Aggregation and partitioning of amyloid peptide fragments in the presence of a lipid bilayer: A coarse grained molecular dynamics study.

Amyloidogenicity and toxicity of amyloid peptides have been linked to the peptide aggregation and interactions with lipid bilayers. In this work we used the coarse grained MARTINI model to study the aggregation and partitioning of amyloid peptide fragments Aß(1-28) and Aß(25-35) in the presence of a dipalmitoylphosphatidylcholine bilayer. We explored the peptide aggregation starting from three initial spatial arrangements where free monomers were placed in solution outside the membrane, at the membrane-solution interface, or in the membrane. We found that Aß(1-28) and Aß(25-35) interact with the bilayer quite differently. The Aß(1-28) fragments show strong peptide-peptide and peptide-lipid interactions leading to irreversible aggregation where the aggregates stay confined to their initial spatial location. The Aß(25-35) fragments show weaker peptide-peptide and peptide-lipid interaction leading to reversible aggregation and accumulation at the membrane-solution interface irrespective of their initial spatial arrangement. Those findings can be explained in terms of the shape of the potential of mean force for the single-peptide translocation across the membrane.

Modified Smoluchowski Rate Equations for Aggregation and Fragmentation in Finite Systems.

Protein self-assembly into supramolecular structures is important for cell biology. Theoretical methods employed to investigate protein aggregation and analogous processes include molecular dynamics simulations, stochastic models, and deterministic rate equations based on the mass-action law. In molecular dynamics simulations, the computation cost limits the system size, simulation length, and number of simulation repeats. Therefore, it is of practical interest to develop new methods for the kinetic analysis of simulations. In this work we consider the Smoluchowski rate equations modified to account for reversible aggregation in finite systems. We present several examples and argue that the modified Smoluchowski equations combined with Monte Carlo simulations of the corresponding master equation provide an effective tool for developing kinetic models of peptide aggregation in molecular dynamics simulations.

Side Chain Geometry Determines the Fibrillation Propensity of a Minimal Two-Beads-per-Residue Peptide Model.

The molecular mechanism of fibrillation is an important issue for understanding peptide aggregation. In our previous work, we demonstrated that the interchain attraction and intrachain bending stiffness control the aggregation kinetics and transient aggregate morphologies of a one-bead-per-residue implicit solvent peptide model. However, that model did not lead to fibrillation. In this work, we study the molecular origin of fibril formation using a two-beads-per-residue model, where one bead represents the backbone residue atoms and the other the side chain atoms. We show that the side chain geometry determines the fibrillation propensity that is further modulated by the modified terminal beads. This allows us to bring out the effects of side chain geometry and terminal capping on the fibrillation propensity. Our model does not assume a secondary structure and is, perhaps, the simplest bead-based chain model leading to fibrillation.

Diverse Aggregation Kinetics Predicted by a Coarse-Grained Peptide Model.

Protein and peptide aggregation is a ubiquitous phenomenon with implications in medicine, pharmaceutical industry, and materials science. An important issue in peptide aggregation is the molecular mechanism of aggregate nucleation and growth. In many experimental studies, sigmoidal kinetics curves show a clear lag phase ascribed to nucleation; however, experimental studies also show downhill kinetics curves, where the monomers decay continuously and no lag phase can be seen. In this work, we study peptide aggregation kinetics using a coarse-grained implicit solvent model introduced in our previous work. Our simulations explore the hypothesis that the interplay between interchain attraction and intrachain bending stiffness controls the aggregation kinetics and transient aggregate morphologies. Indeed, our model reproduces the aggregation modes seen in experiment: no observed aggregation, nucleated aggregation, and rapid downhill aggregation. We find that the interaction strength is the primary parameter determining the aggregation mode, whereas the stiffness is a secondary parameter modulating the transient morphologies and aggregation rates: more attractive and stiff chains aggregate more rapidly and the transient morphologies are more ordered. We also explore the effects of the initial monomer concentration and the chain length. As the concentration decreases, the aggregation mode shifts from downhill to nucleated and no-aggregation. This concentration effect is in line with an experimental observation that the transition between downhill and nucleated kinetics is concentration-dependent. We find that longer peptides can aggregate at conditions where short peptides do not aggregate at all. It supports an experimental observation that the elongation of a homopeptide, e.g., polyglutamine, can increase the aggregation propensity.

Clustering and Fibril Formation during GNNQQNY Aggregation: A Molecular Dynamics Study.

