Stochastic Approaches for Systems Biology

Ullah, Mukhtar

doi:10.1007/978-1-4614-0478-1

Cited by 49 publications

(50 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The strategy to capture this situation is to compute the probability that the state of the system (in terms of numbers of molecules of a particular type) changes during a given time interval. The base formulation for this purpose is the chemical master equation (CME), which is a finite‐state, continuous‐time Markov process that can be expressed as a Chapman‐Kolmogorov differential equation . CME describes the probability P k that the chemical system is in state k at time t .…”

Section: Step 3: Choice Of Mathematical Representations For All Procementioning

confidence: 99%

The best models of metabolism

Voit

2017

WIREs Mechanisms of Disease

View full text Add to dashboard Cite

Biochemical systems are among of the oldest application areas of mathematical modeling. Spanning a time period of over one hundred years, the repertoire of options for structuring a model and for formulating reactions has been constantly growing, and yet, it is still unclear whether or to what degree some models are better than others and how the modeler is to choose among them. In fact, the variety of options has become overwhelming and difficult to maneuver for novices and experts alike. This review outlines the metabolic model design process and discusses the numerous choices for modeling frameworks and mathematical representations. It tries to be inclusive, even though it cannot be complete, and introduces the various modeling options in a manner that is as unbiased as that is feasible. However, the review does end with personal recommendations for the choices of default models.

show abstract

Section: Step 3: Choice Of Mathematical Representations For All Procementioning

confidence: 99%

The best models of metabolism

Voit

2017

WIREs Mechanisms of Disease

View full text Add to dashboard Cite

show abstract

“…Unfortunately, the seemingly more abstract notation for stochastic modeling prevents some people from using it. This motivated us to write a textbook on stochastic modeling for systems biology (Ullah and Wolkenhauer, 2011). …”

Section: Examples For the Systems Biology Approachmentioning

confidence: 99%

Why model?

Wolkenhauer

2014

Front. Physiol.

Self Cite

View full text Add to dashboard Cite

Next generation sequencing technologies are bringing about a renaissance of mining approaches. A comprehensive picture of the genetic landscape of an individual patient will be useful, for example, to identify groups of patients that do or do not respond to certain therapies. The high expectations may however not be satisfied if the number of patient groups with similar characteristics is going to be very large. I therefore doubt that mining sequence data will give us an understanding of why and when therapies work. For understanding the mechanisms underlying diseases, an alternative approach is to model small networks in quantitative mechanistic detail, to elucidate the role of gene and proteins in dynamically changing the functioning of cells. Here an obvious critique is that these models consider too few components, compared to what might be relevant for any particular cell function. I show here that mining approaches and dynamical systems theory are two ends of a spectrum of methodologies to choose from. Drawing upon personal experience in numerous interdisciplinary collaborations, I provide guidance on how to model by discussing the question “Why model?”

show abstract

“…While this computational approach to the diffusion approximation proved to be fruitful, such interpretation hides in part the richness and the importance of the result by T. Kurtz [25]. Moreover, stochastic reaction networks attracted a renewed interest recently, see e.g., [5,13,30,36]. New motivations come both from the application in the system biology, demonstrating the emergence of the stochastic effects at small scales, and from new theoretical investigations that allowed to extend mathematical results, previously known in the deterministic setting only, to the stochastic world [2,4,10].…”

Section: Introductionmentioning

confidence: 99%

A review of the deterministic and diffusion approximations for stochastic chemical reaction networks

Mozgunov

Beccuti

Horváth

et al. 2018

Reac Kinet Mech Cat

View full text Add to dashboard Cite

This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena, such as a deficiency and a bistability. It is advocated that the diffusion approximation can be considered as an alternative theoretical approach to study the reaction networks rather than a simulation shortcut. We discuss two examples in which the diffusion approximation is able to catch qualitative properties of reaction networks that the deterministic model misses. We provide an explicit construction of the original process and the diffusion approximation such that the distance between their trajectories is controlled and demonstrate this construction for the examples. We also discuss the limitations and potential directions of the developments. P. Mozgunov and T.

show abstract

Stochastic Approaches for Systems Biology

Cited by 49 publications

References 0 publications

The best models of metabolism

The best models of metabolism

Why model?

A review of the deterministic and diffusion approximations for stochastic chemical reaction networks

Contact Info

Product

Resources

About