Size distribution of ring polymers.

We present an exact solution for the distribution of sample averaged monomer to monomer distance of ring polymers. For non-interacting and local-interaction models these distributions correspond to the distribution of the area under the reflected Bessel bridge and the Bessel excursion respectively, and are shown to be identical in dimension d ≥ 2, albeit with pronounced finite size effects at the critical dimension, d = 2. A symmetry of the problem reveals that dimension d and 4 - d are equivalent, thus the celebrated Airy distribution describing the areal distribution of the d = 1 Brownian excursion describes also a polymer in three dimensions. For a self-avoiding polymer in dimension d we find numerically that the fluctuations of the scaled averaged distance are nearly identical in dimension d = 2, 3 and are well described to a first approximation by the non-interacting excursion model in dimension 5.

Absolute Free Energy of Binding and Entropy of the FKBP12-FK506 Complex: Effects of the Force Field.

The hypothetical scanning molecular dynamics (HSMD) method combined with thermodynamic integration (HSMD-TI) has been extended recently for calculating ΔA(0)-the absolute free energy of binding of a ligand to a protein. With HSMD-TI, ΔA(0) is obtained in a new way as a sum of several components, among them is ΔSligand-the change in the conformational entropy as the ligand is transferred from the bulk solvent to the active site-this entropy is obtained by a specific reconstruction procedure. This unique aspect of HSMD (which is useful in rational drug design) is in particular important for treating large ligands, where ΔSligand might be significant. Technically, one should verify that the results for ΔSligand converge-a property that might become more difficult for large ligands; therefore, studying ligands of increasing size would define the range of applicability of HSMD-TI for binding. In this paper, we check the performance of HSMD-TI by applying it to the relatively large ligand FK506 (126 atoms) complexed with the protein FKBP12, where ΔA(0) = -12.8 kcal/mol is known experimentally as well as the crystal structure of the complex. This structure was initially equilibrated by carrying out a 100 ns molecular dynamics trajectory, where the system is modeled by the AMBER force field, TIP3P water, and Particle Mesh Ewald. HSMD-TI calculations were carried out in three conformational regions defined by the intervals [0.2,2], [2,5], and [5,100] ns along the trajectory, where local equilibration of the total energy has been observed; we obtained ΔA(0) = -13.6 ± 1.1, -16.6 ± 1.4, and -16.7 ± 1.4 kcal/mol, respectively indicating the following: (1) The second and third regions belong to the same conformational subspace of the complex, which is different from the [0.2,2] ns subspace. (2) The unsatisfactory result for ΔA(0) obtained in the well equilibrated (hence theoretically preferred) latter regions reflects the nonperfect modeling used, which however (3) has led to the experimental ΔA(0) in the [0.2,2] ns region close to the crystal structure. Keeping the complex near its crystal structure has been a successful approach in the literature. To check this avenue further, we applied harmonic restraints on backbone atoms and obtained unsatisfactory results for ΔA(0), suggesting that implementation of this approach is not straightforward. Converging results for ΔSligand were obtained in all regions, where the result ΔSligand([0.2,2]) = 7.1 ± 1.2 kcal/mol is less region dependent than ΔA(0) and is relatively large probably due to the large ligand.

Absolute free energy of binding of avidin/biotin, revisited.

The binding of biotin to avidin is one of the strongest in nature with absolute free energy of binding, ΔA(0) = -20.4 kcal/mol. Therefore, this complex became a target for a large number of computational studies, which all, however, are based on approximate techniques or simplified models and have led to a wide range of results Therefore, ΔA(0) is calculated here by rigorous statistical mechanical methods and models that consider long-range electrostatics. (1) We apply our method, "hypothetical scanning molecular dynamics with thermodynamic integration" (HSMD-TI) to avidin-biotin modeled by periodic boundary conditions with particle mesh ewald (PME). (2) We apply the double decoupling method (DDM) to this system modeled by the spherical solvent boundary potential (SSBP) and the generalized solvent boundary potential (GSBP). The corresponding results for neutral biotin, ΔA(0) = -29.1 ± 0.8 and -25.2 ± 0.5 kcal/mol are significantly lower than the experimental value; we also provide the result for a charged biotin, ΔA(0) = -33.3 ± 0.8 kcal/mol. It is plausible to suggest that this disagreement with the experiment may stem from ignoring the (positive) contribution of a mobile loop that changes its structure upon ligand binding.

