Steered molecular dynamics (SMD) permits efficient investigations of molecular processes by focusing on selected degrees of freedom. We explain how one can, in the framework of SMD, employ Jarzynski's equality (also known as the nonequilibrium work relation) to calculate potentials of mean force (PMF). We outline the theory that serves this purpose and connects nonequilibrium processes (such as SMD simulations) with equilibrium properties (such as the PMF). We review the derivation of Jarzynski's equality, generalize it to isobaric--isothermal processes, and discuss its implications in relation to the second law of thermodynamics and computer simulations. In the relevant regime of steering by means of stiff springs, we demonstrate that the work on the system is Gaussian-distributed regardless of the speed of the process simulated. In this case, the cumulant expansion of Jarzynski's equality can be safely terminated at second order. We illustrate the PMF calculation method for an exemplary simulation and demonstrate the Gaussian nature of the resulting work distribution.

Jarzynski's equality is applied to free energy calculations from steered molecular dynamics simulations of biomolecules. The helix-coil transition of deca-alanine in vacuum is used as an example. With about ten trajectories sampled, the second order cumulant expansion, among the various averaging schemes examined, yields the most accurate estimates. We compare umbrella sampling and the present method, and find that their efficiencies are comparable.

Aquaglyceroporin GlpF selectively conducts water and linear polyalcohols, such as glycerol, across the inner membrane of Escherichia coli. We report steered molecular dynamics simulations of glycerol conduction through GlpF, in which external forces accelerate the transchannel conduction in a manner that preserves the intrinsic conduction mechanism. The simulations reveal channel-glycerol hydrogen bonding interactions and the stereoselectivity of the channel. Employing Jarzynski's identity between free energy and irreversible work, we reconstruct the potential of mean force along the conduction pathway through a time series analysis of molecular dynamics trajectories. This potential locates binding sites and barriers inside the channel; it also reveals a low energy periplasmic vestibule suited for efficient uptake of glycerol from the environment.A quaporins (1), a family of water transporting membrane proteins, are present in all life forms, and defects in their function cause physiological disorders (2). Among more than 150 members identified to date (2), the Escherichia coli glycerol facilitator (GlpF) belongs to the aquaglyceroporin subclass, which is permeable to both water and glycerol. GlpF also stereoselectively conducts longer linear polyalcohols (3, 4). At physiological conditions, all aquaporins exclude charged solutes, including protons, and thereby preserve the electrochemical potential across the cell membrane (2).A 2.2-Å resolution x-ray structure of GlpF revealed a homotetrameric architecture with glycerol and water present inside the channel (5). Each monomeric channel has two halfmembrane spanning repeats related by a quasi-two-fold symmetry. About half of each repeat is ␣-helical; the other half adopts a particular nonhelical structure (5, 6). The N termini of the helical repeats meet at the Asn-Pro-Ala (NPA) motifs located at the channel center. The NPA motifs are conserved among all aquaporins (2), and their spatial arrangement is critical for the biological function of the channel (6-8). The nonhelical repeats expose the backbone carbonyl groups of residues 64-66 and 195-201 toward the channel interior, where they serve as hydrogen acceptors for the substrate (6). The channel diameter measures less than 3.5 Å at its narrowest point, the selectivity filter (SF), lined with residues Trp-48, 9). In the constriction region of the channel, approximately 25 Å long, the substrate is translocated in a single file following a curvilinear pathway (6), a feature critical for excluding proton conduction (10). The hydroxyl groups of glycerol make hydrogen bonds with exposed carbonyl oxygen atoms, polar hydrogen atoms, and water, whereas the aliphatic backbone of glycerol faces the opposite hydrophobic side of the channel (6). The amphipathic channel lining in GlpF ensures the selectivity for linear polyalcohols (5). The amphipathicity of the channel's interior also seems to be important for water transport and is found, although to a less extent, in pure water-conducting aquaporins, such as aquaporin-1 ...

Most proteins that participate in cellular signalling networks contain modular protein-interaction domains. Multiple versions of such domains are present within a given organism: the yeast proteome, for example, contains 27 different Src homology 3 (SH3) domains. This raises the potential problem of cross-reaction. It is generally thought that isolated domain-ligand pairs lack sufficient information to encode biologically unique interactions, and that specificity is instead encoded by the context in which the interaction pairs are presented. Here we show that an isolated peptide ligand from the yeast protein Pbs2 recognizes its biological partner, the SH3 domain from Sho1, with near-absolute specificity--no other SH3 domain present in the yeast genome cross-reacts with the Pbs2 peptide, in vivo or in vitro. Such high specificity, however, is not observed in a set of non-yeast SH3 domains, and Pbs2 motif variants that cross-react with other SH3 domains confer a fitness defect, indicating that the Pbs2 motif might have been optimized to minimize interaction with competing domains specifically found in yeast. System-wide negative selection is a subtle but powerful evolutionary mechanism to optimize specificity within an interaction network composed of overlapping recognition elements.