Moment analysis of stochastic hybrid systems using semidefinite programming

Ghusinga, Khem Raj; Lamperski, Andrew; Singh, Abhyudai

doi:10.1016/j.automatica.2019.108634

Cited by 13 publications

(8 citation statements)

References 31 publications

(48 reference statements)

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“…We validate these approximations using exact semianalytical approach based on ref. 67 (SI Appendix, section S4D). The formula for CV 2 Y * above is written in terms of various sources of noise, as previously done for gene-regulation models (68)(69)(70).…”

Section: [13b]mentioning

confidence: 99%

Molecular switch architecture determines response properties of signaling pathways

Ghusinga

Jones

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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Many intracellular signaling pathways are composed of molecular switches, proteins that transition between two states—on and off. Typically, signaling is initiated when an external stimulus activates its cognate receptor that, in turn, causes downstream switches to transition from off to on using one of the following mechanisms: activation, in which the transition rate from the off state to the on state increases; derepression, in which the transition rate from the on state to the off state decreases; and concerted, in which activation and derepression operate simultaneously. We use mathematical modeling to compare these signaling mechanisms in terms of their dose–response curves, response times, and abilities to process upstream fluctuations. Our analysis elucidates several operating principles for molecular switches. First, activation increases the sensitivity of the pathway, whereas derepression decreases sensitivity. Second, activation generates response times that decrease with signal strength, whereas derepression causes response times to increase with signal strength. These opposing features allow the concerted mechanism to not only show dose–response alignment, but also to decouple the response time from stimulus strength. However, these potentially beneficial properties come at the expense of increased susceptibility to upstream fluctuations. We demonstrate that these operating principles also hold when the models are extended to include additional features, such as receptor removal, kinetic proofreading, and cascades of switches. In total, we show how the architecture of molecular switches govern their response properties. We also discuss the biological implications of our findings.

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Section: [13b]mentioning

confidence: 99%

Molecular switch architecture determines response properties of signaling pathways

Ghusinga

Jones

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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“…We validate these approximations using exact semi-analytical approach based on [65] (section S3-B, SI). The formula for CV 2 Y * above is written in terms of various sources of noise, as previously done for gene regulation models [66][67][68].…”

Section: Reaction Population Update Transition Ratementioning

confidence: 99%

“…Here, we exploit the fact that X T is finite to come up with an alternate state space where moment dynamics is closed. The computations follow the formalism proposed in [65]. Another closely related method is the method of conditional moments described in [82].…”

Section: S3-b-d Exact Moment Computationmentioning

confidence: 99%

Molecular switch architecture drives response properties

Ghusinga

Jones

et al. 2020

Preprint

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AbstractMany intracellular signaling pathways are composed of molecular switches, proteins that transition between two states—on and off. Typically, signaling is initiated when an external stimulus activates its cognate receptor that in turn causes downstream switches to transition from off to on using one of the following mechanisms: activation, in which the transition rate from the off state to the on state increases; derepression, in which the transition rate from the on state to the off state decreases; and concerted, in which activation and derepression operate simultaneously. We use mathematical modeling to compare these signaling mechanisms in terms of their dose-response curves, response times, and abilities to process upstream fluctuations. Our analysis elucidates several general principles. First, activation increases the sensitivity of the pathway, whereas derepression decreases sensitivity. Second, activation generates response times that decrease with signal strength, whereas derepression causes response times to increase with signal strength. These opposing features allow the concerted mechanism to not only show dose-response alignment, but also to decouple the response time from stimulus strength. However, these potentially beneficial properties come at the expense of increased susceptibility to up-stream fluctuations. In addition to above response metrics, we also examine the effect of receptor removal on switches governed by activation and derepression. We find that if inactive (active) receptors are preferentially removed then activation (derepression) exhibits a sustained response whereas derepression (activation) adapts. In total, we show how the architecture of molecular switches govern their response properties. We also discuss the biological implications of our findings.

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“…Several moment closure methods that provide approximation to moment dynamics have been proposed in literature [17,[20][21][22][23][24][25][26][27][28][29][30][31]. These methods are based on several themes such as linearization, neglecting some higher order moments/cumulants, assumptions on underlying distribution, preservation of some dynamical, physical or moment properties , etc.…”

Section: Moment Dynamics For Homomermentioning

confidence: 99%

Noise Analysis in Biochemical Complex Formation

Zhao

Singh

2018

Preprint

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Several biological functions are carried out via complexes that are formed via multimerization of either a single species (homomers) or multiple species (heteromers). Given functional relevance of these complexes, it is arguably desired to maintain their level at a set point and minimize fluctuations around it. Here we consider two simple models of complex formation -one for homomer and another for heteromer of two species -and analyze how important model parameters affect the noise in complex level. In particular, we study effects of (i) sensitivity of the complex formation rate with respect to constituting species' abundance, and (ii) relative stability of the complex as compared with that of the constituents. By employing an approximate moment analysis, we find that for a given steady state level, there is an optimal sensitivity that minimizes noise (quantified by fano-factor; variance/mean) in the complex level. Furthermore, the noise becomes smaller if the complex is less stable than its constituents.Finally, for the heteromer case, our findings show that noise is enhanced if the complex is comparatively more sensitive to one constituent. We briefly discuss implications of our result for general complex formation processes.

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Moment analysis of stochastic hybrid systems using semidefinite programming

Cited by 13 publications

References 31 publications

Molecular switch architecture determines response properties of signaling pathways

Molecular switch architecture determines response properties of signaling pathways

Molecular switch architecture drives response properties

Noise Analysis in Biochemical Complex Formation

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