Predicting protein-protein interfaces from a three-dimensional structure is a key task of computational structural proteomics. In contrast to geometrically distinct small molecule binding sites, protein-protein interface are notoriously difficult to predict. We generated a large nonredundant data set of 1494 true protein-protein interfaces using biological symmetry annotation where necessary. The data set was carefully analyzed and a Support Vector Machine was trained on a combination of a new robust evolutionary conservation signal with the local surface properties to predict protein-protein interfaces. Fivefold cross validation verifies the high sensitivity and selectivity of the model. As much as 97% of the predicted patches had an overlap with the true interface patch while only 22% of the surface residues were included in an average predicted patch. The model allowed the identification of potential new interfaces and the correction of mislabeled oligomeric states.

Calogero-Moser models can be generalised for all of the finite reflection groups. These include models based on non-crystallographic root systems, that is the root systems of the finite reflection groups, H 3 , H 4 , and the dihedral group I 2 (m), besides the well-known ones based on crystallographic root systems, namely those associated with Lie algebras. Universal Lax pair operators for all of the generalised Calogero-Moser models and for any choices of the potentials are constructed as linear combinations of the reflection operators. The consistency conditions are reduced to functional equations for the coefficient functions of the reflection operators in the Lax pair. There are only four types of such functional equations corresponding to the two-dimensional sub-root systems, A 2 , B 2 , G 2 , and I 2 (m). The root type and the minimal type Lax pairs, derived in our previous papers, are given as the simplest representations. The spectral parameter dependence plays an important role in the Lax pair operators, which bear a strong resemblance to the Dunkl operators, a powerful tool for solving quantum Calogero-Moser models.A root system ∆ of rank r is a set of vectors in R r which is invariant under reflections in the hyperplane perpendicular to each vector in ∆. In other words,Dual roots are defined by α ∨ = 2α/|α| 2 , in terms of which3)The orbit of β ∈ ∆ is the set of root vectors resulting from the action of the reflections on it {s α (β), α ∈ ∆}. The set of positive roots ∆ + may be defined in terms of a vector V ∈ R r , with V · α = 0, ∀α ∈ ∆, as those roots α ∈ ∆ such that α · V > 0. A unique set of r simple roots Π is defined such that they span the root space and the coefficients {a j } in β = r j=1 a j α j for β ∈ ∆ + , {α j ∈ Π, j = 1, · · · , r} are all positive.The set of reflections {s α , α ∈ ∆} generates a group, known as a Coxeter group. It is generated by products of s α with α ∈ Π subject to the relationsThe set of positive integers m(α, β) uniquely specify the Coxeter group with m(α, α) = 1, ∀α ∈ Π. For example, for two-dimensional crystallographic root systems A 2 , B 2 , and G 2 , the integer m(α, β) is 3, 4, and 6, respectively. Thus s α s β is a twodimensional rotation by an angle ±2π/3, ±π/2, and ±π/3, respectively. This fact will be used in later sections. We consider here only those Coxeter groups with a finite number of roots in Euclidean space, called the finite reflection groups. The root systems for finite reflection groups may be divided into two types: crystallographic and non-crystallographic root systems. Crystallographic root systems satisfy the additional condition5) These root systems are associated with simple Lie algebras: {A r , r ≥ 1}, {B r , r ≥ 2}, {C r , r ≥ 2}, {D r , r ≥ 4}, E 6 , E 7 , E 8 , F 4 , and G 2 and {BC r , r ≥ 2}. The Coxeter groups for these root systems are called Weyl groups. The remaining noncrystallographic root systems are H 3 , H 4 , and the dihedral group of order 2m, {I 2 (m), m ≥ 4}. Weyl chambers are defined as the open subsets of R r that re...

We have developed a method to both predict the geometry and the relative stability of point mutants that may be used for arbitrary mutations. The geometry optimization procedure was first tested on a new benchmark of 2141 ordered pairs of X-ray crystal structures of proteins that differ by a single point mutation, the largest data set to date. An empirical energy function, which includes terms representing the energy contributions of the folded and denatured proteins and uses the predicted mutant side chain conformation, was fit to a training set consisting of half of a diverse set of 1816 experimental stability values for single point mutations in 81 different proteins. The data included a substantial number of small to large residue mutations not considered by previous prediction studies. After removing 22 (approximately 2%) outliers, the stability calculation gave a standard deviation of 1.08 kcal/mol with a correlation coefficient of 0.82. The prediction method was then tested on the remaining half of the experimental data, giving a standard deviation of 1.10 kcal/mol and covariance of 0.66 for 97% of the test set. A regression fit of the energy function to a subset of 137 mutants, for which both native and mutant structures were available, gave a prediction error comparable to that for the complete training set with predicted side chain conformations. We found that about half of the variation is due to conformation-independent residue contributions. Finally, a fit to the experimental stability data using these residue parameters exclusively suggests guidelines for improving protein stability in the absence of detailed structure information.

We present a fast continuum method for the calculation of solvation free energies. It is based on a continuum electrostatics model with MMFF94 atomic charges combined with a nonelectrostatic term, which is a linear function of the solvent-accessible surface area. The model's parameters have been optimized using sets of 410, 382, and 2116 molecules for gas-water, gas-hexadecane, and water-octanol transfer, respectively. These are the largest, most diverse sets of molecules used to date for a similar solvation model. The model's predictive power was verified by using 90% of the molecule set for training and the remainder as a test set. The average test set errors differed by only about 1% from the average training set error, thus demonstrating the transferability of the parameters. The root-mean-square error for gas-water, gas-hexadecane, and wateroctanol transfer are 0.53, 0.38, and 0.58 log P units, respectively. Because the solvation calculation takes on average only about 0.34 s per molecule on a 700 MHz Pentium CPU and contains atom types for essentially all drug molecules, it is suitable for real-time calculations of the ADME properties of molecules in virtual ligand screening libraries.

It is shown that the Calogero-Moser models based on all root systems of the finite reflection groups (both the crystallographic and non-crystallographic cases) with the rational (with/without a harmonic confining potential), trigonometric and hyperbolic potentials can be simply supersymmetrised in terms of superpotentials. There is a universal formula for the supersymmetric ground state wavefunction. Since the bosonic part of each supersymmetric model is the usual quantum Calogero-Moser model, this gives a universal formula for its ground state wavefunction and energy, which is determined purely algebraically. Quantum Lax pair operators and conserved quantities for all the above Calogero-Moser models are established.