Editing Markov chain (section)

===Chemistry===
{{Image frame|content=<chem>{E} + \underset{Substrate\atop binding}{S <=> E}\overset{Catalytic\atop step}{S -> E} + P</chem>
|align=left|width=200|caption=[[Michaelis-Menten kinetics]]. The enzyme (E) binds a substrate (S) and produces a product (P). Each reaction is a state transition in a Markov chain.}}A reaction network is a chemical system involving multiple reactions and chemical species. The simplest stochastic models of such networks treat the system as a continuous time Markov chain with the state being the number of molecules of each species and with reactions modeled as possible transitions of the chain.<ref>{{Citation|last1=Anderson|first1=David F.|title=Continuous Time Markov Chain Models for Chemical Reaction Networks|date=2011|work=Design and Analysis of Biomolecular Circuits|pages=3–42|publisher=Springer New York|isbn=9781441967657|last2=Kurtz|first2=Thomas G.|doi=10.1007/978-1-4419-6766-4_1}}</ref> Markov chains and continuous-time Markov processes are useful in chemistry when physical systems closely approximate the Markov property. For example, imagine a large number ''n'' of molecules in solution in state A, each of which can undergo a chemical reaction to state B with a certain average rate. Perhaps the molecule is an enzyme, and the states refer to how it is folded. The state of any single enzyme follows a Markov chain, and since the molecules are essentially independent of each other, the number of molecules in state A or B at a time is ''n'' times the probability a given molecule is in that state.

The classical model of enzyme activity, [[Michaelis–Menten kinetics]], can be viewed as a Markov chain, where at each time step the reaction proceeds in some direction. While Michaelis-Menten is fairly straightforward, far more complicated reaction networks can also be modeled with Markov chains.<ref>{{Cite journal|last1=Du|first1=Chao|last2=Kou|first2=S. C.|date=September 2012|title=Correlation analysis of enzymatic reaction of a single protein molecule|journal=The Annals of Applied Statistics|volume=6|issue=3|pages=950–976|doi=10.1214/12-aoas541|pmid=23408514|pmc=3568780|bibcode=2012arXiv1209.6210D|arxiv=1209.6210}}</ref>

An algorithm based on a Markov chain was also used to focus the fragment-based growth of chemicals [[in silico]] towards a desired class of compounds such as drugs or natural products.<ref>{{cite journal|title=FOG: Fragment Optimized Growth Algorithm for the de Novo Generation of Molecules occupying Druglike Chemical |last=Kutchukian |first=Peter |author2=Lou, David |author3=Shakhnovich, Eugene |journal=Journal of Chemical Information and Modeling |year=2009 |volume=49 |pages=1630–1642|doi=10.1021/ci9000458|pmid=19527020|issue=7}}</ref> As a molecule is grown, a fragment is selected from the nascent molecule as the "current" state. It is not aware of its past (that is, it is not aware of what is already bonded to it). It then transitions to the next state when a fragment is attached to it. The transition probabilities are trained on databases of authentic classes of compounds.<ref>{{Cite journal |last1=Kutchukian|first1=P.S.|last2=Lou |first2=D.|last3=Shakhnovich |first3=Eugene I.|date=2009-06-15 |title=FOG: Fragment Optimized Growth Algorithm for the de Novo Generation of Molecules Occupying Druglike Chemical Space |journal=Journal of Chemical Information and Modeling |volume=49|issue=7|pages=1630–1642 |doi=10.1021/ci9000458|pmid=19527020 }}</ref>

Also, the growth (and composition) of [[copolymer]]s may be modeled using Markov chains. Based on the reactivity ratios of the monomers that make up the growing polymer chain, the chain's composition may be calculated (for example, whether monomers tend to add in alternating fashion or in long runs of the same monomer). Due to [[steric effects]], second-order Markov effects may also play a role in the growth of some polymer chains.

Similarly, it has been suggested that the crystallization and growth of some epitaxial [[superlattice]] oxide materials can be accurately described by Markov chains.<ref>{{cite journal |last1= Kopp |first1= V. S. |last2= Kaganer |first2= V. M. |last3= Schwarzkopf |first3= J. |last4= Waidick |first4= F. |last5= Remmele |first5= T. |last6= Kwasniewski |first6= A. |last7= Schmidbauer |first7= M. |title= X-ray diffraction from nonperiodic layered structures with correlations: Analytical calculation and experiment on mixed Aurivillius films |doi= 10.1107/S0108767311044874 |journal= Acta Crystallographica Section A |volume= 68 |issue= Pt 1 |pages= 148–155 |year= 2011 |pmid= 22186291 |bibcode= 2012AcCrA..68..148K}}</ref>