Classical Molecular Dynamics with Mobile Protons

An important limitation of standard classical molecular dynamics simulations is the inability to make or break chemical bonds. This restricts severely our ability to study processes that involve even the simplest of chemical reactions, the transfer of a proton. Existing approaches for allowing proton transfer in the context of classical mechanics are rather cumbersome and have not achieved widespread use and routine status. Here we reconsider the combination of molecular dynamics with periodic stochastic proton hops. To ensure computational efficiency, we propose a non-Boltzmann acceptance criterion that is heuristically adjusted to maintain the correct or desirable thermodynamic equilibria between different protonation states and proton transfer rates. Parameters are proposed for hydronium, Asp, Glu, and His. The algorithm is implemented in the program CHARMM and tested on proton diffusion in bulk water and carbon nanotubes and on proton conductance in the gramicidin A channel. Using hopping parameters determined from proton diffusion in bulk water, the model reproduces the enhanced proton diffusivity in carbon nanotubes and gives a reasonable estimate of the proton conductance in gramicidin A

Divergent Diffusion Coefficients in Simulations of Fluids and Lipid Membranes

We investigate the dependence of single-particle diffusion coefficients on the size and shape of the simulation box in molecular dynamics simulations of fluids and lipid membranes. We find that the diffusion coefficients of lipids and a carbon nanotube embedded in a lipid membrane diverge with the logarithm of the box width. For a neat Lennard-Jones fluid in flat rectangular boxes, diffusion becomes anisotropic, diverging logarithmically in all three directions with increasing box width. In elongated boxes, the diffusion coefficients normal to the long axis diverge linearly with the height-to-width ratio. For both lipid membranes and neat fluids, this behavior is predicted quantitatively by hydrodynamic theory. Mean-square displacements in the neat fluid exhibit intermediate regimes of anomalous diffusion, with <i>t</i> ln <i>t</i> and <i>t</i>^3/2 components in flat and elongated boxes, respectively. For membranes, the large finite-size effects, and the apparent inability to determine a well-defined lipid diffusion coefficient from simulation, rationalize difficulties in comparing simulation results to each other and to those from experiments

Formation and Stability of Lipid Membrane Nanotubes

Lipid membrane nanotubes are abundant in living cells, even though tubules are energetically less stable than sheet-like structures. According to membrane elastic theory, the tubular endoplasmic reticulum (ER), with its high area-to-volume ratio, appears to be particularly unstable. We explore how tubular membrane structures can nevertheless be induced and why they persist. In Monte Carlo simulations of a fluid–elastic membrane model subject to thermal fluctuations and without constraints on symmetry, we find that a steady increase in the area-to-volume ratio readily induces tubular structures. In simulations mimicking the ER wrapped around the cell nucleus, tubules emerge naturally as the membrane area increases. Once formed, a high energy barrier separates tubules from the thermodynamically favored sheet-like membrane structures. Remarkably, this barrier persists even at large area-to-volume ratios, protecting tubules against shape transformations despite enormous driving forces toward sheet-like structures. Molecular dynamics simulations of a molecular membrane model confirm the metastability of tubular structures. Volume reduction by osmotic regulation and membrane area growth by lipid production and by fusion of small vesicles emerge as powerful factors in the induction and stabilization of tubular membrane structures

Multi-protein complexes and interface residue overlap.

<p>The subunits of multi-protein complexes bind together simultaneously and therefore these subunit proteins are not competing to bind to the same interface. For each subunit <i>S</i> in the complex, we test all pairs of its binding partners for sharing binding residues on the surface of <i>S</i>. Each binding pair then has <i>n</i> = 0, 1, 2 etc. overlapping residues. Whereas most binding pairs do not share interface residues, clearly there is some overlap. If one accounts for specific atoms in an interface rather than residues, the overlap decreases but is still present. For the proteasome, there are still 22% and 7% of interface pairs that share atoms (at 4 Å and 3.5 Å cutoffs, respectively).</p

Formation and Stability of Lipid Membrane Nanotubes

Lipid membrane nanotubes are abundant in living cells, even though tubules are energetically less stable than sheet-like structures. According to membrane elastic theory, the tubular endoplasmic reticulum (ER), with its high area-to-volume ratio, appears to be particularly unstable. We explore how tubular membrane structures can nevertheless be induced and why they persist. In Monte Carlo simulations of a fluid–elastic membrane model subject to thermal fluctuations and without constraints on symmetry, we find that a steady increase in the area-to-volume ratio readily induces tubular structures. In simulations mimicking the ER wrapped around the cell nucleus, tubules emerge naturally as the membrane area increases. Once formed, a high energy barrier separates tubules from the thermodynamically favored sheet-like membrane structures. Remarkably, this barrier persists even at large area-to-volume ratios, protecting tubules against shape transformations despite enormous driving forces toward sheet-like structures. Molecular dynamics simulations of a molecular membrane model confirm the metastability of tubular structures. Volume reduction by osmotic regulation and membrane area growth by lipid production and by fusion of small vesicles emerge as powerful factors in the induction and stabilization of tubular membrane structures

Local IIN structural properties.

