Theory and simulation of diffusion-influenced, stochastically gated ligand binding to buried sites

We consider the diffusion-influenced rate coefficient of ligand binding to a site located in a deep pocket on a protein; the binding pocket is flexible and can reorganize in response to ligand entrance. We extend to this flexible protein-ligand system a formalism developed previously [A. M. Berezhkovskii, A, Szabo, and H.-X. Zhou, J. Chem. Phys. 135, 075103 (2011)] for breaking the ligand-binding problem into an exterior problem and an interior problem. Conformational fluctuations of a bottleneck or a lid and the binding site are modeled as stochastic gating. We present analytical and Brownian dynamics simulation results for the case of a cylindrical pocket containing a binding site at the bottom. Induced switch, whereby the conformation of the protein adapts to the incoming ligand, leads to considerable rate enhancement.     

NMR spectroscopy techniques for screening and identifying ligand binding to protein receptors

Binding events of ligands to receptors are the key for an understanding of biological processes. Gaining insight into protein-protein and protein-ligand interactions in solution has recently become possible on an atomic level by new NMR spectroscopic techniques. These experiments identify binding events either by looking at the resonance signals of the ligand or the protein. Ideally, both techniques together deliver a complete picture of ligand binding to a receptor. The approaches discussed in this review allow screening of compound libraries as well as a detailed identification of the groups involved in the binding events. Also, characterization of the binding strength and kinetics is possible, competitive binding as well as allosteric effects can be identified, and it has even been possible to identify ligand binding to intact viruses and membrane-bound proteins.     

Rate kernel theory for pseudo-first-order kinetics of diffusion-influenced reactions and application to fluorescence quenching kinetics

Theoretical foundation of rate kernel equation approaches for diffusion-influenced chemical reactions is presented and applied to explain the kinetics of fluorescence quenching reactions. A many-body master equation is constructed by introducing stochastic terms, which characterize the rates of chemical reactions, into the many-body Smoluchowski equation. A Langevin-type of memory equation for the density fields of reactants evolving under the influence of time-independent perturbation is derived. This equation should be useful in predicting the time evolution of reactant concentrations approaching the steady state attained by the perturbation as well as the steady-state concentrations. The dynamics of fluctuation occurring in equilibrium state can be predicted by the memory equation by turning the perturbation off and consequently may be useful in obtaining the linear response to a time-dependent perturbation. It is found that unimolecular decay processes including the time-independent perturbation can be incorporated into bimolecular reaction kinetics as a Laplace transform variable. As a result, a theory for bimolecular reactions along with the unimolecular process turned off is sufficient to predict overall reaction kinetics including the effects of unimolecular reactions and perturbation. As the present formulation is applied to steady-state kinetics of fluorescence quenching reactions, the exact relation between fluorophore concentrations and the intensity of excitation light is derived.     

Multiple-step ligand injection affinity capillary electrophoresis for determining binding constants of ligands to receptors

This work demonstrates the use of multiple-step ligand injection affinity capillary electrophoresis (ACE) using two model systems: vancomycin from Streptomyces orientalis and carbonic anhydrase B (CAB, EC 4.2.1.1). In this technique a sample plug of receptor and non-interacting standards is injected by pressure and electrophoresed in a buffer containing a given concentration of ligand. The sequence is repeated for all concentrations of ligand generating a single electropherogram containing a series of individual sample plugs superimposed on environments of buffer containing increasing concentrations of ligand. Analysis of the change in the relative migration time ratio, RMTR, relative to the non-interacting standards, as a function of the concentration of the ligand, yields a value for the binding constant. A competitive assay using the technique is also demonstrated using neutral ligands for CAB. These values agree well with those estimated using other binding and ACE techniques. Data demonstrating the quantitative potential of this method are presented.     

Kinetics of ligand binding to membrane receptors from equilibrium fluctuation analysis of single binding events

Equilibrium fluctuation analysis of single binding events has been used to extract binding kinetics of ligand interactions with cell-membrane bound receptors. Time-dependent total internal reflection fluorescence (TIRF) imaging was used to extract residence-time statistics of fluorescently stained liposomes derived directly from cell membranes upon their binding to surface-immobilized antibody fragments. The dissociation rate constants for two pharmaceutical relevant antibodies directed against different B-cell expressed membrane proteins was clearly discriminated, and the affinity of the interaction could be determined by inhibiting the interaction with increasing concentrations of soluble antibodies. The single-molecule sensitivity made the analysis possible without overexpressed membrane proteins, which makes the assay attractive in early drug-screening applications.     