Relative stability of the open and closed conformations of the active site loop of streptavidin.

The eight-residue surface loop, 45-52 (Ser, Ala, Val, Gly, Asn, Ala, Glu, Ser), of the homotetrameric protein streptavidin has a "closed" conformation in the streptavidin-biotin complex, where the corresponding binding affinity is one of the strongest found in nature (ΔG ∼ -18 kcal∕mol). However, in most of the crystal structures of apo (unbound) streptavidin, the loop conformation is "open" and typically exhibits partial disorder and high B-factors. Thus, it is plausible to assume that the loop structure is changed from open to closed upon binding of biotin, and the corresponding difference in free energy, ΔF = F(open) - F(closed) in the unbound protein, should therefore be considered in the total absolute free energy of binding. ΔF (which has generally been neglected) is calculated here using our "hypothetical scanning molecular-dynamics" (HSMD) method. We use a protein model in which only the atoms closest to the loop are considered (the "template") and they are fixed in the x-ray coordinates of the free protein; the x-ray conformation of the closed loop is attached to the same (unbound) template and both systems are capped with the same sphere of TIP3P water. Using the force field of the assisted model building with energy refinement (AMBER), we carry out two separate MD simulations (at temperature T = 300 K), starting from the open and closed conformations, where only the atoms of the loop and water are allowed to move (the template-water and template-loop interactions are considered). The absolute F(open) and F(closed) (of loop + water) are calculated from these trajectories, where the loop and water contributions are obtained by HSMD and a thermodynamic integration (TI) process, respectively. The combined HSMD-TI procedure leads to total (loop + water) ΔF = -27.1 ± 2.0 kcal∕mol, where the entropy TΔS constitutes 34% of ΔF, meaning that the effect of S is significant and should not be ignored. Also, ΔS is positive, in accord with the high flexibility of the open loop observed in crystal structures, while the energy ΔE is unexpectedly negative, thus also adding to the stability of the open loop. The loop and the 250 capped water molecules are the largest system studied thus far, which constitutes a test for the efficiency of HSMD-TI; this efficiency and technical issues related to the implementation of the method are also discussed. Finally, the result for ΔF is a prediction that will be considered in the calculation of the absolute free energy of binding of biotin to streptavidin, which constitutes our next project.

New method for calculating the absolute free energy of binding: the effect of a mobile loop on the avidin/biotin complex.

Hypothetical scanning molecular dynamics (HSMD) is a relatively new method for calculating the absolute free energy and entropy. HSMD is extended here for the first time for calculating the absolute free energy of binding, ΔA(0), as applied to the avidin-biotin complex. With HSMD the ligand is built (more accurately reconstructed) from nothing in solvent and in the protein, in contrast to the commonly used methods where the ligand is annihilated (by thermodynamic integration) in these environments. Therefore, the end-point problem encountered with the latter methods does not exist with HSMD and the need for restraints is avoided. Also, the entropy of the ligand and water in both environments is obtained directly as a byproduct of the simulation. The binding mechanism of biotin to avidin involves a mobile loop that is expected to be in an open conformation in unbound avidin, which is changed to a closed one upon binding, that is, the loop moves to cover biotin in the active site. The contribution of the loop's conformational change to the total free energy of binding is calculated here for the first time. Our result, ΔA(0) = -24.9 ± 7 covers the experimental value -20.7 kcal/mol within the error bars.

Calculation of the Absolute Free Energy of Binding and Related Entropies with the HSMD-TI Method: The FKBP12-L8 Complex.

