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Mohammad A. Rezaei

Publications and source records attributed to Mohammad A. Rezaei.

7 recordsLinked to original sources

DeepAtom: A Framework for Protein-Ligand Binding Affinity Prediction

The cornerstone of computational drug design is the calculation of binding affinity between two biological counterparts, especially a chemical compound, i.e., a ligand, and a protein. Predicting the strength of protein-ligand binding with reasonable accuracy is critical for drug discovery. In this paper, we propose a data-driven framework named DeepAtom to accurately predict the protein-ligand binding affinity. With 3D Convolutional Neural Network (3D-CNN) architecture, DeepAtom could automatically extract binding related atomic interaction patterns from the voxelized complex structure. Compared with the other CNN based approaches, our light-weight model design effectively improves the model representational capacity, even with the limited available training data. With validation experiments on the PDBbind v.2016 benchmark and the independent Astex Diverse Set, we demonstrate that the less feature engineering dependent DeepAtom approach consistently outperforms the other state-of-the-art scoring methods. We also compile and propose a new benchmark dataset to further improve the model performances. With the new dataset as training input, DeepAtom achieves Pearson's R=0.83 and RMSE=1.23 pK units on the PDBbind v.2016 core set. The promising results demonstrate that DeepAtom models can be potentially adopted in computational drug development protocols such as molecular docking and virtual screening.

q-bio.BM↗

Green's function for chordal SLE curves

For a chordal SLE$_κ$ ($κ\in(0,8)$) curve in a domain $D$, the $n$-point Green's function valued at distinct points $z_1,\dots,z_n\in D$ is defined to be $$G(z_1,\dots,z_n)=\lim_{r_1,\dots,r_n\downarrow 0} \prod_{k=1}^n r_k^{d-2} \mathbb{P}[\mbox{dist}(γ,z_k)<r_k,1\le k\le n],$$ where $d=1+\fracκ{8}$ is the Hausdorff dimension of SLE$_κ$, provided that the limit converges. In this paper, we will show that such Green's functions exist for any finite number of points. Along the way we provide the rate of convergence and modulus of continuity for Green's functions as well. Finally, we give up-to-constant bounds for them.

math.PR↗

Higher moments of the natural parameterization for SLE curves

In this paper, we will show that the higher moments of the natural parametrization of SLE curves in any bounded domain in the upper half plane is finite. We prove this by estimating the probability that an SLE curve gets near n given points.

math.PR↗

Basic properties of the natural parametrization for the Schramm-Loewner evolution

The natural paramterization or length for the Schramm-Loewner evolution (SLEκ) is the candidate for the scaling limit of the length of discrete curves for κ< 8. We improve the proof of the existence of the parametrization and use this to establish some new results. In particular, we show that the natural parametrization is independent of domain and it is Hölder continuous with respect to the capacity parametrization. We also give up-to-constants bounds for the two-point Green's function. Although we do not prove the conjecture that the natural length is given by the appropriate Minkowski content, we do prove that the corresponding expectations converge.

math.PR↗