<p>The clustering coefficients and the percentages of 4-node motifs present in the observed CME IIN are compared with 1200 randomized versions of the network that preserve the same degree distribution. The values in parentheses are the p-values for the hypothesis that the CME IIN is similar to randomized networks with the same global properties. The low p-values indicate that the CME IIN is quite distinct from the randomized networks and unique in its local structure.</p

Distinct binding interfaces and IIN of yeast actin protein ACT1, and its corresponding PPI network with interfaces overlaid.

<p>(a) Actin surface structure (grey; PDB structure 1YAG) with binding interfaces in van-der-Waals representation and binding partner interfaces listed in matching colors, indicating the IIN for the actin protein. Residues in interfaces ACT1.0 (cyan), ACT1.1 (blue) and ACT1.2 (magenta) were determined from crystal structures of complexes (PDB structures 3J0S and 3LUE for ACT1.0 and ACT1.1, and structures 2A3Z, 2A41, 3LUE and 3J0S for ACT1.2). In the absence of structures for the ACT1.3 (yellow) complex, we used the results of genetic studies <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003065#pcbi.1003065-Rodal1" target="_blank">[61]</a> to highlight surface residues of actin subunit IV that are both essential for binding to AIP1 and not involved in COF1 binding mediated by the ACT1.2 interface. (b) Sub-network of protein interactions involving actin-binding proteins of CME with interfaces defined. Colors indicate specific domain types listed in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003065#pcbi-1003065-g003" target="_blank">Figure 3</a>.</p

Degree distribution for the endocytosis network.

<p><b>a)</b> Endocytosis PPI network. Blue data are for the full interaction network downloaded from the BioGrid, IntAct, MINT, DIP, and BIND databases, before curating the interfaces. The red data are for the protein-protein interaction network with interfaces assigned (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003065#pcbi-1003065-g002" target="_blank">Figure 2b</a>). For the curated PPI, a power-law distribution was best fit with k_min = 4 and γ = 2.37 (black dashed line), but the resulting p-value is less than 0.05, implying that the hypothesis of a power law density for the data is not accurate. The full database PPI can only be fit with k_min = 11, leaving only about half the data points. <b>b)</b>. Endocytosis IIN. A power law (solid line) best fits this data with a k_min = 2 and γ = 2.47, giving a p-value of 0.26 that implies good consistency with a power-law density.</p

Evolutionary Pressure on the Topology of Protein Interface Interaction Networks

The densely connected structure of protein–protein interaction (PPI) networks reflects the functional need of proteins to cooperate in cellular processes. However, PPI networks do not adequately capture the competition in protein binding. By contrast, the interface interaction network (IIN) studied here resolves the modular character of protein–protein binding and distinguishes between simultaneous and exclusive interactions that underlie both cooperation and competition. We show that the topology of the IIN is under evolutionary pressure, and we connect topological features of the IIN to specific biological functions. To reveal the forces shaping the network topology, we use a sequence-based computational model of interface binding along with network analysis. We find that the more fragmented structure of IINs, in contrast to the dense PPI networks, arises in large part from the competition between specific and nonspecific binding. The need to minimize nonspecific binding favors specific network motifs, including a minimal number of cliques (i.e., fully connected subgraphs) and many disconnected fragments. Validating the model, we find that these network characteristics are closely mirrored in the IIN of clathrin-mediated endocytosis. Features unexpected on the basis of our motif analysis are found to indicate either exceptional binding selectivity or important regulatory functions

Cumulative distribution of module size <i>m</i> in the IIN.

<p>The module size is the number of interfaces in a connected fragment of the IIN. The cumulative distribution is shown rather than the probability distribution because of the small sample size. For a power law probability, <i>p(m)</i>∼1/<i>m</i>^γ, the cumulative distribution P<i>(m)</i>∼1/<i>m</i>^γ−1 must also be a power law with an exponent γ−1. The best power-law fit to the probability distribution is for m_min = 3 and γ = 1.94, giving a p-value of 0.21 (red line). The black squares are the distribution for a set of networks that have the same size and degree distribution of the CME IIN, but with randomly reconnected edges. The randomized networks separate into one large component and a few small ones, with a gap between ∼10 and 100, in contrast to the modular structure of the CME IIN.</p