Computing the structural influence matrix for biological systems
(2016) In Journal of Mathematical Biology 72(7). p.19271958 Abstract
We consider the problem of identifying structural influences of external inputs on steadystate outputs in a biological network model. We speak of a structural influence if, upon a perturbation due to a constant input, the ensuing variation of the steadystate output value has the same sign as the input (positive influence), the opposite sign (negative influence), or is zero (perfect adaptation), for any feasible choice of the model parameters. All these signs and zeros can constitute a structural influence matrix, whose (i, j) entry indicates the sign of steadystate influence of the jth system variable on the ith variable (the output caused by an external persistent input applied to the jth variable). Each entry is structurally... (More)
We consider the problem of identifying structural influences of external inputs on steadystate outputs in a biological network model. We speak of a structural influence if, upon a perturbation due to a constant input, the ensuing variation of the steadystate output value has the same sign as the input (positive influence), the opposite sign (negative influence), or is zero (perfect adaptation), for any feasible choice of the model parameters. All these signs and zeros can constitute a structural influence matrix, whose (i, j) entry indicates the sign of steadystate influence of the jth system variable on the ith variable (the output caused by an external persistent input applied to the jth variable). Each entry is structurally determinate if the sign does not depend on the choice of the parameters, but is indeterminate otherwise. In principle, determining the influence matrix requires exhaustive testing of the system steadystate behaviour in the widest range of parameter values. Here we show that, in a broad class of biological networks, the influence matrix can be evaluated with an algorithm that tests the system steadystate behaviour only at a finite number of points. This algorithm also allows us to assess the structural effect of any perturbation, such as variations of relevant parameters. Our method is applied to nontrivial models of biochemical reaction networks and population dynamics drawn from the literature, providing a parameterfree insight into the system dynamics.
(Less)
 author
 Giordano, Giulia ^{LU} ; Cuba Samaniego, Christian; Franco, Elisa and Blanchini, Franco
 publishing date
 20160601
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Influence matrix, Perfect adaptation, Steadystate variation, Structural analysis, Vertex algorithm
 in
 Journal of Mathematical Biology
 volume
 72
 issue
 7
 pages
 32 pages
 publisher
 Springer
 external identifiers

 scopus:84944627209
 ISSN
 03036812
 DOI
 10.1007/s0028501509339
 language
 English
 LU publication?
 no
 id
 63d437f213bf42cfb6483d9c5d8fc2b9
 date added to LUP
 20160706 15:10:35
 date last changed
 20171001 05:21:24
@article{63d437f213bf42cfb6483d9c5d8fc2b9, abstract = {<p>We consider the problem of identifying structural influences of external inputs on steadystate outputs in a biological network model. We speak of a structural influence if, upon a perturbation due to a constant input, the ensuing variation of the steadystate output value has the same sign as the input (positive influence), the opposite sign (negative influence), or is zero (perfect adaptation), for any feasible choice of the model parameters. All these signs and zeros can constitute a structural influence matrix, whose (i, j) entry indicates the sign of steadystate influence of the jth system variable on the ith variable (the output caused by an external persistent input applied to the jth variable). Each entry is structurally determinate if the sign does not depend on the choice of the parameters, but is indeterminate otherwise. In principle, determining the influence matrix requires exhaustive testing of the system steadystate behaviour in the widest range of parameter values. Here we show that, in a broad class of biological networks, the influence matrix can be evaluated with an algorithm that tests the system steadystate behaviour only at a finite number of points. This algorithm also allows us to assess the structural effect of any perturbation, such as variations of relevant parameters. Our method is applied to nontrivial models of biochemical reaction networks and population dynamics drawn from the literature, providing a parameterfree insight into the system dynamics.</p>}, author = {Giordano, Giulia and Cuba Samaniego, Christian and Franco, Elisa and Blanchini, Franco}, issn = {03036812}, keyword = {Influence matrix,Perfect adaptation,Steadystate variation,Structural analysis,Vertex algorithm}, language = {eng}, month = {06}, number = {7}, pages = {19271958}, publisher = {Springer}, series = {Journal of Mathematical Biology}, title = {Computing the structural influence matrix for biological systems}, url = {http://dx.doi.org/10.1007/s0028501509339}, volume = {72}, year = {2016}, }