Development of a constant surface pressure penetration langmuir balance based on axisymmetric drop shape analysis

A new constant pressure pendant-drop penetration surface balance has been developed combining a pendant-drop surface balance, a rapid-subphase-exchange technique, and a fuzzy logic control algorithm. Beside the determination of insoluble monolayer compression-expansion isotherms, it allows performance of noninvasive kinetic studies of the adsorption of surfactants added to the new subphase onto the free surface and of the adsorption/penetration/reaction of the former onto/into/with surface layers, respectively. The interfacial pressure pi is a fundamental parameter in these studies: by working at constant pi one controls the height of the energy barrier to adsorption/penetration and can select different regimes and steps of the adsorption/penetration process. In our device a solution drop is formed at the tip of a coaxial double capillary, connected to a double microinjector. Drop profiles are extracted from digital drop micrographs and fitted to the equation of capillarity, yielding pi, the drop volume V, and the interfacial area A. pi is varied changing V (and hence A) with the microinjector. Control is based on a case-adaptable modulated fuzzy-logic PID algorithm able to maintain constant pi (or A) under a wide range of experimental conditions. The drop subphase liquid can be exchanged quantitatively by the coaxial capillaries. The adsorption/penetration/reaction kinetics at constant pi are then studied monitoring A(t), i.e., determining the relative area change necessary at each instant to compensate the pressure variation due to the interaction of the surfactant in the subsurface with the surface layer. A fully Windows-integrated program manages the whole setup. Examples of experimental protein adsorption and monolayer penetration kinetics are presented.     

Viscosity contribution of an arbitrary shape rigid aggregate to a dilute suspension

The study of rheological response of solid suspensions is essential in understanding the relationships governing their kinematics and dynamics. However the study is complicated mainly by the complex interplay between suspension rheology and hydrodynamic behavior of the suspended solids, which for most of the practically occurring situations have complex and arbitrary shapes, and exact equations accounting for their hydrodynamic contribution are not available. For this reason, using a recently developed methodology capable of computing the average rigid body resistance matrix of arbitrary shaped clusters made of uniform sized spheres, Brownian dynamic simulations under shear conditions are performed for clusters with different geometries with the objective of estimating their intrinsic viscosity. The population of clusters chosen encompassed a broad range of morphologies, such as fractals with a wide range of masses and fractal dimension values, dense clusters with spherical and spheroidal aspect ratios, similar to those produced during coagulation experiments of colloidal suspensions. It was found that fractal clusters with low fractal dimensions and spheroidal clusters have sufficient structural anisotropies to show deviations from Einstein's relationship, and display a moderate shear thinning behavior, as well as a non-negligible linear viscoelasticity. On the other hand, clusters with high fractal dimensions tend to behave progressively more like spheres as their fractal dimension increases. We also found that the intrinsic viscosity of all clusters, independent of their morphology, can be quantitatively predicted by means of an equivalent ellipsoid model, in which clusters are modeled as ellipsoids with the same principal moments of inertia.     

Langevin dynamics for rigid bodies of arbitrary shape

We present an algorithm for carrying out Langevin dynamics simulations on complex rigid bodies by incorporating the hydrodynamic resistance tensors for arbitrary shapes into an advanced rotational integration scheme. The integrator gives quantitative agreement with both analytic and approximate hydrodynamic theories for a number of model rigid bodies and works well at reproducing the solute dynamical properties (diffusion constants and orientational relaxation times) obtained from explicitly solvated simulations.     

Cooperativity during binding of a ligand to a multidentate oligomer

A matrix method to describe the equilibrium binding of a ligand by a multidentate oligomer with a system of binding centers differing in the affinity for the binding ligand has been proposed. The example of a complexation process simulating the formation of a complex between an oligonucleotide and zinc phthalocyanine ZnPc is considered. With the use of the proposed method, diagrams of the relative contents of different forms of DNA-ligand complexes have been constructed and analyzed. It is shown that the cooperativity of complexation has a considerable effect on the equilibrium of the ligand with the system of nonequivalent centers of binding. The experimental data on changes in the intensity of luminescence in the course of binding between zinc tetrakis(diisopropylguanidinio)phthalocyanine and a DNA molecule with the nucleotide sequence GTTA(GAGTTA)4GG have been analyzed.     

Approximate expression for interaction of a two-parallel-plane double layer at constant surface potential and constant surface charge

A fast convergent formula for the interactional energy between two parallel plates at constant surface potential and constant surface charge is derived by a simple method of the series expansion, and the numerical result of only the first five terms of the series is excellent for the dimensionless surface potential of colloidal particle y(0)< or =4.     

