PS#4 due today (in class or before 3pm, Rm ) cannot ignore the spatial dimensions
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- Gyles Parrish
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1 Topic I: Sysms Cll Biology Spaial oscillaion in. coli PS# u oay in class or bfor pm Rm similar o gnic oscillaors s bu now w canno ignor h spaial imnsions biological funcion: rmin h cnr of h cll o prpar for propr cll ivision Summary of main funcions of proins: How os his work? FsZ polymrizs in a conracil Z-ring ha iniias spum formaion moling ffors: Minhar an Bor PNAS 98 ; MinC inhibis formaion of Z-ring Howar al. Phys. Rv. L ; Krus Biophys. J ; Min mmbran associa proin ha rcruis minc an o mmbran Huang Mir an Wingrn PNAS 7. Min jcs minc/ from mmbran ino
2 min mmbran in wors: - firs orr racions for own spcis - inhibis mmbran associaion of MM - nhancs mmbran issociaion of linar - nhancs mmbran associaion of rcruimn linar - inhibis mmbran issociaion of MM - an o no iffus - an iffus 5 min mmbran associaion of ic wih mmbran is inhibi by min in mmbran MM aks car of singulariy as gos o zro. biological inrpraion: min in mmbran spaially blocks mmbran for similar o minc blocking FZ associaion wih mmbran 6 mmbran issociaion of mmbran is simula by min in mmbran afr is jc min says in mmbran biological inrpraion: mmbran issociaion of mmbran min is inhibi by in MM aks car of singulariy biological inrpraion: min bining of min o lowrs affiniy of wih mmbran bu mmbran affiniy of min rmains unchang min? 7 8
3 mmbran associaion of ic wih mmbran is simula by in afr livry of o h b i i b k mmbran ivs back in h biological inrpraion: biological inrpraion: - compl has high affiniy o mmbran min affiniy o mmbran sinc h iffusion of his compl osn appar in h mol i shoul b vry fas. 9 y sysm of quaions: sysm of quaions: sabiliy analysis. fin fi poin.g. numrically: how_homog.m iffrn ranom iniial coniions rla o sam fi poin p rsul: on fi poin: fin sabiliy mari Jacobian A
4 . s sabiliy of flucuaions aroun homognous soluion cos ˆ q δ ˆ cos ˆ q q δ cos ˆ cos q q δ δ cos q δ δ. s sabiliy of flucuaions aroun homognous soluion q ˆ q A. - rmin ignvalus of sabiliy mari fin ral par of ign al s - fin ral par of ignvalus - plo h largs as a funcion of q..g. how_ig.m q5μm - q.5 μm λ π/q. μm /s q. μm - λ π/q.7 μm alus Ralignva 5 q Ma Howar al.: Rsuls 6
5 Huang Mir an Wingrn PNAS 7. main iffrncs: - ATP cycl - vrsus projc on 7 : mmbran boun :ATP compls : mmbran boun ::ATP compls :AP : concnraion ic boun o AP :ATP :concnraion ic boun o ATP : concnraion ic only -ATP can associa wih mmbran only bins -ATP oligomrs in mmbran 8 only --ATPcompl can issocia from mmbran Racion : -ATP bins boh linarlyl an auocaalyically o -ATP in mmbran forms polymrs in mmbran 9 : :AP : AP :ATP ATP AP ATP :AP AP ATP :AP [ ] [ ]
6 Racion : bins -ATP in mmbran ~ []*[] Racion : --ATP i compl isassociasi from mmbran hyrolyzing ATP ~ [min] : :AP : AP :ATP ATP AP ATP :AP AP ATP :AP [ ] [ ] : :AP : AP :ATP ATP AP ATP :AP AP ATP :AP [ ] [ ] Racion : charging of in from AP o ATP boun Sochasic racion-iffusion quaions: : :AP : AP :ATP ATP AP ATP :AP AP ATP :AP [ ] [ ] hp://msor.sourcforg.n/
7 Comparision of racions of wo mols craion of mmbran associa rmoval of mmbran associa firs orr auocaalyic linar oligomrizaion firs orr inhibi by mmbran MM linar wih min also lavs mmbran linar wih min says in mmbran Huang Howar 5 Huang Howar 6 craion of mmbran associa rmoval of mmbran associa linar wih an ~ o in mmbran mmbran rcruimn by Huang linar wih an ic rcruimn by os no nr mmbran Howar 7 linar wih min lavs mmbran oghr wih Huang linar wih min is no boun o min inhibi by ic Howar 8
8 Wha abou sphrical clls: Nissria gonorrhoa -ATP oscillas boh no ring hp://bookofbacriology.n/nissria.hml hml 9 Huang an Wingrn Phys. Biol. 9-5 Clls always fin h long-ais Rconsrucing minc wav in viro Loos al. Scinc 8
9 Rconsrucing minc wav in viro Loos al. Scinc 8
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