The hypothetical scanning molecular dynamics (HSMD) method is used here for calculating the absolute free energy of binding, ΔA(0) of the complex of the protein FKBP12 with the ligand SB2 (also denoted L8) - a system that has been studied previously for comparing the performance of different methods. Our preliminary study suggests that considering long-range electrostatics is imperative even for a hydrophobic ligand such as L8. Therefore the system is modeled by the AMBER force field using Particle Mesh Ewald (PME). HSMD consists of three stages applied to both the ligand-solvent and ligand-protein systems. (1) A small set of system configurations (frames) is extracted from an MD trajectory. (2) The entropy of the ligand in each frame is calculated by a reconstruction procedure. (3) The contribution of water and protein to ΔA(0) is calculated for each frame by gradually increasing the ligand-environment interactions from zero to their full value using thermodynamic integration (TI). Unlike the conventional methods, the structure of the ligand is kept fixed during TI, and HSMD is thus free from the end-point problem encountered with the double annihilation method (DAM); therefore, the need for applying restraints is avoided. Furthermore, unlike the conventional methods, the entropy of the ligand and water is obtained directly as a byproduct of the simulation. In this paper, in addition to the difference in the internal entropies of the ligand in the two environments, we calculate for the first time the external entropy of the ligand, which provides a measure for the size of the active site. We obtain ΔA(0) = -10.7 ±1.0 as compared to the experimental values -10.9 and -10.6 kcal/mol. However, a protein/water system treated by periodic boundary conditions grows significantly with increasing protein size and the computation of ΔA(0) would become expensive by all methods. Therefore, we also apply HSMD to FKBP12-L8 described by the GSBP/SSBP model of Roux's group (implemented in the software CHARMM) where only part of the protein and water around the active site are considered and long-range electrostatic effects are taken into account. For comparison this model was also treated by the double decoupling method (DDM). The two methods have led to comparable results for ΔA(0) which are somewhat lower than the experimental value. The ligand was found to be more confined in the active site described by GSBP/SSBP than by PME where its entropy in solvent is larger than in the active site by 1.7 and by 5.5 kcal/mol, respectively.

Methods for calculating the absolute entropy and free energy of biological systems based on ideas from polymer physics.

The commonly used simulation techniques, Metropolis Monte Carlo (MC) and molecular dynamics (MD) are of a dynamical type which enables one to sample system configurations i correctly with the Boltzmann probability, P(i)(B), while the value of P(i)(B) is not provided directly; therefore, it is difficult to obtain the absolute entropy, S approximately -ln P(i)(B), and the Helmholtz free energy, F. With a different simulation approach developed in polymer physics, a chain is grown step-by-step with transition probabilities (TPs), and thus their product is the value of the construction probability; therefore, the entropy is known. Because all exact simulation methods are equivalent, i.e. they lead to the same averages and fluctuations of physical properties, one can treat an MC or MD sample as if its members have rather been generated step-by-step. Thus, each configuration i of the sample can be reconstructed (from nothing) by calculating the TPs with which it could have been constructed. This idea applies also to bulk systems such as fluids or magnets. This approach has led earlier to the "local states" (LS) and the "hypothetical scanning" (HS) methods, which are approximate in nature. A recent development is the hypothetical scanning Monte Carlo (HSMC) (or molecular dynamics, HSMD) method which is based on stochastic TPs where all interactions are taken into account. In this respect, HSMC(D) can be viewed as exact and the only approximation involved is due to insufficient MC(MD) sampling for calculating the TPs. The validity of HSMC has been established by applying it first to liquid argon, TIP3P water, self-avoiding walks (SAW), and polyglycine models, where the results for F were found to agree with those obtained by other methods. Subsequently, HSMD was applied to mobile loops of the enzymes porcine pancreatic alpha-amylase and acetylcholinesterase in explicit water, where the difference in F between the bound and free states of the loop was calculated. Currently, HSMD is being extended for calculating the absolute and relative free energies of ligand-enzyme binding. We describe the whole approach and discuss future directions.

Entropy and Free Energy of a Mobile Loop Based on the Crystal Structures of the Free and Bound Proteins.

