scholarly journals Stationary Equations for Non-Markovian Biochemical Systems

2018 ◽  
Author(s):  
Jiajun Zhang ◽  
Tianshou Zhou
Keyword(s):  
Master Equation ◽  
Stochastic Analysis ◽  
Waiting Times ◽  
Reaction Network ◽  
State Variables ◽  
New Approach ◽  
Reaction Systems ◽  
Linear Noise Approximation ◽  
Biochemical Systems ◽  
Markovian System

AbstractWe develop a new approach for stochastic analysis of biochemical reaction systems with arbitrary distributions of waiting times between reaction events. Specifically, we derive a stationary generalized chemical master equation for a non-Markovian reaction network. Importantly, this equation allows to transform the original non-Markovian problem into a Markovian one by introducing a mean reaction propensity function for every reaction in the network. Furthermore, we derive a stationary generalized linear noise approximation for the non-Markovian system, which is convenient to the direct estimation of the stationary noise in state variables. These derived equations can have broad applications, and exemplars of two representative non-Markovian models provide evidence of their applicability.

scholarly journals Novel domain expansion methods to improve the computational efficiency of the Chemical Master Equation solution for large biological networks

2020 ◽  
Vol 21 (1) ◽  
Author(s):  
Rahul Kosarwal ◽  
Don Kulasiri ◽  
Sandhya Samarasinghe
Keyword(s):  
Master Equation ◽  
State Space ◽  
Performance Management ◽  
Numerical Solutions ◽  
De Novo ◽  
Exact Analytical Solution ◽  
Chemical Master Equation ◽  
The State ◽  
Biochemical System ◽  
Biochemical Systems

Abstract Background Numerical solutions of the chemical master equation (CME) are important for understanding the stochasticity of biochemical systems. However, solving CMEs is a formidable task. This task is complicated due to the nonlinear nature of the reactions and the size of the networks which result in different realizations. Most importantly, the exponential growth of the size of the state-space, with respect to the number of different species in the system makes this a challenging assignment. When the biochemical system has a large number of variables, the CME solution becomes intractable. We introduce the intelligent state projection (ISP) method to use in the stochastic analysis of these systems. For any biochemical reaction network, it is important to capture more than one moment: this allows one to describe the system’s dynamic behaviour. ISP is based on a state-space search and the data structure standards of artificial intelligence (AI). It can be used to explore and update the states of a biochemical system. To support the expansion in ISP, we also develop a Bayesian likelihood node projection (BLNP) function to predict the likelihood of the states. Results To demonstrate the acceptability and effectiveness of our method, we apply the ISP method to several biological models discussed in prior literature. The results of our computational experiments reveal that the ISP method is effective both in terms of the speed and accuracy of the expansion, and the accuracy of the solution. This method also provides a better understanding of the state-space of the system in terms of blueprint patterns. Conclusions The ISP is the de-novo method which addresses both accuracy and performance problems for CME solutions. It systematically expands the projection space based on predefined inputs. This ensures accuracy in the approximation and an exact analytical solution for the time of interest. The ISP was more effective both in predicting the behavior of the state-space of the system and in performance management, which is a vital step towards modeling large biochemical systems.

RASON: A new approach to the scheduling radiotherapy problem that considers the current waiting times

2016 ◽  
Vol 64 ◽  
pp. 287-295 ◽  
Author(s):  
María-Cristina Riff ◽  
Juan Pablo Cares ◽  
Bertrand Neveu
Keyword(s):  
Waiting Times ◽  
New Approach

scholarly journals Improved estimations of stochastic chemical kinetics by finite-state expansion

2021 ◽  
Vol 477 (2251) ◽  
pp. 20200964
Author(s):  
Tabea Waizmann ◽  
Luca Bortolussi ◽  
Andrea Vandin ◽  
Mirco Tribastone
Keyword(s):  
Master Equation ◽  
State Space ◽  
Stochastic Dynamics ◽  
Reaction Network ◽  
Discrete State ◽  
State Expansion ◽  
Analytical Approximations ◽  
Finite State ◽  
Stochastic Reaction ◽  
Discrete State Space

Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite-state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into an expanded one where each discrete state is represented as a further distinct species. This translation exactly preserves the stochastic dynamics, but the DRE of the expanded network can be interpreted as a correction to the original one. The effectiveness of FSE is demonstrated in models that challenge state-of-the-art techniques due to intrinsic noise, multi-scale populations and multi-stability.