The precise kinetic pathways of peptide clustering and fibril formation are not fully understood. Here we study the initial clustering kinetics and transient cluster morphologies during aggregation of the heptapeptide fragment GNNQQNY from the yeast prion protein Sup35. We use a mid-resolution coarse-grained molecular dynamics model of Bereau and Deserno to explore the aggregation pathways from the initial random distribution of free monomers to the formation of large clusters. By increasing the system size to 72 peptides we could follow directly the molecular events leading to the formation of stable fibril-like structures. To quantify those structures we developed a new cluster helicity parameter. We found that the formation of fibril-like structures is a cooperative processes that requires a critical number of monomers, M⋆≈25, in a cluster. The terminal tyrosine residue is the structural determinant in the formation of helical fibril-like structures. This work supports and quantifies the two-step aggregation model where the initially formed amorphous clusters grow and, when they are large enough, rearrange into mature twisted structures. However, in addition to the nucleated fibrillation, growing aggregates undergo further internal reorganization, which leads to more compact structures of large aggregates.

Chiral structure fluctuations predicted by a coarse-grained model of peptide aggregation.

This work reports on the chiral structure fluctuations of peptide clusters at the early stages of aggregation in a coarse-grained peptide model. Our model reproduces a variety of aggregate structures, from disordered to crystal-like, that are observed experimentally. Unexpectedly, our molecular dynamics simulations showed that the small peptide cluster undergoes chiral structure fluctuations although the underlying implicit solvent model does not assume the chirality of peptides. The chiral fluctuations are quantified through a cluster twist parameter. A simple model is presented where the twist parameter undergoes a stochastic diffusion on a 1D potential surface. The shape of the potential surface changes with the cluster size. The model shows semi-quantitative agreement with the simulations. We hypothesize that the chiral fluctuations at the early stages of peptide aggregation can contribute to the selection of the final fibril structures.

Aggregation kinetics of short peptides: All-atom and coarse-grained molecular dynamics study.

Peptides can aggregate into ordered structures with different morphologies. The aggregation mechanism and evolving structures are the subject of intense research. In this paper we have used molecular dynamics to examine the sequence-dependence of aggregation kinetics for three short peptides: octaalanine (Ala8), octaasparagine (Asn8), and the heptapeptide GNNQQNY (abbreviated as GNN). First, we compared the aggregation of 20 randomly distributed peptides using the coarse-grained MARTINI force field and the atomistic OPLS-AA force field. We found that the MARTINI and OPLS-AA aggregation kinetics are similar for Ala8, Asn8, and GNN. Second, we used the MARTINI force field to study the early stages of aggregation kinetics for a larger system with 72 peptides. In the initial stage of aggregation small clusters grow by monomer addition. In the second stage, when the free monomers are depleted, the dominant cluster growth path is cluster-cluster coalescence. We quantified the aggregation kinetics in terms of rate equations. Our study shows that the initial aggregation kinetics are similar for Ala8, Asn8, and GNN but the molecular details can be different, especially for MARTINI Ala8. We hypothesize that peptide aggregation proceed in two steps. In the first step amorphous aggregates are formed, and then, in the second step, they reorganize into ordered structures. We conclude that sequence-specific differences show up in the second step of aggregation.

Sequence-Dependent Unzipping Dynamics of DNA Hairpins in a Nanopore.

By applying an electric field to an insulating membrane, movement of charged particles through a nanopore can be induced. The measured ionic current reports on biomolecules passing through the nanopore. In this paper, we explore the sequence-dependent dynamics of DNA unzipping using our recently developed coarse-grained model. We estimated three molecular profiles (the potential of mean force, position-dependent diffusion coefficient, and position-dependent effective charge) for the DNA unzipping of four hairpins with different sequences. We found that the molecular profiles are correlated with the ionic current and molecular events. We also explored the unzipping kinetics using Brownian dynamics. We found that the effect of hairpin structure on the unzipping/translocation times is not only energetic (weaker hairpins unzip more quickly) but also kinetic (different unzipping and translocation pathways play an important role).

Diffusive dynamics of DNA unzipping in a nanopore.

When an electric field is applied to an insulating membrane, movement of charged particles through a nanopore is induced. The measured ionic current reports on biomolecules passing through the nanopore. In this work, we explored the kinetics of DNA unzipping in a nanopore using our coarse-grained model (Stachiewicz and Molski, J. Comput. Chem. 2015, 36, 947). Coarse graining allowed a more detailed analysis for a wider range of parameters than all-atom simulations. Dependence of the translocation mode (unzipping or distortion) on the pore diameter was examined, and the threshold voltages were estimated. We determined the potential of mean force, position-dependent diffusion coefficient, and position-dependent effective charge for the DNA unzipping. The three molecular profiles were correlated with the ionic current and molecular events. On the unzipping/translocation force profile, two energy maxima were found, one of them corresponding to the unzipping, and the other to the translocation barriers. The unzipping kinetics were further explored using Brownian dynamics.