Subtype selectivity and flexibility of ionotropic glutamate receptors upon antagonist ligand binding

The binding modes of a set of known ionotropic glutamate receptor antagonist-ligands have been studied using homology modeling, molecular docking, molecular dynamics (MD) simulations and ab initio quantum mechanical calculations. The core structure of the studied ligands is the decahydroisoquinoline ring, which has a carboxylic acid group at position three and different negatively-charged substituents (R) at position six. The binding affinities of these molecules have been reported earlier. From the current study, the carboxylate group of the decahydroisoquinoline ring hydrogen bonds with Arg485, the amino group with Pro478 and Thr480, and the negatively charged substituent R interacts with the positively charged N-terminus of helix-F. The subtype selectivity of these ligands seems to be strongly dependent on the amino acid at position 650 (GluR2: leucine, GluR5: valine), which affects the conformation of the ligand and ligand-receptor interactions, but depends considerably on the size of the R-group of the ligand. In addition, the MD simulations also revealed that the relative positions of the S1 and S2 domains can alter significantly showing different "closure" and "rotational movements" depending on the antagonist-ligand that is bound. Accordingly, molecular docking of antagonist ligands into static crystal structures cannot sufficiently explain ligand binding and subtype selectivity.     

Direct linkage of thrombin to its cell surface receptors in different cell types

When 125I-thrombin was incubated with foreskin fibroblasts, cervical carcinoma cells or fibrosarcoma cells of human origin, or with secondary chick embryo cells or Chinese hamster lung cells, it became directly linked to its cell surface receptors. The thrombin-receptor complex (TH-R) was derived exclusively from a pool of 125I-thrombin that had become specifically bound to the cell surface. The linkage was probably covalent, since the complex was resistant to boiling in sodium dodecyl sulfate and 2-mercaptoethanol. Raising the pH to 12 disrupted TH-R, but did not affect a similar complex between epidermal growth factor and its receptor, suggesting that the linkage of these mitogens to their receptors was different. Mild trypsin treatment removed the ability of cells to form TH-R; however, after a 24-h incubation in serum-free medium, trypsin-treated cells recovered the capacity to form TH-R, suggesting that TH-R resulted from interaction of 125I-thrombin with a cellular rather than a serum component. The mitogenic response of cells to thrombin was inversely related to the fraction of specifically bound 125I-thrombin represented by TH-R. The role of TH-R in mitogenesis may be clarified in future studies by obtaining clones of Chinese hamster lung cells that vary in their capacities to form TH-R and to respond to the mitogenic action of thrombin.     

Enhanced ligand affinity for receptors in which components of the binding site are independently mobile

Using calmodulin antagonism as a model, it is demonstrated that, under circumstances in which binding sites are motionally independent, it is possible to create bifunctional ligands that bind with significant affinity enhancement over their monofunctional counterparts. Suitable head groups were identified by using a semiquantitative screen of monofunctional tryptophan analogs. Two bifunctional ligands, which contained two copies of the highest-affinity head group tethered by rigid linkers, were synthesized. The bifunctional ligands bound to calmodulin with a stoichiometry of 1:1 and with an affinity enhancement over their monofunctional counterparts; the latter bound with a stoichiometry of 2:1 ligand:protein. A lower limit to the effective concentrations of the domains of calmodulin relative to each other (0.2-2 mM) was determined. A comparable effective concentration was achieved for bifunctional ligands based on higher-affinity naphthalene sulphonamide derivatives.     

AFM imaging of ligand binding to platelet integrin alphaIIbbeta3 receptors reconstituted into planar lipid bilayers

The platelet integrin alphaIIbbeta3 plays a key role in platelet adhesion, activation, and aggregation at the subendothelium and at protein-coated synthetic biomaterials. In this study, interactions between alphaIIbbeta3 and both protein and peptide ligands for the receptor were imaged under physiological conditions by high-resolution atomic force microscopy (AFM). To directly image the ligand-receptor interactions, alphaIIbbeta3 receptors were reconstituted into a supported lipid bilayer formed on a mica surface in the AFM fluid cell assembly and subsequently activated with Mn2+. Fibrinogen, the natural protein ligand for the integrin, as well as a nanogold-labeled peptide ligand (an RGD-containing heptamer) were infused into the AFM fluid cell, incubated with the reconstituted and activated receptors, and imaged under buffer. Height images illustrating topographical features showed the integrin reconstituted in the bilayer. Fibrinogen molecules binding to the receptors were easily observed in the height images, with fibrinogen showing its characteristic trinodular structure and occasionally bridging integrin receptors. Fibrinogen was observed to bind to integrins at the D-domain consistent with the location of the gamma-chain dodecapeptide, while fibrinogen bridging integrins bound to receptors on opposite sides of the protein consistent with a 2-fold axis of symmetry. Peptide ligands were not visible in height images; however, phase images that map the mechanical properties detected the nanogold labels and demonstrated the presence of peptide ligands bound to the receptors. The results demonstrate the ability of this high-resolution microscopy technique to directly visualize single ligand/receptor interactions in a dynamic and physiologically relevant environment, and establish a framework for future fundamental studies of single protein/receptor interactions during normal pathological processes as well as biomaterial surface-induced thrombosis.     

