Contribution of changes in translational, rotational, and vibrational degrees of freedom to the energy of complex formation of aromatic ligands with DNA

A method for calculation and analysis of the contribution of changes in translational, rotational, and vibrational degrees of freedom to the energy of complex formation of aromatic compounds with DNA duplex has been developed. The results of calculations of the thermodynamic parameters (ΔG, ΔH, ΔS) indicate that changes in the translational and rotational degrees of freedom destabilize, and changes in the vibrational degree of freedom stabilize the complexes, the energy contribution from the movements under consideration being predominantly of entropic character. It is shown that the energy components of changes in translational, rotational, and vibrational degrees of freedom are in the main comparable with the experimentally determined thermodynamic parameters, which requires consideration of these components in the energy analysis of complex formation of aromatic molecules with DNA. It has been found that the total contribution of changes in translational, rotational, and vibrational degrees of freedom to the Gibbs energy of complexing of aromatic molecules with DNA can be assumed to be on the average the same for different ligands and equal to 8.2 kcal/mol.     

Direct estimation of entropy loss due to reduced translational and rotational motions upon molecular binding

The entropic cost due to the loss of translational and rotational (T-R) degree of freedom upon binding has been well recognized for several decades. Tightly bound ligands have higher entropic costs than loosely bound ligands. Quantifying the ligand's residual T-R motions after binding, however, is not an easy task. We describe an approach that uses a reduced Hessian matrix to estimate the contributions due to translational and rotational degrees of freedom to entropy change upon molecular binding. The calculations use a harmonic model for the bound state but only include the T-R degrees of freedom. This approximation significantly speeds up entropy calculations because only 6 x 6 matrices need to be treated, which makes it easier to be used in computer-aided drug design for studying many ligands. The methodological connection with other methods is discussed as well. We tested this approximation by applying it to study the binding of ATP, peptide inhibitor (PKI), and several bound water molecules to protein kinase A (PKA). These ligands span a wide range in size. The model gave reasonable estimates of the residual T-R entropy of bound ligands or water molecules. The residual T-R entropy demonstrated a wide range of values, e.g., 4 to 16 cal/K.mol for the bound water molecules of PKA.     

Conformational entropy limits the transition from nucleation to elongation in amyloid aggregation

The formation of β-sheet-rich amyloid fibrils in Alzheimer’s disease and other neurodegenerative disorders is limited by a slow nucleation event. To understand the initial formation of β-sheets from disordered peptides, we used all-atom simulations to parameterize a lattice model that treats each amino acid as a binary variable with β- and non-β-sheet states. We show that translational and conformational entropy give the nascent β-sheet an anisotropic surface tension that can be used to describe the nucleus with 2D classical nucleation theory. Since translational entropy depends on concentration, the aspect ratio of the critical β-sheet changes with protein concentration. Our model explains the transition from the nucleation phase to elongation as the point where the β-sheet core becomes large enough to overcome the conformational entropy cost to straighten the terminal molecule. At this point the β-strands in the nucleus spontaneously elongate, which results in a larger binding surface to capture new molecules. These results suggest that nucleation is relatively insensitive to sequence differences in coaggregation experiments because the nucleus only involves a small portion of the peptide.     

Association entropy in adsorption processes

The association of two species to form a bound complex, e.g., the binding of a ligand to a protein or the adsorption of a peptide on a lipid membrane, involves an entropy loss, reflecting the conversion of free translational and rotational degrees of freedom into bound motions. Previous theoretical estimates of the standard entropy change in bimolecular binding processes, DeltaS(o), have been derived from the root-mean-square fluctuations in protein crystals, suggesting DeltaS(o) approximately -50 e.u., i.e., TDeltaS degrees approximately -25 kT = -15 kcal/mol. In this work we focus on adsorption, rather than binding processes. We first present a simple statistical-thermodynamic scheme for calculating the adsorption entropy, including its resolution into translational and rotational contributions, using the known distance-orientation dependent binding (adsorption) potential. We then utilize this scheme to calculate the free energy of interaction and entropy of pentalysine adsorption onto a lipid membrane, obtaining TDeltaS(o) approximately -1.7 kT approximately -1.3 kcal/mol. Most of this entropy change is due to the conversion of one free translation into a bound motion, the rest arising from the confinement of two rotational degrees of freedom. The smaller entropy loss in adsorption compared to binding processes arises partly because a smaller number of degrees of freedom become restricted, but mainly due to the fact that the binding potential is much "softer."     

