!"# "$%!! &' ( ) * ( + ", % - . ( / ( / % 0 / ( / % & / 1 ( ( ( / % 2 ( / % 0 ( / ( % 2 ( 3 % 4 ( / 3 1 / % 2 ( ( ( / 1 % 2 % . ( / 3 % 5 ( / ( 1 % 5 / 1 ( 3 % 5 1 ( / / ( / % 1 3 ( 6 3/ % ( / ( / % ( / / % 2 7%% 3 8 % 0 / ( 3 ( / ( % 4 ( / ( / ( 1 % !"# 9:: %% : ; < 99 9 93"=$" >? @#3@"3@3AA 3$ >? @#3@"3@3AAA3" ! ! ( "!, @" A COMPUTATIONAL APPROACH TO CURVATURE SENSING IN LIPID BILAYERS )HGHULFR(O¯DV:ROII A computational approach to curvature sensing in lipid bilayers )HGHULFR(O¯DV:ROII ©Federico Elías-Wolff, Stockholm University 2018 ISBN print 978-91-7797-332-4 ISBN PDF 978-91-7797-333-1 Printed in Sweden by Universitetsservice US-AB, Stockholm 2018 Distributor: Department of Biochemistry and Biophysics, Stockholm University List of Papers The following papers, referred to in the text by their Roman numerals, are included in this thesis. PAPER I: Computing curvature sensitivity of biomolecules in mem- branes by simulated buckling F. Elías-Wolff, M. Lindén, A.P.Lyubartsev, and E.G. Brandt J. Chem. Theory Comput., 14, 1643-1655 (2018). DOI: 10.1021/acs.jctc.7b00878 PAPER II: Curvature sensing by cardiolipin in a simulated buck- led membrane F. Elías-Wolff, M. Lindén, A.P.Lyubartsev, and E.G. Brandt Submitted (2018). PAPER III: Anisotropic membrane curvature sensing by amphipathic peptides J. Gómez-Llobregat, F. Elías-Wolff, and M. Lindén Biophys. J., 110, 197-204 (2016). DOI: 10.1016/j.bpj.2015.11.3512 PAPER IV: Curvature sensing by multimeric proteins M. Lindén, F. Elías-Wolff, A.P.Lyubartsev, and E.G. Brandt Manuscript in preparation Reprints were made with permission from the publishers. The following is a list of papers by the author not included in this thesis. PAPER V: Metapopulation dynamics on the brink of extinction A. Eriksson, F. Elías-Wolff, and B. Mehlig Theor. Popul. Biol, 83, 101-122 (2013). DOI: 10.1016/j.tpb.2012.08.001 PAPER VI: The emergence of the rescue effect from explicit within- and between-patch dynamics in a metapopulation A. Eriksson, F. Elías-Wolff, B. Mehlig, and A. Manica Proc. R. Soc. B, 281, 20133127 (2014). DOI: 10.1098/rspb.2013.3127 PAPER VII: How Levins’ dynamics emerges from a Ricker metapop- ulation model F. Elías-Wolff, A. Eriksson, A. Manica, and B. Mehlig Theor. Ecol., 9, 173-183 (2016). DOI: 10.1007/s12080-015-0271-y Abbreviations ACS American Chemical Society CG coarse-grained CL cardiolipin FENE finite extensible nonlinear elastic lipB big-headed Cooke lipid lipC cylindrical Cooke lipid lipS small-headed Cooke lipid MD molecular dynamics PME particle mesh Ewald POPE 1-palmitoyl-2-oleoyl phosphatidylethanolamine POPG 1-palmitoyl-2-oleoyl phosphatidylglycerol RMSD root-mean-square deviation Contents 1 Introduction 1 2 Lipid bilayers 3 2.1 Elasticity of cell membranes ................. 4 2.2 Cardiolipin as a curvature sensor in lipid membranes . 6 3 Curvature sensing 9 3.1 Curvature sensing and generation mechanisms ...... 10 3.2 Curvature sensing experiments ............... 10 4 Molecular dynamics 13 4.1 Coarse-grained models .................... 14 4.1.1 The Cooke lipid model ................ 15 4.1.2 The Martini force field ................ 16 5 Simulated buckling (I) 19 5.1 Frame alignment ....................... 20 5.2 Orientation Analysis ..................... 22 5.3 Method evaluation ...................... 23 6 Lipid Sorting (I,II) 27 6.1 Geometric effects of curvature on lipid packing ...... 27 6.2 Curvature-dependent lipid distribution and structure . 30 6.3 Theoretical analysis of lipid sorting for two- and three- component bilayers ...................... 33 7 Curvature sensing by proteins and peptides (I,III,IV) 39 7.1 Position- and orientation-dependent curvature sensing . 39 7.2 Trimer in a buckled membrane (Paper I) .......... 43 7.3 Amphipathic helices in a buckled membrane (Paper III) . 44 7.4 Symmetric proteins in cylindrical bilayers (Paper IV) . 