A mobile loop changes its conformation from "open" (free enzyme) to "closed" upon ligand binding. The difference in the Helmholtz free energy, ΔF(loop) between these states sheds light on the mechanism of binding. With our "hypothetical scanning molecular dynamics" (HSMD-TI) method ΔF(loop) = F(free) - F(bound) where F(free) and F(bound) are calculated from two MD samples of the free and bound loop states; the contribution of water is obtained by a thermodynamic integration (TI) procedure. In previous work the free and bound loop structures were both attached to the same "template" which was "cut" from the crystal structure of the free protein. Our results for loop 287-290 of AcetylCholineEsterase agree with the experiment, ΔF(loop)~ -4 kcal/mol if the density of the TIP3P water molecules capping the loop is close to that of bulk water, i.e., N(water) = 140 - 180 waters in a sphere of a 18 Å radius. Here we calculate ΔF(loop) for the more realistic case, where two templates are "cut" from the crystal structures, 2dfp.pdb (bound) and 2ace.pdb (free), where N(water) = 40 - 160; this requires adding a computationally more demanding (second) TI procedure. While the results for N(water) ≤ 140 are computationally sound, ΔF(loop) is always positive (18 ± 2 kcal/mol for N(water) = 140). These (disagreeing) results are attributed to the large average B-factor, 41.6 of 2dfp (23.4 Å(2) for 2ace). While this conformational uncertainty is an inherent difficulty, the (unstable) results for N(water) = 160 suggest that it might be alleviated by applying different (initial) structural optimizations to each template.

Methods for calculating the entropy and free energy and their application to problems involving protein flexibility and ligand binding.

The Helmholtz free energy, F and the entropy, S are related thermodynamic quantities with a special importance in structural biology. We describe the difficulties in calculating these quantities and review recent methodological developments. Because protein flexibility is essential for function and ligand binding, we discuss the related problems involved in the definition, simulation, and free energy calculation of microstates (such as the alpha-helical region of a peptide). While the review is broad, a special emphasize is given to methods for calculating the absolute F (S), where our HSMC(D) method is described in some detail.

Absolute free energy and entropy of a mobile loop of the enzyme acetylcholinesterase.

The loop 287-290 (Ile, Phe, Arg, and Phe) of the protein acetylcholinesterase (AChE) changes its structure upon interaction of AChE with diisopropylphosphorofluoridate (DFP). Reversible dissociation measurements suggest that the free-energy (F) penalty for the loop displacement is DeltaF=Ffree-Fbound approximately -4 kcal/mol. Therefore, this loop has been the target of two studies by Olson's group for testing the efficiency of procedures for calculating F. In this paper, we test for the first time the performance of our "hypothetical scanning molecular dynamics" (HSMD) method and the validity of the related modeling for a loop with bulky side chains in explicit water. Thus, we consider only atoms of the protein that are the closest to the loop (they constitute the "template"), where the rest of the atoms are ignored. The template's atoms are fixed in the X-ray coordinates of the free protein, and the loop is capped with a sphere of TIP3P water molecules; also, the X-ray structure of the bound loop is attached to the free template. We carry out two separate MD simulations starting from the free and bound X-ray structures, where only the atoms of the loop and water are allowed to move while the template-water and template-loop (AMBER) interactions are considered. The absolute Ffree and Fbound (of the loop and water) are calculated from the corresponding trajectories. A main objective of this paper is to assess the reliability of this model, and for this several template sizes are studied capped with 80-220 water molecules. We find that consistent results for the free energy (which also agree with the experimental data above) require a template larger than a minimal size and a number of water molecules approximately equal to the experimental density of bulk water. For example, we obtain DeltaFtotal=DeltaFwater+DeltaFloop=-3.1+/-2.5 and -3.6+/-4 kcal/mol for a template consisting of 944 atoms and a sphere containing 160 and 180 waters, respectively. Our calculations demonstrate the important contribution of water to the total free energy. Namely, for water densities close to the experimental value, DeltaFwater is always negative leading thereby to a negative DeltaFtotal (while DeltaFloop is always positive). Also, the contribution of the water entropy TDeltaSwater to DeltaFtotal is significant. Various aspects related to the efficiency of HSMD are tested and improved, and plans for future studies are discussed.