Rotational motions of myosin heads in myofibril studied by phosphorescence anisotropy decay measurements

We studied the rotational Brownian motions of myosin heads, of which the sulfhydryl group was selectively labeled with the triplet probe 5-eosinylmaleimide, in myofibril by using flash-induced phosphorescence anisotropy decay measurements. The anisotropy decay curve under relaxing conditions consisted of a fast (submicrosecond) and a slow (a few microseconds) component and a small constant part as in the synthetic myosin filaments in solution. The decay curves could be analyzed by assuming that a head part, i.e. subfragment 1 (S1), wobbles in the first cone and a part connecting S1 and the tail of a myosin molecule of which the length is shorter than subfragment 2 (S2) wobbles in the second cone (a double-cone model); the semiangles of the former and the latter cones were about 30 degrees and 50 degrees, respectively. The rotational freedom of myosin heads was only slightly restricted by the limited space of the filament lattice in myofibrils. Under rigor conditions, no motion of myosin heads was observed in the 10-microseconds time scale.     

Distance-constrained molecular docking by simulated annealing

An optimized method based on the principle of simulated annealing is presented for determining the relative position and orientation of interacting molecules. The spatial relationships of these molecules are described by intermolecular distance constraints between specific pairs of atoms, such as found in hydrogen bonds or from experimentally determined data. The method makes use of a random walk through six rotational and translational degrees of freedom where the constituent molecules are treated as rigid bodies. Van der Waals repulsions are used only to define a lower bound on distances between constrained atom pairs within the docking procedure. A cost function comprised of purely geometric constraints is optimized via simulated annealing, in order to search for the best orientation and position of the two molecules. Our docking procedure is applied to eight serine proteinase complexes from the Brookhaven Protein Data Bank. For each simulation 100 computations were performed. A typical docking computation requires only a few seconds of CPU time on a VAXserver 3500. The influence of the number of constraints on the final docked positions was studied. The sensitivity of the docking procedure to a ligand structure which is not well defined is also addressed. Possible applications of this method include using approximate distances incorporating complete energy functions.     

Fluorescence anisotropy decay studies upon hemoglobin A and its subunits

Fluorescent conjugates of hemoglobin A, its isolated β-chain, and the apo-derivative of the β-chain have been prepared in which the β-93 sulfhydryl was conjugated with 1,5-AEDANS. Radiationless enery transfer to the heme group results in a major decrease in fluorescence intensity and decay time. Measurements of the time decay of fluorescence anisotropy, employing single-photon counting, indicate that the apparent rotational correlation time is, in each case, substantially reduced from the value expected for a rigid molecule of the same molecular weight. This observation raises the possibility that internal degrees of rotational freedom exist.     

Kinetics of nanochain formation in a simplified model of amelogenin biomacromolecules

We show that the kinetics of nanochain formation of amelogenin molecules is well described by a combination of translational and rotational diffusion of a simplified anisotropic bipolar model consisting of hydrophobic spherical colloid particles and a point charge located on each particle surface. The colloid particles interact via a standard depletion attraction whereas the point charges interact through a screened Coulomb repulsion. We study the kinetics via a Brownian dynamics simulation of both translational and rotational motions and show that the anisotropy brought in by the charge dramatically affects the kinetic pathway of cluster formation and our simple model captures the main features of the experimental observations.     

2D fast rotational matching for image processing of biophysical data

In 3D single particle reconstruction, which involves the translational and rotational matching of a large number of electron microscopy (EM) images, the algorithmic performance is largely dependent on the efficiency and accuracy of the underlying 2D image alignment kernel. We present a novel fast rotational matching kernel for 2D images (FRM2D) that significantly reduces the cost of this alignment. The alignment problem is formulated using one translational and two rotational degrees of freedom. This allows us to take advantage of fast Fourier transforms (FFTs) in rotational space to accelerate the search of the two angular parameters, while the remaining translational parameter is explored, within a limited range, by exhaustive search. Since there are no boundary effects in FFTs of cyclic angular variables, we avoid the expensive zero padding associated with Fourier transforms in linear space. To verify the robustness of our method, efficiency and accuracy tests were carried out over a range of noise levels in realistic simulations of EM images. Performance tests against two standard alignment methods, resampling to polar coordinates and self-correlation, demonstrate that FRM2D compares very favorably to the traditional methods. FRM2D exhibits a comparable or higher robustness against noise and a significant gain in efficiency that depends on the fineness of the angular sampling and linear search range.     

Separation of translational and rotational contributions in solution studies using fluorescence photobleaching recovery

Although fluorescence photobleaching recovery (FPR) experiments are usually interpreted in terms of the translational motions of a fluorescently labeled species, rotational motions can also modulate recovery through the cosine-squared laws for dipolar absorption and emission processes. In a complex interacting system, translational and rotational contributions may both be simultaneously present. We show how these contributions can be separated in solution studies using an FPR setup in which (a) the linear polarization of the low-intensity observation beam and the high-intensity photobleaching pulse can be varied independently, and (b) all emitted fluorescent photons are counted equally. The fluorescence recovery signal obtained with the observation beam polarized at the magic angle, 54.7 degrees, from the bleach polarization direction is independent of label orientation, whereas the anisotropy function formed from a combination of parallel and perpendicular polarizations isolates the orientational recovery. The anisotropy function is identical to that in fluorescence correlation spectroscopy and, for rigid-body rotational diffusion, can be expressed as a sum of five exponential terms.     

