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- Elías-Wolff, Federico, 1983-
(author)
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A computational approach to curvature sensing in lipid bilayers
- 2018
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Doctoral thesis (other academic/artistic)abstract
- Local curvature is a key driving force for spatial organization of cellular membranes, via a phenomenon known as membrane curvature sensing, where the binding energy of membrane associated macromolecules depends on the local membrane shape. However, the microscopic mechanisms of curvature sensing are not well understood. Molecular dynamics simulations offer a powerful complement to biochemical experiments, yet their contribution to the study of curvature sensing has been limited, due in part to the lack of efficient methods, not least because of methodological difficulties in dealing with curved membranes. We develop a method based on simulated buckling, which has been previously employed to study mechanical properties of membranes. Here, we describe, validate and evaluate this method. We then apply to study curvature sensing properties of three model systems, using coarse-grained simulations. On the first system, we study lipid sorting in a three-component lipid mixture with emphasis on cardiolipin. We find that if curvature is high, curvature sensing is strong enough to drive cardiolipin molecules to negative curvature regions, outcompeting other lipids, without the need of external interactions or cooperative effects. We then simulated three systems consisting of a short amphipathic peptide attached to the surface of a buckled membrane. All three peptides localize to positive curvature, in agreement with the so-called cylindrical hydrophobic insertion mechanism. Their orientational preferences, however, defy the prediction of alignment perpendicular to the direction of maximum curvature. They also fail to show expected symmetries, indicating there is more to the picture than purely shape-based effects. The curvature sensing probe of the next system is a transmembrane trimeric protein, which shows preference to intermediate curvature, in agreement with theoretical predictions. But the lack of an expected 2-fold rotation symmetry indicates that the trimer senses the local curvature gradient, and not just the point-wise local curvature. Finally, dispensing with the buckling methodology, we simulated a series of symmetric transmembrane multimers embedded in cylindrical bilayers. Based on the results of these simulations and theoretical arguments, we discuss the relationship between structural symmetry and curvature sensitivity. We conclude that anisotropic (i.e. orientation-dependent) curvature sensing is strongly limited by odd and high order rotational symmetries. However, measurements of in-plane orientation on peptides and asymmetric proteins, as well as dimers and tetramers, should yield valuable information. Our method, along with our initial conclusions, provides an useful tool for the understanding of the relationship between membrane shape and membrane protein function, and should prove useful to biophysicists in the design and interpretation of experimental curvature sensing assays.
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| 2. |
- Elías-Wolff, Federico, et al.
(author)
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Computing Curvature Sensitivity of Biomolecules in Membranes by Simulated Buckling
- 2018
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In: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 14:3, s. 1643-1655
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Journal article (peer-reviewed)abstract
- Membrane curvature sensing, where the binding free energies of membrane-associated molecules depend on the local membrane curvature, is a key factor to modulate and maintain the shape and organization of cell membranes. However, the microscopic mechanisms are not well understood, partly due to absence of efficient simulation methods. Here, we describe a method to compute the curvature dependence of the binding free energy of a membrane associated probe molecule that interacts with a buckled membrane, which has been created by lateral compression of a flat bilayer patch. This buckling approach samples a wide range of curvatures in a single simulation, and anisotropic effects can be extracted from the orientation statistics. We develop an efficient and robust algorithm to extract the motion of the probe along the buckled membrane surface, and evaluate its numerical properties by extensive sampling of three coarse-grained model systems: local lipid density in a curved environment for single-component bilayers, curvature preferences of individual lipids in two-component membranes, and curvature sensing by a homotrimeric transmembrane protein. The method can be used to complement experimental data from curvature partition assays and provides additional insight into mesoscopic theories and molecular mechanisms for curvature sensing.
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| 3. |
- Elias-Wolff, Federico, et al.
(author)
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Curvature sensing by cardiolipin in simulated buckled membranes
- 2019
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In: Soft Matter. - : Royal Society of Chemistry (RSC). - 1744-683X .- 1744-6848. ; 15:4, s. 792-802
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Journal article (peer-reviewed)abstract
- Cardiolipin is a non-bilayer phospholipid with a unique dimeric structure. It localizes to negative curvature regions in bacteria and is believed to stabilize respiratory chain complexes in the highly curved mitochondrial membrane. Cardiolipin's localization mechanism remains unresolved, because important aspects such as the structural basis and strength for lipid curvature preferences are difficult to determine, partly due to the lack of efficient simulation methods. Here, we report a computational approach to study curvature preferences of cardiolipin by simulated membrane buckling and quantitative modeling. We combine coarse-grained molecular dynamics with simulated buckling to determine the curvature preferences in three-component bilayer membranes with varying concentrations of cardiolipin, and extract curvature-dependent concentrations and lipid acyl chain order parameter profiles. Cardiolipin shows a strong preference for negative curvatures, with a highly asymmetric chain order parameter profile. The concentration profiles are consistent with an elastic model for lipid curvature sensing that relates lipid segregation to local curvature via the material constants of the bilayers. These computations constitute new steps to unravel the molecular mechanism by which cardiolipin senses curvature in lipid membranes, and the method can be generalized to other lipids and membrane components as well.
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| 4. |
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| 5. |
- Elias Wolff, Federico, et al.
