7052
2019
2019
eng
1779
1829
50
79
article
Journal of Mathematical Biology
0
2019-08-03
2018-09-24
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Algebraic Expressions of Conditional Expectations in Gene Regulatory Networks
Gene Regulatory Networks are powerful models for describing the mechanisms and dynamics inside a cell. These networks are generally large in dimension and seldom yield analytical formulations. It was shown that studying the conditional expectations between dimensions (vertices or species) of a network could lead to drastic dimension reduction. These conditional expectations were classically given by solving equations of motions derived from the Chemical Master Equation. In this paper we deviate from this convention and take an Algebraic approach instead. That is, we explore the consequences of conditional expectations being described by a polynomial function. There are two main results in this work. Firstly: if the conditional expectation can be described by a polynomial function, then coefficients of this polynomial function can be reconstructed using the classical moments. And secondly: there are dimensions in Gene Regulatory Networks which inherently have conditional expectations with algebraic forms. We demonstrate through examples, that the theory derived in this work can be used to develop new and effective numerical schemes for forward simulation and parameter inference. The algebraic line of investigation of conditional expectations has considerable scope to be applied to many different aspects of Gene Regulatory Networks; this paper serves as a preliminary commentary in this direction.
Journal of Mathematical Biology
1438-0064
urn:nbn:de:0297-zib-70526
10.1007/s00285-019-01410-y
Journal of Mathematical Biology
Vikram Sunkara
Erlinda Körnig
ZIB-Report
18-52
eng
uncontrolled
Markov Chains
eng
uncontrolled
Chemical Master Equations
eng
uncontrolled
Dimension Reduction
Generalized stochastic processes
Computational Markov chains
General biology and biomathematics
Numerical Mathematics
Sunkara, Vikram
https://opus4.kobv.de/opus4-zib/files/7052/ZIB-Report_1852_Sunkara.pdf