Thermodynamics, Information Theory, and Chaotic Systems
Thermodynamics, Information Theory, and Chaotic Systems PHYS 597B
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This 0 page Class Notes was uploaded by Otha Leffler on Sunday November 1, 2015. The Class Notes belongs to PHYS 597B at Pennsylvania State University taught by Staff in Fall. Since its upload, it has received 39 views. For similar materials see /class/233091/phys-597b-pennsylvania-state-university in Physics 2 at Pennsylvania State University.
Reviews for Thermodynamics, Information Theory, and Chaotic Systems
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Date Created: 11/01/15
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FEEdfurwfnrddluup d m m c 792 irecan 39 El indirect regulaiun ndise 1 niter El EM Single input rnciddie slim andnzganve PD cine TF reddiates feedback lamps Ei mm and Wm several genes ternpcirai feedfamdlaaps prdgrarn mm M m Eiranscdrnpinatdnai regulan sends A h snen eerr et al i Nature Genetics 2DLI2 Scandid prdteincdrnpieltes PDSitiVE and negative rncmts aaiance nu cistasis Mdre pusmve idndtenn inrp stdrage j teeetei Suenuezg i rsstzuuzi Ma evsn et ei seenee me me was Importance of a dynamical understanding Only sdpsets crttne gEanErWidE interactidn netwurks are actve in a glvEri externai cdnditidn Hdll quoti ii llllil dynamical rnciddianty crt prutein irteractcin netwurks L lSEDliiUE SubnEIWEIrKS see next Wu siides rpra recap ai mm 7 Endugeneus and exugeneds transcripticinai o Huw can We incdrpdratetne intcinnaticin cin ne presenceapsence ur apdndance uttne rnciiecdies represented as nudes Not all interactions are simultaneously active W caicdiatetne cuneiatdn petweentne 7 Expressiuntimercuurse cit genes encdding tnenrst neignburs crt ndp prdteins Twu peaks 7 MD dl erErV types nr iitins Party hubs are inside cdnnected rndduies tnat interact simultaneuusly Dame hubs cdnnectdirrerentrndduies Fromm vCensW 51min mime xxiziimi Conditiondependent transcription sub tworks ne Endoge ous Exogenous 52 Complex TF combination Simple TF combination Fewtargets per TF Manytargets per TF m m M Long path length Short path length 4 m lnter connected TF Few Inter connected TF Many FFL Single input motifs Toward network dynamics 4 hh r First step pseudodynamics propagation of reactions in chemical interaction space starting from a source signal proper ies do hey re ect r39 39 39r39 39 39 uetwum modules Signal transduction in bacterial chemotaxis NFkB signaling module he yeast cell cycle Drosophila embryonic segmentation Pseudodynamic signal propagation QAct dist 2 Act dlSt 4 0th dlStZ Pseudodynamic effects of knockouts Forward and reverse dynamic modeling Dynamic modeling of interaction network Input com ponents interactions states of components Hypotheses interactions kinetics rates parameters 39 39 of components in ime Validation capture known behavior Explore study cases that are not accessible experimentally change parameters change assump ions Input com ponents states of components On time Hypotheses regulatory fr mewor Output proposed regulatory network Validation capture known interactions We Will study network inference later in the course Types of dynamic models 1 Continuous similar to chemical kinetics differential equa ions 2 Discrete assume a small set of qualitative states e g active or inactive basal intermediate high the changes in state are given by discrete logical rules 1 Deterministic no randomness is involved in the development of future states or the systern 2 Stochastic riOrirdeterrniriiStiC in that the next state or is notruiiy deterrnined by tne previous state can take into accou nttne fluctuations in mRNAprotein numbers and external noise Basics of Chemical Kinetics 1 A gt Product gtRate or reaction rate or disappearance or A iA uAut disappearing per unit tirne per unit voiurne or moles or A reacting A concentration utA mulesNulume i mule s uzaviuv mulecules gtReaction rate law is an algebraic eguation involving concentrations not a dirrerentiai equation k1 Al MAD gtFor a given reaction the rate law is determined experimentally gtMeasure A as a runction or tirne and caicuiate siope dAdt at varioustirne points Basics of Chemical Kinetics 2 A B gt Pr aduct Other factors irnpacting rate constant gtin general rA t T rtiAiiBi L Concentration 39 CMW Temperature d d pregame e en ence dependence 7 ionic strength pH Rate Constant I Solvent Not really constant iust independent or concentration gtReaction Order power rne reaction is ptorder evvitn respect to A and Murder Witn respect to 5 gtReaction order can be fractional gtNot every reaction nas an orderi A l t2 3 Temperature and concentration dependence not separaoie Basics of Chemical Kinetics 3 Basics of Chemical Kinetics 4 gtReacti0n Stoichiometry Law of Conservation of Mass gtElementary Reaction Reaction order or eacn species is identicai WiththeWo hatspecles MbBcCdD i C d v A2B gtC ran A 82 J A irrespective erwnetnerreactien is Elementary ernet Ream W gtElementary reactions