Integral functionals under the excursion measure

2020 ◽  
Vol 57 (1) ◽  
pp. 137-155
Author(s):  
Maciej Wiśniewolski
Keyword(s):  
Brownian Motion ◽  
Local Time ◽  
Stochastic Analysis ◽  
New Method ◽  
Theoretic Approach ◽  
Integral Functionals ◽  
New Approach ◽  
Brownian Motion With Drift ◽  
Classical Potential ◽  
Excursion Measure

AbstractA new approach to the problem of finding the distribution of integral functionals under the excursion measure is presented. It is based on the technique of excursion straddling a time, stochastic analysis, and calculus on local time, and it is done for Brownian motion with drift reflecting at 0, and under some additional assumptions for some class of Itó diffusions. The new method is an alternative to the classical potential-theoretic approach and gives new specific formulas for distributions under the excursion measure.

Robust Approach for Identification of Bad Data in State Estimation Using SLP Technique

2007 ◽  
Vol 8 (4) ◽  
Author(s):  
Thukaram Dhadbanjan ◽  
H. P. Khincha ◽  
M. S.S. Phaniram
Keyword(s):  
State Estimation ◽  
Optimization Technique ◽  
Robust Estimator ◽  
State Variables ◽  
New Approach ◽  
Set Constraints ◽  
Leverage Point ◽  
Illustrative Purpose ◽  
Bad Data ◽  
Bound Optimization

This paper proposes a new approach for solving the state estimation problem. The approach is aimed at producing a robust estimator that rejects bad data, even if they are associated with leverage-point measurements. This is achieved by solving a sequence of Linear Programming (LP) problems. Optimization is carried via a new algorithm which is a combination of ``upper bound optimization technique" and ``an improved algorithm for discrete linear approximation". In this formulation of the LP problem, in addition to the constraints corresponding to the measurement set, constraints corresponding to bounds of state variables are also involved, which enables the LP problem more efficient in rejecting bad data, even if they are associated with leverage-point measurements. Results of the proposed estimator on IEEE 39-bus system and a 24-bus EHV equivalent system of the southern Indian grid are presented for illustrative purpose.

Partial Stabilization Approach to 3-Dimensional Guidance Law Design

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
T. Binazadeh ◽  
M. J. Yazdanpanah
Keyword(s):  
System Dynamics ◽  
The State ◽  
Guidance System ◽  
Missile Guidance ◽  
State Variables ◽  
New Approach ◽  
3 Dimensional ◽  
Guidance Law ◽  
Maneuvering Targets

In this paper, a new approach to design the 3-dimensional missile guidance law, based on partial stabilization, is presented. The approach is based on the classification of the state variables within the guidance system dynamics with respect to their required stabilization properties. The resulting guidance law enables the missile to intercept highly maneuvering targets within a finite interception time. Effectiveness of the proposed guidance law is demonstrated through analysis and simulations.

ASSESSING OPTIMAL DESIGNS IN METABOLIC PATHWAYS

1995 ◽  
Vol 03 (01) ◽  
pp. 197-206 ◽  
Author(s):  
J. PUIGJANER ◽  
M. CASCANTE ◽  
A. SORRIBAS
Keyword(s):  
Metabolic Pathways ◽  
Reaction Network ◽  
Metabolic Control Analysis ◽  
Optimal Designs ◽  
Control Analysis ◽  
Chemical Transformations ◽  
Evolution Of Metabolic Pathways ◽  
Biochemical Systems ◽  
Optimum Reaction ◽  
Alternative Designs

The evolution of metabolic pathways is characterized by the search of the optimum reaction network, both as for chemical transformations and for the associated pattern of regulation. Understanding this process requires the evaluation of alternative designs for a given function. After this evaluation, we would be in a good situation for drawing general conclusions on the evolution of the considered system. This goal can be undertaken by means of different complementary approaches. The method of Control Comparisons, first developed within Biochemical Systems Analysis, has produced some valuable insights on this kind of problems. In this contribution, we present this method within the context of Metabolic Control Analysis.

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