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SUMMARY:Closure Scheme for Chemical Master Equations - Is the Gibbs entrop
 y maximum for stochastic reaction networks at steady state? - Yiannis Kazn
 essis ()
DTSTART:20160408T080000Z
DTEND:20160408T084500Z
UID:TALK65376@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Stochasticity is a defining feature of biochemical reaction ne
 tworks\, with molecular fluctuations influencing cell physiology. In princ
 iple\, master probability equations completely govern the dynamic and stea
 dy state behavior of stochastic reaction networks. In practice\, a solutio
 n had been elusive for decades\, when there are second or higher order rea
 ctions. A large community of scientists has then reverted to merely sampli
 ng the probability distribution of biological networks with stochastic sim
 ulation algorithms. Consequently\, master equations\, for all their promis
 e\, have not inspired biological discovery.<br><br>We recently presented a
  closure scheme that solves chemical master equations of nonlinear reactio
 n networks&nbsp\;[1]. The zero-information closure (ZI-closure) scheme is 
 founded on the observation that although higher order probability moments 
 are not numerically negligible\, they contain little information to recons
 truct the master probability [2]. Higher order moments are then related to
  lower order ones by maximizing the entropy of the network. Using several 
 examples\, we show that moment-closure techniques may afford the quick and
  accurate calculation of steady-state distributions of arbitrary reaction 
 networks.<br><br>With the ZI-closure scheme\, the stability of the systems
  around steady states can be quantitatively assessed computing eigenvalues
  of the moment Jacobian [3]. This is analogous to Lyapunov&rsquo\;s stabil
 ity analysis of deterministic dynamics and it paves the way for a stabilit
 y theory and the design of controllers of stochastic reacting systems [4\,
  5].<br><br>In this seminar\, we will present the ZI-closure scheme\, the 
 calculation of steady state probability distributions\, and discuss the st
 ability of stochastic systems.<br><br>1.	Smadbeck P\, Kaznessis YN. A clos
 ure scheme for chemical master equations. Proc Natl Acad Sci U S A. 2013 A
 ug 27\;110(35):14261-5.<br><br>2.	Smadbeck P\, Kaznessis YN. Efficient mom
 ent matrix generation for arbitrary chemical networks\, Chem Eng Sci\, 20
LOCATION:Seminar Room 1\, Newton Institute
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