Path-integral method for predicting relative binding affinities of protein-ligand complexes

Solving Fokker-Planck equation using deep learning

The probability density function of stochastic differential equations is governed by the Fokker-Planck (FP) equation. A novel machine learning method is developed to solve the general FP equations based on deep neural networks. The proposed algorithm does not require any interpolation and coordinate transformation, which is different from the traditional numerical methods. The main novelty of this paper is that penalty factors are introduced to overcome the local optimization for the deep learning approach, and the corresponding setting rules are given. Meanwhile, we consider a normalization condition as a supervision condition to effectively avoid that the trial solution is zero. Several numerical examples are presented to illustrate performances of the proposed algorithm, including one-, two-, and three-dimensional systems. All the results suggest that the deep learning is quite feasible and effective to calculate the FP equation. Furthermore, influences of the number of hidden layers, the penalty factors, and the optimization algorithm are discussed in detail. These results indicate that the performances of the machine learning technique can be improved through constructing the neural networks appropriately.

Structure-kinetic relationship analysis of the therapeutic complement inhibitor compstatin

Compstatin is a 13-residue peptide that inhibits activation of the complement system by binding to the central component C3 and its fragments C3b and C3c. A combination of theoretical and experimental approaches has previously allowed us to develop analogs of the original compstatin peptide with up to 264-fold higher activity; one of these analogs is now in clinical trials for the treatment of age-related macular degeneration (AMD). Here we used functional assays, surface plasmon resonance (SPR), and isothermal titration calorimetry (ITC) to assess the effect of modifications at three key residues (Trp-4, Asp-6, Ala-9) on the affinity and activity of compstatin and its analogs, and we correlated our findings to the recently reported co-crystal structure of compstatin and C3c. The K(D) values for the panel of tested analogs ranged from 10(-6) to 10(-8) M. These differences in binding affinity could be attributed mainly to differences in dissociation rather than association rates, with a >4-fold range in k(on) values (2-10 x 10(5) M(-1) s(-1)) and a k(off) variation of >35-fold (1-37 x 10(-2) s(-1)) being observed. The stability of the C3b-compstatin complex seemed to be highly dependent on hydrophobic effects at position 4, and even small changes at position 6 resulted in a loss of complex formation. Induction of a beta-turn shift by an A9P modification resulted in a more favorable entropy but a loss of binding specificity and stability. The results obtained by the three methods utilized here were highly correlated with regard to the activity/affinity of the analogs. Thus, our analyses have identified essential structural features of compstatin and provided important information to support the development of analogs with improved efficacy.