Protein-protein docking in CAPRI using ATTRACT to account for global and local flexibility

A reduced protein model combined with a systematic docking approach has been employed to predict protein-protein complex structures in CAPRI rounds 6-11. The docking approach termed ATTRACT is based on energy minimization in translational and rotational degrees of freedom of one protein with respect to the second protein starting from many thousand initial protein partner placements. It also allows for approximate inclusion of global flexibility of protein partners during systematic docking by conformational relaxation of the partner proteins in precalculated soft collective backbone degrees of freedom. We have submitted models for six targets, achieved acceptable docking solutions for two targets, and predicted >20% correct contacts for five targets. Possible improvements of the docking approach in particular at the scoring and refinement steps are discussed.     

Crystallographic analysis of the thermal motion of the inclusion complex of cyclomaltoheptaose (beta-cyclodextrin) with hexamethylenetetramine

The crystal structure of the inclusion complex of cyclomaltoheptaose (beta-cyclodextrin) with hexamethylenetetramine was determined at temperatures of 123, 173, 223, and 293 K. The rigid-body motion of the host and guest molecules was evaluated by means of the TLS method that represents the molecular motion in terms of translation, libration, and screw motion. In increasing the temperature from 123 to 293 K, the amplitude of the rigid body vibration of the host molecule was increased from 1.0 to 1.3 degrees in the rotational motion and from 0.16 to 0.17 A in the translational motion. The cyclomaltoheptaose molecule has the flexibility in seven alpha-(1-->4)-linkages, and each glucose unit was in the rotational vibration around an axis through two glycosidic oxygen atoms. As a result, the rigid-body parameters of cyclomaltoheptaose were considered to be overestimated because of including the contribution from the local motion of glucose units. In contrast, for the guest molecule having no structural flexibility, the TLS analysis demonstrated that the atomic thermal vibration was mostly derived from the rigid body motion. The rotational amplitude of hexamethylenetetramine was changed from 5.2 to 6.6 degrees in increasing the temperature from 123 to 293 K, while the change of the translational amplitude was from 0.20 to 0.23 A. The translational motion of the guest molecule was hindered by the inside wall of the host cavity. The molecular motion was characterized by the rotational vibration around the axis through two nitrogen atoms that were involved in the hydrogen-bond formation.     

Lattices for ab initio protein structure prediction

In the study of the protein folding problem with ab initio methods, the protein backbone can be built on some periodic lattices. Any vertex of these lattices can be occupied by a "ball," which can represent the mass center of an amino acid in a simplified coarse-grained model of the protein. The backbone, at a coarse-grained level, can be constituted of a No Reverse Self Avoiding Walk, which cannot intersect itself and cannot go back on itself. There is still much debate between those who use lattices to simplify the study of the protein folding problem and those preferring to work by using an off-lattice approach. Lattices can help to identify the protein tertiary structure in a computational less-expensive way, than off-lattice approaches that have to consider a potentially infinite number of possible structures. However, the use of a lattice, constituted of insufficiently accurate direction vectors, constrains the predictive ability of the model. The aim of this study is to perform a systematic screening of 7 known classic and 11 newly proposed lattices in terms of predictive power. The crystal structures of 42 different proteins (14 mainly alpha helical, 14 mainly beta sheet and 14 mixed structure proteins) were compared to the most accurate simulated models for each lattice. This strategy defines a scale of fitness for all the analyzed lattices and demonstrates that an increase in the coordination number and in the degrees of freedom is necessary but not sufficient to reach the best result. Instead, the introduction of a good set of direction vectors, as developed and tested in this study, strongly increases the lattice performance.     