The effect of loops on the structural organization of alpha-helical membrane proteins.

Loops connecting the transmembrane (TM) alpha-helices in membrane proteins are expected to affect the structural organization of the thereby connected helices and the helical bundles as a whole. This effect, which has been largely ignored previously, is studied here by analyzing the x-ray structures of 41 alpha-helical membrane proteins. First we define the loop flexibility ratio, R, and find that 53% of the loops are stretched, where a stretched loop constrains the distance between the two connected helices. The significance of this constraining effect is supported by experiments carried out with bacteriorhodopsin and rhodopsin, in which cutting or eliminating their (predominately stretched) loops has led to a decrease in protein stability, and for rhodopsin, in most cases, also to the destruction of the structure. We show that for nonstretched loops in the extramembranous regions, the fraction of hydrophobic residues is comparable to that for soluble proteins; furthermore (as is also the case for soluble proteins), the hydrophobic residues in these regions are preferentially buried. This is expected to lead to the compact structural organization of the loops, which is transferred to the TM helices, causing them to assemble. We argue that a soluble protein complexed with a membrane protein similarly promotes compactness; other properties of such complexes are also studied. We calculate complementary attractive interactions between helices, including hydrogen bonds and van der Waals interactions of sequential motifs, such as GXXXG. The relative and combined effects of all these factors on the association of the TM helices are discussed and protein structures with only a few of these factors are analyzed. Our study emphasizes the need for classifying membrane proteins into groups according to structural organization. This classification should be considered when procedures for structural analysis or prediction are developed and applied. Detailed analysis of each structure is provided at http://flan.blm.cs.cmu.edu/memloop/

Entropy and free energy of a mobile protein loop in explicit water.

Estimation of the energy from a given Boltzmann sample is straightforward since one just has to average the contribution of the individual configurations. On the other hand, calculation of the absolute entropy, S (hence the absolute free energy F) is difficult because it depends on the entire (unknown) ensemble. We have developed a new method called "the hypothetical scanning molecular dynamics" (HSMD) for calculating the absolute S from a given sample (generated by any simulation technique). In other words, S (like the energy) is "written" on the sample configurations, where HSMD provides a prescription of how to "read" it. In practice, each sample conformation, i, is reconstructed with transition probabilities, and their product leads to the probability of i, hence to the entropy. HSMD is an exact method where all interactions are considered, and the only approximation is due to insufficient sampling. In previous studies HSMD (and HS Monte CarloHSMC) has been extended systematically to systems of increasing complexity, where the most recent is the seven-residue mobile loop, 304-310 (Gly-His-Gly-Ala-Gly-Gly-Ser) of the enzyme porcine pancreatic alpha-amylase modeled by the AMBER force field and AMBER with the implicit solvation GB/SA (paper I, Cheluvaraja, S.; Meirovitch, H. J. Chem. Theory Comput. 2008, 4, 192). In the present paper we make a step further and extend HSMD to the same loop capped with TIP3P explicit water at 300 K. As in paper I, we are mainly interested in entropy and free energy differences between the free and bound microstates of the loop, which are obtained from two separate MD samples of these microstates. The contribution of the loop to S and F is calculated by HSMD and that of water by a particular thermodynamic integration procedure. As expected, the free microstate is more stable than the bound microstate by a total free energy difference, Ffree-Fbound=-4.8+/-1, as compared to -25.5 kcal/mol obtained with GB/SA. We find that relatively large systematic errors in the loop entropies, Sfree(loop) and Sbound(loop) are cancelled in their difference which is thus obtained efficiently and with high accuracy, i.e., with a statistical error of 0.1 kcal/mol. This cancellation, which has been observed in previous HSMD studies, is in accord with theoretical arguments given in paper I.

Stability of the Free and Bound Microstates of a Mobile Loop of α-Amylase Obtained from the Absolute Entropy and Free Energy.