47 8 Conclusions 55 Appendix A Autocorrelation times 59 Sammanfattning lxi Acknowledgements lxiii References lxv 1. Introduction How do cells create and maintain their geometry? This is one of the central questions in cell biology. For many cellular processes, the asso- ciated machinery of the cell needs to be recruited to the proper place at specific times. For example, during endocytosis (a cellular process where the cell absorbs a molecule by engulfing it) appropriate concen- trations of certain membrane lipids and proteins need to be present at the site of absorption in order to form the engulfing vesicle. What is the mechanism by which these biomolecules localize to the specific mem- brane region? The ancients saw the cell membrane as a lipid barrier with selec- tive permeability. The modern picture is far more complex. Membrane proteins typically constitute about 50% of the membrane volume. Each of these proteins performs some biological activity, including the pas- sive or active transport of molecules which are involved in the cell’s metabolism, in the communication of the cell with other cells, among many others. While some of these functions can happen anywhere in the membrane and thus the associated proteins are distributed all over it (for example proteins acting as mechanosensitive channels that let water out when the cell’s internal pressure is too high), others require the localization of the corresponding proteins to a specific region, for examples during cell division or endocytosis mentioned above. Several mechanisms are responsible for localizing biomolecules to appropriate regions within cells. One of these mechanisms is the sens- ing of membrane curvature by proteins and other biomolecules, that is, by expressing a positional preference for membrane regions within a certain range of local curvature. In this project we study how mem- brane proteins and lipids interact to sense the shape of lipid mem- branes. Thus, we develop a novel computational method based on molecular dynamics simulations of buckled membranes. The basic idea is to construct a lipid bilayer, compress it so it acquires a buckled shape with known curvature parameters, and observe how probe molecules, like an embedded peptide, or a particular lipid species, prefer a certain 1 curved regions within the bilayer patch. For pure lipid membranes, we develop a simple theory, based on the Helfrich model of cell mem- brane elasticity, to describe how lipids sort themselves between curva- ture regions. When we consider the localization of peptides and mem- brane proteins, not only the position but also the orientation of the molecules becomes relevant. Similarly, we propose a phenomenolog- ical model to describe the curvature sensing properties of the peptides, in terms of position- and direction-dependent curvature. In addition to tracking the joint distribution of position and orientation along buckled membranes, we also simulate multimeric model proteins in cylindrical membrane patches, where only the orientation is relevant. For this case we develop a theory to explain why monomeric, dimeric an tetrameric protein models have much stronger orientational preferences than their trimeric, pentameric and hexameric analogues. The main focus of this research are the mechanisms by which pro- teins and lipids induce and regulate the spatial organization of the cell membrane. The principal questions we attempt to investigate can be formulated in terms of the curvature dependent free energy of the sys- tems we study. What is the shape of the free energy landscape for dis- tinct types of curvature sensing molecules? How does the shape asym- metry of these peptides, which brings an orientational dependance on the binding energy, affect the free energy landscape? We thus test if the orientation of curvature sensors corresponds to theoretical predictions of the corresponding curvature sensing mechanisms. Our first goal is to develop a computational method that is fast and accurate, and ideally suited to answer these questions. Aside from the intrinsic interest associated with the study of curva- ture sensing and generation, and the identification of its underlying mechanisms, our method should provide a novel tool in membrane biophysics, which complements existing approaches. Particular ap- plications include finding the orientational preferences of key mem- brane peptides, and the examination of adsorption of biomolecules or nanoparticles in curved interfaces. This, we hope, will promote the de- velopment of experimental techniques to tackle these issues. On the side of medical applications, we believe that deeper understanding of the interplay between antimicrobial peptides, as described above, will prove useful in antibiotic development. 2 2. Lipid bilayers Biological bilayers are composed of amphiphilic phospholipids, which typically consist of two hydrophobic fatty acid tails, a hydrophilic phos-