Rotational dynamics of surface probes in lipid vesicles

Translational and rotational diffusion of fluorescent molecules on the surface of small biological systems such as vesicles, proteins and micelles depolarize the fluorescence. A recent study has treated the case of the translational dynamics of surface probes (M.M.G. Krishna, R. Das, N. Periasamy and R. Nityananda, J. Chem. Phys., 112 (2000) 8502-8514) using Monte Carlo and theoretical methods. Here we extend the application of the methodologies to apply the case of rotational dynamics of surface probes. The corresponding fluorescence anisotropy decays were obtained using the Monte Carlo simulation methods for the two cases: surface probes undergoing rotational dynamics on a plane and on a sphere. The results were consistent with the theoretical equations which show that Monte Carlo methods can be used to simulate the surface diffusion problems. The anisotropy decay for the rotational diffusion of a molecule on a planar surface is single exponential and the residual anisotropy is zero. However, residual anisotropy is finite for the case of rotational diffusion on a sphere because of the spatial averaging of the anisotropy function. The rotational correlation time in both the cases is (4Drot)(-1) with Drot being the rotational diffusion coefficient. Rotational dynamics of a surface bound dye in a single giant liposome and in sonicated vesicles were studied and the results were explained according to the theoretical equations. A fast component of fluorescence depolarization was also observed for sonicated vesicles which was interpreted as wobbling-in-cylinder dynamics of the surface-bound dye.     

How dinoflagellates swim

Dinoflagellates possess two flagella; usually these are directed perpendicular to one another constituting a transversal flagellum and a longitudinal, trailing flagellum, respectively. The transversal flagellum causes the cell to rotate around its length axis. The trailing flagellum is responsible for the translation of the cell; due to its asymmetric insertion it also causes a rotation of the cell around an axis perpendicular to the longitudinal axis. Together, these two rotational components result in a helical swimming path. Cells can vary the two rotational components independently as well as the translational velocity. With these three degrees of freedom, cells can vary the parameters of their helical swimming paths for steering. Dinoflagellates use this mechanism for orientation in chemical concentration gradients (“helical klinotaxis”).     

Contribution of translational and rotational motions to molecular association in aqueous solution

Much uncertainty and controversy exist regarding the estimation of the enthalpy, entropy, and free energy of overall translational and rotational motions of solute molecules in aqueous solutions, quantities that are crucial to the understanding of molecular association/recognition processes and structure-based drug design. A critique of the literature on this topic is given that leads to a classification of the various views. The major stumbling block to experimentally determining the translational/rotational enthalpy and entropy is the elimination of vibrational perturbations from the measured effects. A solution to this problem, based on a combination of energy equi-partition and enthalpy-entropy compensation, is proposed and subjected to verification. This method is then applied to analyze experimental data on the dissociation/unfolding of dimeric proteins. For one translational/rotational unit at 1 M standard state in aqueous solution, the results for enthalpy (H degrees (tr)), entropy (S degrees (tr)), and free energy (G degrees (tr)) are H (degrees) (tr) = 4.5 +/- 1.5RT, S (degrees) (tr) = 5 +/- 4R, and G (degrees) (tr) = 0 +/- 5RT. Therefore, the overall translational and rotational motions make negligible contribution to binding affinity (free energy) in aqueous solutions at 1 M standard state.     

Reorientational dynamics of enzymes adsorbed on quartz: a temperature-dependent time-resolved TIRF anisotropy study

The preservation of enzyme activity and protein binding capacity upon protein adsorption at solid interfaces is important for biotechnological and medical applications. Because these properties are partly related to the protein flexibility and mobility, we have studied the internal dynamics and the whole-body reorientational rates of two enzymes, staphylococcal nuclease (SNase) and hen egg white lysozyme, over the temperature range of 20-80 degrees C when the proteins are adsorbed at the silica/water interface and, for comparison, when they are dissolved in buffer. The data were obtained using a combination of two experimental techniques, total internal reflection fluorescence spectroscopy and time-resolved fluorescence anisotropy measurements in the frequency domain, with the protein Trp residues as intrinsic fluorescence probes. It has been found that the internal dynamics and the whole-body rotation of SNase and lysozyme are markedly reduced upon adsorption over large temperature ranges. At elevated temperatures, both protein molecules appear completely immobilized and the fractional amplitudes for the whole-body rotation, which are related to the order parameter for the local rotational freedom of the Trp residues, remain constant and do not approach zero. This behavior indicates that the angular range of the Trp reorientation within the adsorbed proteins is largely restricted even at high temperatures, in contrast to that of the dissolved proteins. The results of this study thus provide a deeper understanding of protein activity at solid surfaces.     

A coarse-grained force field for Protein-RNA docking

The awareness of important biological role played by functional, non coding (nc) RNA has grown tremendously in recent years. To perform their tasks, ncRNA molecules typically unite with protein partners, forming ribonucleoprotein complexes. Structural insight into their architectures can be greatly supplemented by computational docking techniques, as they provide means for the integration and refinement of experimental data that is often limited to fragments of larger assemblies or represents multiple levels of spatial resolution. Here, we present a coarse-grained force field for protein-RNA docking, implemented within the framework of the ATTRACT program. Complex structure prediction is based on energy minimization in rotational and translational degrees of freedom of binding partners, with possible extension to include structural flexibility. The coarse-grained representation allows for fast and efficient systematic docking search without any prior knowledge about complex geometry.