We introduce a derangement model of ligand-receptor binding that allows us to quantitatively frame the question "How can ligands seek out and bind to their optimal receptor sites in a sea of other competing ligands and suboptimal receptor sites?" To answer the question, we first derive a formula to count the number of partial generalized derangements in a list, thus extending the derangement result of Gillis and Even. We then compute the general partition function for the ligand-receptor system and derive the equilibrium expressions for the average number of bound ligands and the average number of optimally bound ligands. A visual model of squares assembling onto a grid allows us to easily identify fully optimal bound states. Equilibrium simulations of the system reveal its extremes to be one of two types, qualitatively distinguished by whether optimal ligand-receptor binding is the dominant form of binding at all temperatures and quantitatively distinguished by the relative values of two critical temperatures. One of those system types (termed "search-limited," as it was in previous work) does not exhibit kinetic traps and we thus infer that biomolecular systems where optimal ligand-receptor binding is functionally important are likely to be search-limited.
Fragment molecular orbital (FMO) calculations were performed in aqueous media which allowed us to obtain the interaction energy between the human estrogen receptor $α$ ligand-binding domain (ER) and the selected ligands (L): 17$β$-estradiol (E2), 17$α$-estradiol (17$α$-E2), estriol (E3), genistein (GNT), diethylstilbestrol (DES), bisphenol A (BPA), bisphenol AF (BPAF), hydroxychlor (HPTE) and methoxychlor (DMDT). These calculations were carried out on representative structures of L-ER complexes obtained from molecular dynamics simulations. The MP2/6-31G(d) L-ER FMO interaction energy in kcal/m…
Most widely used ligand docking methods assume a rigid protein structure. This leads to problems when the structure of the target protein deforms upon ligand binding. In particular, the ligand's true binding pose is often scored very unfavorably due to apparent clashes between ligand and protein atoms, which lead to extremely high values of the calculated van der Waals energy term. Traditionally, this problem has been addressed by explicitly searching for receptor conformations to account for the flexibility of the receptor in ligand binding. Here we present a deep learning model trained to ta…
The human neurotensin receptor 1 (NTSR1) is a G protein-coupled receptor. The receptor is activated by a small peptide ligand neurotensin. NTSR1 can be expressed in HEK cells by stable transfection. Previously we used the fluorescent protein markers mRuby3 or mNeonGreen fused to NTSR1 for EMCCD-based structured illumination microscopy (SIM) in living HEK cells. Ligand binding induced conformational changes in NTSR1 which triggered the intracellular signaling processes. Recent single-molecule studies revealed a dynamic monomer/dimer equilibrium of this receptor in artificial lipid bilayers. Her…
Eukaryotic cells transmit extracellular signal information to cellular interiors through the formation of a ternary complex made up of a ligand (or agonist), G-protein, and G-protein coupled receptor (GPCR). Previously formalized theories of ternary complex formation have mainly assumed that observable states of receptors can only take the form of monomers. Here, we propose a multiary complex model of GPCR signaling activations via the vector representation of various unobserved aggregated receptor states. Our results from model simulations imply that receptor aggregation processes can govern …
The estrogen receptor is a nuclear hormone receptor activated by the natural steroid hormone 17$β$-estradiol (E2). Fragment molecular orbital (FMO) calculations were performed which allowed us to obtain the interaction energy ($E_{int}$) between E2, 17$α$-estradiol (17$α$-E2) and the human estrogen receptor $α$ ligand-binding domain. In aqueous media the MP2/6-31G(d) $E_{int}$ was of -88.52 kcal/mol for E2 and -78.73 kcal/mol for 17$α$-E2. Attractive dispersion interactions were observed between ligands and all surrounding hydrophobic residues. Water molecules were found at the binding site an…
Data-driven Discovery of Biophysical T Cell Receptor Co-specificity Rules
Department of Physics, Princeton University, Princeton, NJ, USA（普林斯顿大学物理系）；Division of Infection and Immunity, University College London, London, UK（伦敦大学学院感染与免疫系）；Division of Medicine, University College London, London, UK（伦敦大学学院医学系）；Cancer Institute, University College London, London, UK（伦敦大学学院癌症研究所）；Institute for the Physics of Living Systems, University College London, London, UK（伦敦大学学院生命系统物理研究所）；Department of Computer Science, University College London, London, UK（伦敦大学学院计算机科学系）；Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA（普林斯顿大学整合基因组学研究所）；Department of Molecular Biology, Princeton University, Princeton, NJ, USA（普林斯顿大学分子生物学系）
Deep generative models have been applied with increasing success to the generation of two dimensional molecules as SMILES strings and molecular graphs. In this work we describe for the first time a deep generative model that can generate 3D molecular structures conditioned on a three-dimensional (3D) binding pocket. Using convolutional neural networks, we encode atomic density grids into separate receptor and ligand latent spaces. The ligand latent space is variational to support sampling of new molecules. A decoder network generates atomic densities of novel ligands conditioned on the recepto…
International Institute of Information Technology, Hyderabad（海得拉巴国际信息技术学院）
Protein-ligand complex structures have been utilised to design benchmark machine learning methods that perform important tasks related to drug design such as receptor binding site detection, small molecule docking and binding affinity prediction. However, these methods are usually trained on only ligand bound (or holo) conformations of the protein and therefore are not guaranteed to perform well when the protein structure is in its native unbound conformation (or apo), which is usually the conformation available for a newly identified receptor. A primary reason for this is that the local struc…
Implementation of the Tangent Sphere and Cutting Plane Methods in the Quantitative Determination of Ligand Binding Site Burial Depths in Proteins Using FORTRAN 77/90 Language
配体埋藏深度是蛋白质柔性的指标，因为结合配体所需的受体构象变化的程度通常直接随其埋藏深度而变化。在一篇配套论文中（Reyes，V.M. 2015年a），我们报告了切线球（TS）和切割平面（CP）方法-定量的互补方法，独立于蛋白质大小，蛋白质受体中配体埋葬的程度。在这份报告中，我们提出的结果，证明了一组FORTRAN 77和90源代码的有效性，用于实现两个相关的程序，以及精确的实施程序。特别是，我们在这里表明，TS和CP方法的理论模型蛋白质的球形网格点的形式的应用程序准确地描绘了TS和CP指数的行为，从这两种方法获得的预测参数。我们还表明，TS和CP方法对6种蛋白质受体的实施结果（Laskowski et al. 1996）与他们关于这些蛋白质中空腔大小的发现不一致。我们在这里介绍的六个FORTRAN程序是：find_molec_centr.f、tangent_sphere.f、find_CP_coeffs.f、CPM_Neg_Side.f、CPM_Pos_Side.f和CPM_Zero_Side. f。第一个程序计算蛋白质的分子几何质心（全局质心，GC）（TS的中心）的x、y和z坐标。其半径是GC和局部质心（LC）、结合配体的质心或其结合位点的一部分之间的距离。第二个程序计算TS内部、外部和上的蛋白质原子数。第三步确定CP方程的四个系数A、B、C和D，Ax + By + Cz + …