The hypothetical scanning molecular dynamics (HSMD) method is a relatively new technique for calculating the absolute entropy, S, and free energy, F, from a given sample generated by any simulation procedure. Thus, each sample conformation, i, is reconstructed by calculating transition probabilities that their product leads to the probability of i, hence to the entropy. HSMD is an exact method where all interactions are considered, and the only approximation is due to insufficient sampling. In previous studies HSMD (and HS Monte Carlo - HSMC) has been applied very successfully to liquid argon, TIP3P water, self-avoiding walks, and peptides in a α-helix, extended, and hairpin microstates. In this paper HSMD is developed further as applied to the flexible 7-residue surface loop, 304-310 (Gly-His-Gly-Ala-Gly-Gly-Ser) of the enzyme porcine pancreatic α-amylase. We are mainly interested in entropy and free energy differences ΔS = Sfree - Sbound (and ΔF=Ffree-Fbound) between the free and bound microstates of the loop, which are obtained from two separate MD samples of these microstates without the need to carry out thermodynamic integration. As for peptides, we find that relatively large systematic errors in Sfree and Sbound (and Ffree and Fbound) are cancelled in ΔS (ΔF) which is thus obtained efficiently with high accuracy, i.e., with a statistical error of 0.1-0.2 kcal/mol (T=300 K) using the AMBER force field and AMBER with the implicit solvation GB/SA. We provide theoretical arguments in support of this cancellation, discuss in detail the problems involved in the computational definition of a microstate in conformational space, suggest potential ways for enhancing efficiency further, and describe the next development where explicit water will replace implicit solvation.

Recent developments in methodologies for calculating the entropy and free energy of biological systems by computer simulation.

The Helmholtz free energy, F, plays an important role in proteins because of their rugged potential energy surface, which is 'decorated' with a tremendous number of local wells (denoted microstates, m). F governs protein folding, whereas differences DeltaF(mn) determine the relative populations of microstates that are visited by a flexible cyclic peptide or a flexible protein segment (e.g. a surface loop). Recently developed methodologies for calculating DeltaF(mn) (and entropy differences, DeltaS(mn)) mainly use thermodynamic integration and calculation of the absolute F; interesting new approaches in these categories are the adaptive integration method and the hypothetical scanning molecular dynamics method, respectively.

Calculation of the entropy and free energy of peptides by molecular dynamics simulations using the hypothetical scanning molecular dynamics method.

Hypothetical scanning (HS) is a method for calculating the absolute entropy S and free energy F from a sample generated by any simulation technique. With this approach each sample configuration is reconstructed with the help of transition probabilities (TPs) and their product leads to the configuration's probability, hence to the entropy. Recently a new way for calculating the TPs by Monte Carlo (MC) simulations has been suggested, where all system interactions are taken into account. Therefore, this method--called HSMC--is in principle exact where the only approximation is due to insufficient sampling. HSMC has been applied very successfully to liquid argon, TIP3P water, self-avoiding walks on a lattice, and peptides. Because molecular dynamics (MD) is considered to be significantly more efficient than MC for a compact polymer chain, in this paper HSMC is extended to MD simulations as applied to peptides. Like before, we study decaglycine in vacuum but for the first time also a peptide with side chains, (Val)(2)(Gly)(6)(Val)(2). The transition from MC to MD requires implementing essential changes in the reconstruction process of HSMD. Results are calculated for three microstates, helix, extended, and hairpin. HSMD leads to very stable differences in entropy TDeltaS between these microstates with small errors of 0.1-0.2 kcal/mol (T=100 K) for a wide range of calculation parameters with extremely high efficiency. Various aspects of HSMD and plans for future work are discussed.

Free volume hypothetical scanning molecular dynamics method for the absolute free energy of liquids.