(author)
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How Levins’ dynamics emerges from a Ricker metapopulation model
- 2016
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In: Theoretical Ecology. - : Springer Science and Business Media LLC. - 1874-1738 .- 1874-1746. ; 9:2, s. 173-183
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Journal article (peer-reviewed)abstract
- Understanding the dynamics of metapopulations close to extinction is of vital importance for management. Levins-like models, in which local patches are treated as either occupied or empty, have been used extensively to explore the extinction dynamics of metapopulations, but they ignore the important role of local population dynamics. In this paper, we consider a stochastic metapopulation model where local populations follow a stochastic, density-dependent dynamics (the Ricker model), and use this framework to investigate the behaviour of the metapopulation on the brink of extinction. We determine under which circumstances the metapopulation follows a time evolution consistent with Levins’ dynamics. We derive analytical expressions for the colonisation and extinction rates (c and e) in Levins-type models in terms of reproduction, survival and dispersal parameters of the local populations, providing an avenue to parameterising Levins-like models from the type of information on local demography that is available for a number of species. To facilitate applying our results, we provide a numerical algorithm for computing c and e.
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| 6. |
- Eriksson, Anders, 1975, et al.
(author)
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Metapopulation dynamics on the brink of extinction
- 2013
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In: Theoretical Population Biology. - : Elsevier BV. - 0040-5809. ; 83, s. 101-122
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Journal article (peer-reviewed)abstract
- We analyse metapopulation dynamics in terms of an individual-based, stochastic model of a finite metapopulation. We suggest a new approach, using the number of patches in the population as a large parameter. This approach does not require that the number of individuals per patch is large, neither is it necessary to assume a time-scale separation between local population dynamics and migration. Our approach makes it possible to accurately describe the dynamics of metapopulations consisting of many small patches. We focus on metapopulations on the brink of extinction. We estimate the time to extinction and describe the most likely path to extinction. We find that the logarithm of the time to extinction is proportional to the product of two vectors, a vector characterising the distribution of patch population sizes in the quasi-steady state, and a vector–related to Fisher’s reproduction vector–that quantifies the sensitivity of the quasi-steady state distribution to demographic fluctuations. We compare our analytical results to stochastic simulations of the model, and discuss the range of validity of the analytical expressions. By identifying fast and slow degrees of freedom in the metapopulation dynamics, we show that the dynamics of large metapopulations close to extinction is approximately described by a deterministic equation originally proposed by Levins (1969). We were able to compute the rates in Levins’ equation in terms of the parameters of our stochastic, individual-based model. It turns out, however, that the interpretation of the dynamical variable depends strongly on the intrinsic growth rate and carrying capacity of the patches. Only when the local growth rate and the carrying capacity are large does the slow variable correspond to the number of patches, as envisaged by Levins. Last but not least, we discuss how our findings relate to other, widely used metapopulation models.
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| 7. |
- Eriksson, Anders, 1975, et al.
(author)
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The emergence of the rescue effect from explicit within- and between-patch dynamics in a metapopulation
- 2014
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In: Proceedings of the Royal Society of London. Biological Sciences. - : The Royal Society. - 0962-8452 .- 1471-2954. ; 281:1780
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Journal article (peer-reviewed)abstract
- Immigration can rescue local populations from extinction, helping to stabilise a metapopulation. Local population dynamics is important for determining the strength of this rescue effect, but the mechanistic link between local demographic parameters and the rescue effect at the metapopulation level has received very little attention by modellers. We develop an analytical framework that allows us to describe the emergence of the rescue effect from interacting local stochastic dynamics. We show this framework to be applicable to a wide range of spatial scales, providing a powerful and convenient alternative to individual‐based models for making predictions concerning the fate of metapopulations. We show that the rescue effect plays an important role in minimising the increase in local extinction probability associated with high demographic stochasticity, but its role is more limited in the case of high local environmental stochasticity of recruitment or survival. While most models postulate the rescue effect, our framework provides an explicit mechanistic link between local dynamics and the emergence of the rescue effect, and more generally the stability of the whole metapopulation.
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| 8. |
- Gómez-Llobregat, Jordi, et al.
(author)
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Anisotropic Membrane Curvature Sensing by Amphipathic Peptides
- 2016
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In: Biophysical Journal. - : Elsevier BV. - 0006-3495 .- 1542-0086. ; 110:1, s. 197-204
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Journal article (peer-reviewed)abstract
- Many proteins and peptides have an intrinsic capacity to sense and induce membrane curvature, and play crucial roles for organizing and remodeling cell membranes. However, the molecular driving forces behind these processes are not well understood. Here, we describe an approach to study curvature sensing by simulating the interactions of single molecules with a buckled lipid bilayer. We analyze three amphipathic antimicrobial peptides, a class of membrane-associated molecules that specifically target and destabilize bacterial membranes, and find qualitatively different sensing characteristics that would be difficult to resolve with other methods. Our findings provide evidence for direction-dependent curvature sensing mechanisms in amphipathic peptides and challenge existing theories of hydrophobic insertion. The buckling approach is generally applicable to a wide range of curvature-sensing molecules, and our results provide strong motivation to develop new experimental methods to track position and orientation of membrane proteins.
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