We have developed a web server that implements two complementary methods to quantify the depth of ligand binding site (LBS) in protein-ligand complexes: the "secant plane" (SP) and "tangent sphere" (TS) methods. The protein molecular centroid (global centroid, GC), and the LBS centroid (local centroid, LC) are first determined. The SP is the plane passing through the LC and normal to the line passing through the LC and the GC. The "exterior side" of the SP is the side opposite GC. The TS is the sphere with center at GC and tangent to the SP at LC. The percentage of protein atoms inside the TS (TS index) and on the exterior side of the SP (SP index), are complementary measures of LBS depth. The SPi is directly proportional to LBS depth while the TSi is inversely proportional. We tested the two methods using a test set of 67 well-characterized protein-ligand structures (Laskowski, et al. 1996), as well as that of an artificial protein in the form of a grid of points in the overall shape of a sphere and in which LBS of any depth can be specified. Results from both the SP and TS methods agree well with reported data (ibid.), and results from the artificial case confirm that both methods are suitable measures of LBS depth. The web server may be used in two modes. In the "ligand mode", user inputs the protein PDB coordinates as well as those of the ligand. The "LBS mode" is the same as the former, except that the ligand coordinates are assumed to be unavailable; hence the user inputs what s/he believes to be the coordinates of the LBS amino acid residues. In both cases, the web server outputs the SP and TS indices. LBS depth is usually directly related to the amount of conformational change a protein undergoes upon ligand binding - ability to quantify it could allows meaningful comparison of protein flexibility and dynamics. The URL of our web server will be announced publicly in due course.
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…
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 numbe…
Alchemical Grid Dock (AlGDock) is open-source software designed to compute the binding potential of mean force (BPMF) - the binding free energy between a flexible ligand and a rigid receptor - for a small organic ligand and a biological macromolecule. Multiple BPMFs can be used to rigorously compute binding affinities between flexible partners. AlGDock uses replica exchange between thermodynamic states at different temperatures and receptor-ligand interaction strengths. Receptor-ligand interaction energies are represented by interpolating precomputed grids. Thermodynamic states are adaptively …
The human neurotensin receptor 1 (NTSR1) is a G protein-coupled receptor that can be expressed in HEK293T cells by stable transfection. Its ligand is a 13-amino-acid peptide that binds with nanomolar affinity from the extracellular side to NTSR1. Ligand binding induces conformational changes that trigger the intracellular signaling processes. Recent single-molecule studies revealed a dynamic monomer - dimer equilibrium of the receptor in vitro. Here we report on the oligomerization state of the human NTSR1 in the plasma membrane of HEK293T cells in vivo. We fused different fluorescent marker p…
The adhesion of cell membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. In this article, we review recent results from simulations and theory that lead to novel insights on how the binding equilibrium and kinetics of these proteins is affected by the membranes and by the membrane anchoring and molecular properties of the proteins. Simulations and theory both indicate that the binding equilibrium constant K2D and the on- and off-rate constants of anchored receptors and ligands in their 'two-dimensional' (2D) membrane environment strongly depend on the membra…
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…
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…
Pentameric ligand-gated ion channels (pLGICs) of the Cys-loop superfamily are important neuroreceptors that mediate fast synaptic transmission. They are activated by the binding of a neurotransmitter, but the details of this process are still not fully understood. As a prototypical pLGIC, here we choose the insect resistance to dieldrin (RDL) receptor, involved in the resistance to insecticides, and investigate the binding of the neurotransmitter GABA to its extracellular domain at the atomistic level. We achieve this by means of $μ$-sec funnel-metadynamics simulations, which efficiently enhan…
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 …
We study the binding of plant hormone IAA on its receptor TIR1 introducing a novel computational method that we call tomographic docking and that accounts for interactions occurring along the depth of the binding pocket. Our results suggest that selectivity is related to constraints that potential ligands encounter on their way from the surface of the protein to their final position at the pocket bottom. Tomographic docking helps develop specific hypotheses about ligand binding, distinguishing binders from non-binders, and suggests that binding is a three-step mechanism, consisting of engageme…
Estrogen receptors (ERs) are a group of proteins activated by 17$β$-estradiol. The endocrine-disrupting chemicals (EDCs) mimic estrogen action by bind directly to the ligand binding domain of ER. From this perspective, ER represent a good model for identifying and assessing the health risk of potential EDCs. This ability is best reflected by the ligand-ER binding energy. Multilayer fragment molecular orbital (MFMO) calculations were performed which allowed us to obtain the binding energy using a calculation scheme that considers the molecular interactions that occur on the following model syst…
We report the performance of our newly introduced Ensemble Docking with Enhanced sampling of pocket Shape (EDES) protocol coupled to a template-based algorithm to generate near-native ligand conformations in the 2019 iteration of the Grand Challenge organized by the D3R consortium. Using either AutoDock4.2 or HADDOCK2.2 docking programs (each software in two variants of the protocol) our method generated native-like poses among the top 5 submitted for evaluation for most of the 20 targets with similar performances. The protein selected for GC4 was the human beta-site amyloid precursor protein …
The progesterone receptor (PR) mediates progesterone regulation of female reproductive physiology, as well as gene transcription in non-reproductive tissues, such as brain, bone, lung and vasculature, in both women and men. An unusual property of progesterone is its high affinity for the mineralocorticoid receptor (MR), which regulates electrolyte transport in the kidney in humans and other terrestrial vertebrates. In humans, rats, alligators and frogs, progesterone antagonizes activation of the MR by aldosterone, the physiological mineralocorticoid in terrestrial vertebrates. In contrast, in …
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 + …
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）
According to implicit ligand theory, the standard binding free energy is an exponential average of the binding potential of mean force (BPMF), an exponential average of the interaction energy between the ligand apo ensemble and a rigid receptor. Here, we use the Fast Fourier Transform (FFT) to efficiently estimate BPMFs by calculating interaction energies as rigid ligand configurations from the apo ensemble are discretely translated across rigid receptor conformations. Results for standard binding free energies between T4 lysozyme and 141 small organic molecules are in good agreement with prev…
We present a new method that combines alchemical transformation with physical pathway to accurately and efficiently compute the absolute binding free energy of receptor-ligand complex. Currently, the double decoupling method (DDM) and the potential of mean force approach (PMF) methods are widely used to compute the absolute binding free energy of biomolecules. The DDM relies on alchemically decoupling the ligand from its environments, which can be computationally challenging for large ligands and charged ligands because of the large magnitude of the decoupling free energies involved. On the ot…
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…
Ligand diffusion through proteins is a fundamental process governing biological signaling and enzymatic catalysis. The complex topology of protein tunnels results in difficulties with computing ligand escape pathways by standard molecular dynamics (MD) simulations. Here, two novel methods for searching of ligand exit pathways and cavity exploration are proposed: memory random acceleration MD (mRAMD), and memetic algorithms (MA). In mRAMD, finding exit pathways is based on a non-Markovian biasing that is introduced to optimize the unbinding force. In MA, hybrid learning protocols are exploited …