The hypothetical scanning (HS) method is a general approach for calculating the absolute entropy, S, and free energy, F, by analyzing Boltzmann samples obtained by Monte Carlo (MC) or molecular dynamics (MD) techniques. With HS applied to a fluid, each configuration i of the sample is reconstructed by gradually placing the molecules in their positions at i using transition probabilities (TPs). With our recent version of HS, called HSMC-EV, each TP is calculated from MC simulations, where the simulated particles are excluded from the volume reconstructed in previous steps. In this paper we remove the excluded volume (EV) restriction, replacing it by a "free volume" (FV) approach. For liquid argon, HSMC-FV leads to an improvement in efficiency over HSMC-EV by a factor of 2-3. Importantly, the FV treatment greatly simplifies the HS implementation for liquids, allowing a much more natural application of the method for MD simulations. Given the success and popularity of MD, the present development of the HSMD method for liquids is an important advancement for HS methodology. Results for the HSMD-FV approach presented here agree well with our HSMC and thermodynamic integration results. The efficiency of HSMD-FV is equivalent to HSMC-EV. The potential use of HSMC(MD)-FV in protein systems with explicit water is discussed.

Optimization of the GB/SA solvation model for predicting the structure of surface loops in proteins.

Implicit solvation models are commonly optimized with respect to experimental data or Poisson-Boltzmann (PB) results obtained for small molecules, where the force field is sometimes not considered. In previous studies, we have developed an optimization procedure for cyclic peptides and surface loops in proteins based on the entire system studied and the specific force field used. Thus, the loop has been modeled by the simplified solvation function E(tot) = E(FF) (epsilon = 2r) + Sigma(i) sigma(i)A(i), where E(FF) (epsilon = nr) is the AMBER force field energy with a distance-dependent dielectric function, epsilon = nr, A(i) is the solvent accessible surface area of atom i, and sigma(i) is its atomic solvation parameter. During the optimization process, the loop is free to move while the protein template is held fixed in its X-ray structure. To improve on the results of this model, in the present work we apply our optimization procedure to the physically more rigorous solvation model, the generalized Born with surface area (GB/SA) (together with the all-atom AMBER force field) as suggested by Still and co-workers (J. Phys. Chem. A 1997, 101, 3005). The six parameters of the GB/SA model, namely, P(1)-P(5) and the surface area parameter, sigma (programmed in the TINKER package) are reoptimized for a "training" group of nine loops, and a best-fit set is defined from the individual sets of optimized parameters. The best-fit set and Still's original set of parameters (where Lys, Arg, His, Glu, and Asp are charged or neutralized) were applied to the training group as well as to a "test" group of seven loops, and the energy gaps and the corresponding RMSD values were calculated. These GB/SA results based on the three sets of parameters have been found to be comparable; surprisingly, however, they are somewhat inferior (e.g, of larger energy gaps) to those obtained previously from the simplified model described above. We discuss recent results for loops obtained by other solvation models and potential directions for future studies.

An introduction to simulation and visualization of biological systems at multiple scales: a summer training program for interdisciplinary research.

Advances in biomedical research require a new generation of researchers having a strong background in both the life and physical sciences and a knowledge of computational, mathematical, and engineering tools for tackling biological problems. The NIH-NSF Bioengineering and Bioinformatics Summer Institute at the University of Pittsburgh (BBSI @ Pitt; www.ccbb.pitt.edu/bbsi) is a multi-institutional 10-week summer program hosted by the University of Pittsburgh, Duquesne University, the Pittsburgh Supercomputing Center, and Carnegie Mellon University, and is one of nine Institutes throughout the nation currently participating in the NIH-NSF program. Each BBSI focuses on a different area; the BBSI @ Pitt, entitled "Simulation and Computer Visualization of Biological Systems at Multiple Scales", focuses on computational and mathematical approaches to understanding the complex machinery of molecular-to-cellular systems at three levels, namely, molecular, subcellular (microphysiological), and cellular. We present here an overview of the BBSI @ Pitt, the objectives and focus of the program, and a description of the didactic training activities that distinguish it from other traditional summer research programs. Furthermore, we also report several challenges that have been identified in implementing such an interdisciplinary program that brings together students from diverse academic programs for a limited period of time. These challenges notwithstanding, presenting an integrative view of molecular-to-system analytical models has introduced these students to the field of computational biology and has allowed them to make an informed decision regarding their future career prospects.