Effects of depolarizing agents and Na+-channel inhibitors on ligand binding to muscarinic receptors from rat cerebral cortex

In a vesicle preparation from rat cerebral cortex, carbachol recognizes a high-affinity and a low-affinity muscarinic agonist binding site. A number of agents, including veratridine (10 microM), gramicidin (10 microM) and valinomycin (10 microM), which depolarize the vesicles also appear to block the high-affinity muscarinic agonist binding site. Lowering [Na+] (from 137 to 80 mM) or raising [K+] (from 5 to 50 mM) produced effects similar to those of the depolarizing agents. Agents such as tetrodotoxin (1 microM), which block the Na+-channel, also appear to block the high-affinity agonist binding site or to convert it into a low-affinity agonist binding form.     

Communication: translational Brownian motion for particles of arbitrary shape

A single Brownian particle of arbitrary shape is considered. The time-dependent translational mean square displacement W(t) of a reference point at this particle is evaluated from the Smoluchowski equation. It is shown that at times larger than the characteristic time scale of the rotational Brownian relaxation, the slope of W(t) becomes independent of the choice of a reference point. Moreover, it is proved that in the long-time limit, the slope of W(t) is determined uniquely by the trace of the translational-translational mobility matrix μ(tt) evaluated with respect to the hydrodynamic center of mobility. The result is applicable to dynamic light scattering measurements, which indeed are performed in the long-time limit.     

Assessment of free energy predictors for ligand binding to a methyllysine histone code reader

Methyllysine histone code readers constitute a new promising group of potential drug targets. For instance, L3MBTL1, a malignant brain tumor (MBT) protein, selectively binds mono- and di-methyllysine epigenetic marks (KMe, KMe(2) ) that eventually results in the negative regulation of multiple genes through the E2F/Rb oncogenic pathway. There is a pressing need in potent and selective small-molecule probes that would enable further target validation and might become therapeutic leads. Such an endeavor would require efficient tools to assess the free energy of protein-ligand binding. However, due to an unparalleled function of the MBT binding pocket (i.e., selective binding to KMe/KMe(2) ) and because of its distinctive structure representing a small aromatic "cage," an accurate assessment of its binding affinity to a ligand appears to be a challenging task. Here, we report a comparative analysis of computationally affordable affinity predictors applied to a set of seven small-molecule ligands interacting with L3MBTL1. The analysis deals with novel ligands and targets, but applies widespread computational approaches and intuitive comparison metrics that makes this study compatible with and incremental to earlier large scale accounts on the efficiency of affinity predictors. Ultimately, this study has revealed three top performers, far ahead of the other techniques, including two scoring functions, PMF04 and PLP, along with a simulation-based method MM-PB/SA. We discuss why some methods may perform better than others on this target class, the limits of their application, as well as how the efficiency of the most CPU-demanding techniques could be optimized.     

Quantitative surface field analysis: learning causal models to predict ligand binding affinity and pose

We introduce the QuanSA method for inducing physically meaningful field-based models of ligand binding pockets based on structure-activity data alone. The method is closely related to the QMOD approach, substituting a learned scoring field for a pocket constructed of molecular fragments. The problem of mutual ligand alignment is addressed in a general way, and optimal model parameters and ligand poses are identified through multiple-instance machine learning. We provide algorithmic details along with performance results on sixteen structure-activity data sets covering many pharmaceutically relevant targets. In particular, we show how models initially induced from small data sets can extrapolatively identify potent new ligands with novel underlying scaffolds with very high specificity. Further, we show that combining predictions from QuanSA models with those from physics-based simulation approaches is synergistic. QuanSA predictions yield binding affinities, explicit estimates of ligand strain, associated ligand pose families, and estimates of structural novelty and confidence. The method is applicable for fine-grained lead optimization as well as potent new lead identification.