Constructing Simplicial Complexes over Topological Spaces

The first step in topological data analysis is often the construction of a simplicial complex. This complex approximates the lost topology of a sampled point set. Current techniques often assume that the input is embedded in a metric -- often Euclidean -- space, and make significant use of the underlying geometry for efficient computation. Consequently, these techniques do not extend to non-Euclidean or non-metric spaces. In this thesis, we present an oracle-based framework for constructing simplicial complexes over arbitrary topological spaces. The framework consists of an oracle and an algorithm that builds the simplicial complex by making calls to the oracle. We compare different algorithmic approaches for the construction, as well as alternate ways of representing the simplicial complex in the computation. Finally, we demonstrate the utility of our framework as a tool for approaching problems of diverse nature by presenting three applications: to multiword search in Google, to the computational analysis of a language and to the study of protein structure

Gramicidin Increases Lipid Flip-Flop in Symmetric and Asymmetric Lipid Vesicles

© 2019 Biophysical Society Unlike most transmembrane proteins, phospholipids can migrate from one leaflet of the membrane to the other. Because this spontaneous lipid translocation (flip-flop) tends to be very slow, cells facilitate the process with enzymes that catalyze the transmembrane movement and thereby regulate the transbilayer lipid distribution. Nonenzymatic membrane-spanning proteins with unrelated primary functions have also been found to accelerate lipid flip-flop in a nonspecific manner and by various hypothesized mechanisms. Using deuterated phospholipids, we examined the acceleration of flip-flop by gramicidin channels, which have well-defined structures and known functions, features that make them ideal candidates for probing the protein-membrane interactions underlying lipid flip-flop. To study compositionally and isotopically asymmetric proteoliposomes containing gramicidin, we expanded a recently developed protocol for the preparation and characterization of lipid-only asymmetric vesicles. Channel incorporation, conformation, and function were examined with small angle x-ray scattering, circular dichroism, and a stopped-flow spectrofluorometric assay, respectively. As a measure of lipid scrambling, we used differential scanning calorimetry to monitor the effect of gramicidin on the melting transition temperatures of the two bilayer leaflets. The two calorimetric peaks of the individual leaflets merged into a single peak over time, suggestive of scrambling, and the effect of the channel on the transbilayer lipid distribution in both symmetric 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine and asymmetric 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine/1,2-dimyristoyl-sn-glycero-3-phosphocholine vesicles was quantified from proton NMR measurements. Our results show that gramicidin increases lipid flip-flop in a complex, concentration-dependent manner. To determine the molecular mechanism of the process, we used molecular dynamics simulations and further computational analysis of the trajectories to estimate the extent of membrane deformation. Together, the experimental and computational approaches were found to constitute an effective means for studying the effects of transmembrane proteins on lipid distribution in both symmetric and asymmetric model membranes

Peptide-Induced Lipid Flip-Flop in Asymmetric Liposomes Measured by Small Angle Neutron Scattering

© 2019 American Chemical Society. Despite the prevalence of lipid transbilayer asymmetry in natural plasma membranes, most biomimetic model membranes studied are symmetric. Recent advances have helped to overcome the difficulties in preparing asymmetric liposomes in vitro, allowing for the examination of a larger set of relevant biophysical questions. Here, we investigate the stability of asymmetric bilayers by measuring lipid flip-flop with time-resolved small-angle neutron scattering (SANS). Asymmetric large unilamellar vesicles with inner bilayer leaflets containing predominantly 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and outer leaflets composed mainly of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) displayed slow spontaneous flip-flop at 37 -C (half-time, t1/2 = 140 h). However, inclusion of peptides, namely, gramicidin, alamethicin, melittin, or pHLIP (i.e., pH-low insertion peptide), accelerated lipid flip-flop. For three of these peptides (i.e., pHLIP, alamethicin, and melittin), each of which was added externally to preformed asymmetric vesicles, we observed a completely scrambled bilayer in less than 2 h. Gramicidin, on the other hand, was preincorporated during the formation of the asymmetric liposomes and showed a time resolvable 8-fold increase in the rate of lipid asymmetry loss. These results point to a membrane surface-related (e.g., adsorption/insertion) event as the primary driver of lipid scrambling in the asymmetric model membranes of this study. We discuss the implications of membrane peptide binding, conformation, and insertion on lipid asymmetry

All-atom Gromacs Trajectory of POPC/TOCL bilayer mixture

All-atom bilayer mixture of POPC/TOCL 1:1 simulated in an NPT ensemble with Gromacs and the CHARMM36 force field from Castillo et al, 2022, Mol. Pharmaceutics. 19:1839-1852 (https://doi.org/10.1021/acs.molpharmaceut.1c00926). The trajectory represents 540 ns with frames output every 20 ps. The bilayer has 120 lipids total (60 lipids per leaflet) and is hydrated with 100 waters/lipid and sodium ions to neutralize the system. The simulation was done at 37C (310.15K). POPC is 16:0,18:1 PC; TOCL is tetraoleoyl cardiolipinAttached files include the structure (.gro), trajectory (.xtc) and input gromacs file (.mdp) with simulation parameters for the production run