n potnesized to nappen exactly how they are written 599W rate laW Concentration Tiine Course dA dt a v One molecule or A coiiiding Witn 2 molecules or Bto produce C V 7k W W or gtEiernentary reactions are typically is or 2nd order dlBl l 39b V V k A B E New Probability or tnree molecules coiiiding very low dm rdt C V gt Specify initiai conditions gtReversible reactions A 213 lt C dD dt d V Ni ui Ale rams A25 C A2Blt C Forward Reaction Backward Reaction E W Ex1 AB C Ex1 AB gtC Determine the relation between the reaction rates and he reaction ux Assume the reac ion is elementary Determine the rate of change of Ali Bli C Determine the rela ion between he reaction rates and the reaction ux Assume the reaction is elementary Determine the rate of change of Ali Bli C 4M 43 dIC Jt T kIAIIBI TkIAIIBI Ex 2 Write the conditions of mass conservation Hint think ofthe reac ion as a complex formation A B AB Reversible reactions Example A B C For simplicity we39ll leave offthe brackets from A 14 dB EE kABkC 11C EkAB kc Mass conservation AC Ag BCBo Units k molvoumetime39t kV time39t Steady states lfthe rates of he forward and backward reac ions are equal he system is able to reach a steady state where he concentrations do not change in time 39a AB L C EE o if kABkco at at at k k CsilAsBsil1o CsBa Cs k k SolveforCSS Enzymecatalyzed reactions Most reactions in biological systems would not take place at perceptible rates in he absence of enzymes Enzymes are specialized proteins that bind speci c reactants get them close toge her and by this accelerate the reac ion up to a million imes In his context the reactants are called substrates In enzymecatalyzed reactions the rate ofproduct synthesis depends nonlinearly on the concentra ion ofthe substrate MichaelisMenten model of enzymatic reactions Leonor Michaelis Maud Menten 1913 1 A speci c enzymesubstrate complex is a necessary In ermediate in catal sIs 2 The product does not revert to the original substrates h E s 4 ESLgtEP Ex Draw two possible network representations ofthis process MichaelisMenten kinetics E s 4 ELgtEP as 4E kESkES kESkESk2ES 111 at 11 kES kES k2ES k2ES at 11 Mass conservation E EE I H skim41 113 k 0 EEs at kk2 Michaelis Menten kinetics cont E s 7quot ELE P Goal express the rate ofproduct synthesis as a func ion of substrate concentra ion 1P k2 at EES7 kk2 1P ETEE Fk2ETKMs k KM kl k2 Michaelis Menten kinetics cont h ES ESLgtEP K kk2 2 T M 11 KM S k Ex 1 Draw he dependence of he rate of product syn hesis on the substrate concentration Characterize three limitspoints on the curve Ex2 What is the upper limit for kzKM 7 Enzymecatalyzed reactions 111 S i szT 7 a K M S u u u u m r is half its maximal value L39 quott 1 dP quotquot39 s gtgtKM m szT dt szT is the number of substrate molecules converted in a unit time when the enzyme is fully saturated with substrate dP 2 mi SltltKM gt m METS The ef ciency of an enzyme can be described by kzKM The ultimate limit for enzyme ef ciency is the diffusionlimited encounter of enzyme and substrate or 10 squotmolquot Chemical kineticslike models of cellular rocesses Assurnption cellular syntnesis and degradation processes can be described as sirnple or enzyrnecatalyzed reactions Ex receptore ligand binding rnetnylation reactions 7 catalyzed by rne nylating enzyrnes pnospnorylation 7 catalyzed by klnases depnospnorylation e spontaneous or catalyzed by pnospnatases protein syntnesis ecatalyzed oy mRNA protein degradation 7 spontaneous or catalyzed iiii iriiiiii eii Bring l i lust Protein synthesis and degradation Protein syntnesis mRNA gt protein surricient supply or arninoacids Protein degradation protein gt Notations in Tyson etal 2003 The source elernent here tne mRNA is denoted s tor signal One cornponent here tne protein is designated as tne response Network diagram ld edge in ass rlow Dasned edge regulation 1 0 Draw an alterna iye network rnore in line Witn What We naye seen oetore Where edges connect two nodes and signity regulation Kinetics of protein synthesis and degradation Protein syntnesis mRNA gt protein sutticient supply or arninoacids Protein degradation protein gt JR ks S R Stead state a kl 9 v Rm 9 syntnesis Pusrn39si ini The points Where tne syntnesis and swim rnis is tne iri c edual indicate tne Drtne sys steady states putr output naracteristic tern Kinetics of phosphotransfer Pnospnorylation protein gt pnospnoprotein Depnospnorylation pnospnoprotein gt protein The rirst reaction is catalyzed by a klnase assurne rirst eorder kinetics 4R th kzkr RTRRP steady state RP RT L kzkl 5 production Riswnu in i Signer lhl degradation Phosphotransfer with Michaelis Menten kinetics Assume thatthe phosphoryiation and dephosphoryia iOi i reactions foiioW MichaeiiSrMenten kinetics R R kSR gtks szP gtk2 P Km R KM2 RP ks amp a 39KMRT RP KM2RP gt9 mm Phosphotransfer with Michaelis Menten kinetics 3 RT RP amp a KMR RP KM2RP Steady state RP RTGrkSk2 Km ampW R7 RT G r GoidbeteryKoShiand function 5W iii
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