A coarse-grained MARTINI-like force field for DNA unzipping in nanopores.

In nanopore force spectroscopy (NFS) a charged polymer is threaded through a channel of molecular dimensions. When an electric field is applied across the insulating membrane, the ionic current through the nanopore reports on polymer translocation, unzipping, dissociation, and so forth. We present a new model that can be applied in molecular dynamics simulations of NFS. Although simplified, it does reproduce experimental trends and all-atom simulations. The scaled conductivities in bulk solution are consistent with experimental results for NaCl for a wide range of electrolyte concentrations and temperatures. The dependence of the ionic current through a nanopore on the applied voltage is symmetric and, in the voltage range used in experiments (up to 2 V), linear and in good agreement with experimental data. The thermal stability and geometry of DNA is well represented. The model was applied to simulations of DNA hairpin unzipping in nanopores. The results are in good agreement with all-atom simulations: the scaled translocation times and unzipping sequence are similar.

Manual lymphatic drainage improves the quality of life in patients with chronic venous disease: a randomized controlled trial.

INTRODUCTION: Manual lymphatic drainage (MLD) is an adjunctive method of chronic venous disease (CVD) therapy. Evaluation of the change at the clinical stage, hemodynamic parameters and quality of life (QoL) following venous system surgery in CVD patients undergoing MLD preoperatively are the most interesting aspects of the study. MATERIAL AND METHODS: The CVD patients qualified for elective surgery of the venous system were randomly divided into 2 groups: the MLD group (n = 38) and the control group (n = 32). In the preoperative period, the MLD group underwent a series of MLD through a period of 2 weeks. The control group did not undergo MLD preoperatively. Both groups were evaluated for CVD staging on the day of qualification for surgery and between 25 and 30 days post-operatively. Additionally, the MLD group was evaluated after the series of MLD. The CVD staging was evaluated in both groups with a QoL questionnaire (CIVIQ), CEAP classification, foot volumetry (FV) and venous refilling time (VRT). RESULTS: PARAMETER VALUES OBTAINED IN THE MLD GROUP (BEFORE TREATMENT/AFTER MLD/AFTER SURGERY): CEAP 2.23/2.15/2.10, VRT 15/13/15.6, FV 3625/3472/3418, CIVIQ-complaints: 54.4/43.8/38.2 and CIVIQ-meaning: 57.3/49.3/43.1. Parameter values obtained in control group (before surgery/after surgery): CEAP 2.4/2.12, VRT 13/14.9, FV 3581/3559, CIVIQ-complaints: 51.9/38.7 and CIVIQ-meaning: 53.7/40.6. The CVD patients statistically improved in CEAP staging, FV and QoL in both groups (p < 0.05). CONCLUSIONS: The MLD alone significantly reduced FV in patients with CVD, also improving their QoL. The MLD applied in CVD patients at the preoperative stage results in better surgical outcome, which is demonstrated by reduced disease progression, FV reduction and improvement in the QoL.

Maximum likelihood-based analysis of single-molecule photon arrival trajectories.

In this work we explore the statistical properties of the maximum likelihood-based analysis of one-color photon arrival trajectories. This approach does not involve binning and, therefore, all of the information contained in an observed photon strajectory is used. We study the accuracy and precision of parameter estimates and the efficiency of the Akaike information criterion and the Bayesian information criterion (BIC) in selecting the true kinetic model. We focus on the low excitation regime where photon trajectories can be modeled as realizations of Markov modulated Poisson processes. The number of observed photons is the key parameter in determining model selection and parameter estimation. For example, the BIC can select the true three-state model from competing two-, three-, and four-state kinetic models even for relatively short trajectories made up of 2 × 10(3) photons. When the intensity levels are well-separated and 10(4) photons are observed, the two-state model parameters can be estimated with about 10% precision and those for a three-state model with about 20% precision.

Determination of photophysical parameters from photon arrival time trajectories in single molecule fluorescence spectroscopy.

Triplet blinking is a phenomenon observed commonly in single molecule fluorescence spectroscopy. At high to moderate excitation intensities one can distinguish bright (on) and dark (off) periods in the fluorescence intensity trajectory caused by sojourns into the nonemissive triplet state. In this work, we focus on triplet blinking of an immobilized molecule in the low excitation regime, where a threshold between on and off intensity levels cannot be set, and, therefore, a standard on/off analysis of fluorescence intensity trajectories is not possible. In the low excitation regime triplet blinking parameters can be recovered from photon arrival time trajectories, i.e., records of individual photon arrival time. We use computer-generated data to compare the recovery of the triplet blinking parameters from the intensity correlation function (ICF) and the histogram of interarrival time. We have found that the ICF offers a better statistics for the recovery of the triplet blinking parameters.