). We then show that these BMA target functions can be used to reconstruct complex networks, which can correctly predict many known genetic perturbations. This new library supports the accessibility ethos behind the creation of BMA, providing a toolbox for the construction of complex cell signalling models without the need for extensive experience in computer programming or mathematical modelling, and allows for construction and simulation of complex biological systems with only small amounts of quantitative data.AUTHOR SUMMARYOrdinary differential equation (ODE) based models are a popular approach for modelling biological networks. A limitation of ODE models is that they require complete networks and detailed kinetic parameterisation. An alternative is the use of discrete, executable models, in which nodes are assigned discrete value ranges, and the relationship between them defined with simple mathematical operations. One tool for constructing such models is the BioModelAnalyzer (BMA), an open source and publicly available (https://www.biomodelanalyzer.org) software, aimed to be fully usable by researchers without extensive computational or mathematical experience. A fundamental question for executable models is whether the high level of abstraction substantially reduces expressivity relative to continuous approaches. Here, we present a canonical library of biological signalling motifs, initially defined by Tyson et al (2003), translated for the first time into the BMA. We show that; 1) these motifs are easily and fully translatable from continuous to discrete models, 2) Combining these motifs in a computationally naïve way generates a fully functional and predictive model of the yeast cell cycle.


2021 ◽  
Author(s):  
Samaneh Gholami

Modeling and simulation of biochemical systems are some of the important research areas in the rapid rise of Systems Biology. Often biochemical kinetic models represent cellular processes as systems of chemical reactions. The dynamics of these systems is typically described by using stochastic models. We introduce a method for an accurate sensitivity analysis of continuous such models of well-stirred biochemical systems. Sensitivity analysis plays a central role in the study of biochemical systems, being an important tool in their model construction, investigation and validation. In particular, it enables the identification of the key reaction rate parameters and it gives insight on how to effectively reduce the system while maintaining its overall behavior. The efficiency and accuracy of the method discussed are tested on several examples of practical interest.


2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Hemalatha Sasidharakurup ◽  
Shyam Diwakar

Abstract Computational and mathematical modelling towards understanding the structure and dynamics of biological systems has significantly impacted on translational neuroscience to face novel approaches toward neurological disorders such as Alzheimer’s (AD) and Parkinson’s disease (PD). In this study, a computational model of AD and PD have been modelled using biochemical systems theory, and shows how Tumour Necrosis Factor alpha (TNF훼) regulated neuroinflammation, oxidative stress and insulin pathways can dysregulate its downstream signalling cascade that lead to neurodegeneration observed in AD and PD. The experimental data for initial conditions for this model and validation of the model was based on data reported in literature. In simulations, elevations in the aggregations of major proteins involved in the pathology of AD and PD including amyloid beta, alpha synuclein, tau have been modelled. Abnormal aggregation of these proteins and hyperphosphorylation of tau were observed in the model. This aggregation may lead to developing Lewy bodies, fibrils, plaques and tangles inside neurons that trigger apoptosis. An increase in the concentrations of TNF훼 and glutamate during diseased conditions was noted in the model. Accumulation of these proteins may be related to the feedback mechanism of TNF훼 that initiates its own release and the production of excess glutamate. This could lead to the prolonged activation of microglia that result in death of surrounding neurons. With the elevation in reactive oxygen species, oxidative stress also increased. Simulations suggest insulin may be an important factor identifying neurodegeneration in AD and PD, through its action along with the neuroinflammation and oxidative stress. Low insulin level was noticed in the diseased condition due to abnormal protein aggregation that leads to TNFα release. Given the role towards better design of real experiments, accumulation of oligomers of mutated proteins in AD and PD activating microglia and secreting TNFα along with other cytokines map to oxidative stress that led to cell death.


Sign in / Sign up

Export Citation Format

Share Document