All-atom Gromacs Trajectory of POPE/TOCL bilayer mixture

All-atom bilayer mixture of POPE/TOCL 1:1 simulated in an NPT ensemble with Gromacs and the CHARMM36 force field from Castillo et al, 2022, Mol. Pharmaceutics. 19:1839-1852 (https://doi.org/10.1021/acs.molpharmaceut.1c00926). The trajectory represents 530 ns with frames output every 20 ps. The bilayer has 120 lipids total (60 lipids per leaflet) and is hydrated with 100 waters/lipid and sodium ions to neutralize the system. The simulation was done at 37C (310.15K). POPE is 16:0,18:1 PE; TOCL is tetraoleoyl cardiolipinAttached files include the structure (.gro), trajectory (.xtc) and input gromacs file (.mdp) with simulation parameters for the production run

NAMD Trajectory of a Tetraoleoyl Cardiolipin Bilayer

All-atom TOCL (tetraoleoyl cardiolipin) bilayer simulated in NPT ensemble with NAMD and the CHARMM36 force field from Doktorova et al. 2017 Phys. Chem. Chem. Phys. article (DOI 10.1039/c7cp01921a). The trajectory represents the last 155 ns used for analysis where the area per lipid is equilibrated (the file has 7752 frames output every 20 ps). The bilayer has 100 lipids total (50 lipids per leaflet) and is hydrated with 60 waters/lipid and 140mM NaCl. The simulation was done at 30C (303.15K) and the trajectory is centered on the bilayer midplane.Attached files include the structure (.psf and .pdb), trajectory (.dcd) and a copy of the NAMD input file with simulation parameters

Biophysics Of Asymmetric Membranes: Protocols And Revelations

Lipid membranes enclose cells and organelles, and actively participate in cellular processes. Their many functional roles require tight regulation of properties including structure and dynamics. Cells achieve this by producing and dynamically tuning the concentration and organization of hundreds of structurally different types of lipid molecules in the various cellular membranes. The cell-bounding plasma membranes of eukaryotes in particular, exhibit an actively maintained asymmetric lipid distribution across their two leaflets. In addition to exposing certain types of lipids to the extracellular space or intracellular milieu, this specialized transbilayer lipid arrangement also affects the properties of the membrane itself and its interactions with proteins, in ways that are difficult to explore and thus not understood. To address this problem and enable further advancements in the field, we have developed both in vitro and in silico protocols for building asymmetric model membranes with finely controlled lipid compositions. These protocols allowed us to investigate the dynamics, energetics and structural consequences of interleaflet communication: with small-angle scattering we uncovered asymmetry-mediated changes in the lipid packing of individual leaflets in free-floating liposomes; with electron spin resonance we revealed the ensuing trends in lipid order; and nuclear magnetic resonance helped us bring new appreciation of the interplay between asymmetric bilayers and transmembrane protein inclusions. To interpret and better understand the experimental observations, we developed a new in silico protocol for constructing atomistic models of tension-free asymmetric bilayers and used it to simulate the experimentally measured membranes and validate the simulation conditions. By devising a novel computational framework for calculating the compressibility of individual bilayer leaflets, we analyzed the energetics of protein interaction with the asymmetric membranes and obtained an estimate of the elastic energy of mixing the two leaflets. Together with additional experimental and computational studies of symmetric membrane systems, the results revealed fascinating ways in which cells can mediate the functional diversity of their membranes. The new methods and protocols leading to these insights generate previously unattainable opportunities for dissecting and exploring membrane-mediated cellular processes

Biophysics of Asymmetric Membranes: Protocols and Revelations

Lipid membranes enclose cells and organelles, and actively participate in cellular processes. Their many functional roles require tight regulation of properties including structure and dynamics. Cells achieve this by producing and dynamically tuning the concentration and organization of hundreds of structurally different types of lipid molecules in the various cellular membranes. The cell-bounding plasma membranes of eukaryotes in particular, exhibit an actively maintained asymmetric lipid distribution across their two leaflets. In addition to exposing certain types of lipids to the extracellular space or intracellular milieu, this specialized transbilayer lipid arrangement also affects the properties of the membrane itself and its interactions with proteins, in ways that are difficult to explore and thus not understood. To address this problem and enable further advancements in the field, we have developed both in vitro and in silico protocols for building asymmetric model membranes with finely controlled lipid compositions. These protocols allowed us to investigate the dynamics, energetics and structural consequences of interleaflet communication: with small-angle scattering we uncovered asymmetry-mediated changes in the lipid packing of individual leaflets in free-floating liposomes; with electron spin resonance we revealed the ensuing trends in lipid order; and nuclear magnetic resonance helped us bring new appreciation of the interplay between asymmetric bilayers and transmembrane protein inclusions. To interpret and better understand the experimental observations, we developed a new in silico protocol for constructing atomistic models of tension-free asymmetric bilayers and used it to simulate the experimentally measured membranes and validate the simulation conditions. By devising a novel computational framework for calculating the compressibility of individual bilayer leaflets, we analyzed the energetics of protein interaction with the asymmetric membranes and obtained an estimate of the elastic energy of mixing the two leaflets. Together with additional experimental and computational studies of symmetric membrane systems, the results revealed fascinating ways in which cells can mediate the functional diversity of their membranes. The new methods and protocols leading to these insights generate previously unattainable opportunities for dissecting and exploring membrane-mediated cellular processes