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Pulling of biomolecules: lessons from toy models

Banff International Research Station for Mathematical Innovation and Discovery

In recent years, atomic force microscopy (AFM) has been used to look into the elasticity of modular proteins, which comprise a certain number of identical protein domains [3]. The molecule is typically pulled from one end while the other is kept fixed, and either the length of the biomolecule or the force applied on it is controlled. In the above experiments, the force-extension curve (FEC) is recorded, which gives the force needed to stretch the biomolecule as a function of its length. In modular proteins, the FEC shows a sawtooth behaviour under length- control: the unfolding of the different units that constitute the polyprotein is accompanied by a drop of the force. Moreover, the force at which the unfolding takes place, increases with the stretching rate [4–8]. On the other hand, there are also protein domains that are composed of several stable structural units or “un- foldons”. The unfolding pathway is defined as the order and the way in which these “unfoldons” unravel, and it depends on the pulling speed. Consistently with the physical intuition, the weakest unfoldon opens first at low pulling rates. At higher rates, no longer is the first unit that unfolds but the pulled one [9–12]. In this talk, we discuss how some key aspects of these pulling experiments can be understood by using “toy” models [13–15]. Basically, the extension of each unit follows an overdamped Langevin equation. First, for the analysis of the FEC, the units are independent except for the global constraint given by the length-control condi- tion. Second, we study the unfolding pathway by taking into account the spatial structure of the molecule, which introduces crucial additional couplings among the units. References [1] F.Ritort,J.Phys.:Condens.Matter18,R531-R583(2006) [2] S.KumarandM.S.Li,Phys.Rep.486,1(2010) [3] P.E.MarszalekandY.F.Dufrêne,Chem.Soc.Rev.41,3523(2012) [4] S.B.Smith,Y.CuiandC.Bustamante,Science271,795-799(1996) [5] M. Carrion-Vázquez, A. F. Oberhauser, S. B. Fowler, P. E. Marszalek, S. E. Broedel, J. Clarke and J. M. Fernandez, Proc. Natl. Acad. Sci. USA 96, 3694-3699 (1999) [6] H.LuandK.Schulten,ProteinsStruct.Funct.Genet.35,453-463(1999) [7] T.E.Fisher,P.E.MarszalekandJ.M.Fernandez,NatureStruct.Biol.7,719-724(2000) [8] Y.Cao,R.KuskeandH.Li,Biophys.J.95,782-788(2008) [9] C.Hyeon,R.I.Dima,andD.Thirumalai,Structure14,1633(2006) [10] M.S.LiandM.Kouza,J.Chem.Phys.130,145102(2009) [11] C.Guardiani,D.DiMarino,A.Tramontano,M.ChinappiandF.Cecconi,J.Chem.TheoryComput.10,3589(2014) [12] M.Kouza,C.K.Hu,M.S.LiandK.Kolinski,J.Chem.Phys.139,065103(2013) [13] L.L.Bonilla,A.Carpio,andA.Prados,EPL108,28002(2014)[HighlightedinRevistaEspañoladeFísica29(3),29(2015)] [14] L. L. Bonilla, A. Carpio, and A. Prados, Phys. Rev. E 91, 052712 (2015). [Highlighted in Revista Española de Física 29 (3), 29 (2015)] [15] C.A.Plata,F.Cecconi,M.Chinappi,andA.Prados,J.Stat.Mech.P08003(2015)

Mathematics; Quantum theory; Mechanics of deformable solids; Applied analysis / inverse problems

video/mp4

Author affiliation: Universidad de Sevilla

2017-02-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60730

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/