Modeling protein-induced configurational changes in DNA minicircles

A method is offered for obtaining minimum energy configurations of DNA minicircles constrained by one or more DNA-binding proteins. The minicircles are modeled as elastic rods, while the presence of bound protein is implied by rigidly fixing portions of these chains. The configurations of the geometrically constrained circular rods are sampled stochastically and optimized according to a simple elastic energy model of nicked DNA. The shapes of the minimum energy structures identified after a simulated annealing process are analyzed in terms of relative protein orientation and writhing number. The procedure is applied to minicircles 500 base pairs in length, bound to two evenly spaced DNA-wrapping proteins. The presence of histone octamers is suggested by rigidly fixing the two protein-bound portions of each minicircle as small superhelices similar in dimension to nucleosomal DNA. The folded minimum energy forms of sample chains with different degrees of protein wrapping are noteworthy in themselves in that they offer a new resolution to the well-known minichromosome linking number paradox and point to future minicircle simulations of possible import. © 1997 John Wiley & Sons, Inc.     

Sequence-dependent motions of DNA: a normal mode analysis at the base-pair level

Computer simulation of the dynamic structure of DNA can be carried out at various levels of resolution. Detailed high resolution information about the motions of DNA is typically collected for the atoms in a few turns of double helix. At low resolution, by contrast, the sequence-dependence features of DNA are usually neglected and molecules with thousands of base pairs are treated as ideal elastic rods. The present normal mode analysis of DNA in terms of six base-pair "step" parameters per chain residue addresses the dynamic structure of the double helix at intermediate resolution, i.e., the mesoscopic level of a few hundred base pairs. Sequence-dependent effects are incorporated into the calculations by taking advantage of "knowledge-based" harmonic energy functions deduced from the mean values and dispersion of the base-pair "step" parameters in high-resolution DNA crystal structures. Spatial arrangements sampled along the dominant low frequency modes have end-to-end distances comparable to those of exact polymer models which incorporate all possible chain configurations. The normal mode analysis accounts for the overall bending, i.e., persistence length, of the double helix and shows how known discrepancies in the measured twisting constants of long DNA molecules could originate in the deformability of neighboring base-pair steps. The calculations also reveal how the natural coupling of local conformational variables affects the global motions of DNA. Successful correspondence of the computed stretching modulus with experimental data requires that the DNA base pairs be inclined with respect to the direction of stretching, with chain extension effected by low energy transverse motions that preserve the strong van der Waals' attractions of neighboring base-pair planes. The calculations further show how one can "engineer" the macroscopic properties of DNA in terms of dimer deformability so that polymers which are intrinsically straight in the equilibrium state exhibit the mesoscopic bending anisotropy essential to DNA curvature and loop formation.     

Modeling chain folding in protein-constrained circular DNA.

An efficient method for sampling equilibrium configurations of DNA chains binding one or more DNA-bending proteins is presented. The technique is applied to obtain the tertiary structures of minimal bending energy for a selection of dinucleosomal minichromosomes that differ in degree of protein-DNA interaction, protein spacing along the DNA chain contour, and ring size. The protein-bound portions of the DNA chains are represented by tight, left-handed supercoils of fixed geometry. The protein-free regions are modeled individually as elastic rods. For each random spatial arrangement of the two nucleosomes assumed during a stochastic search for the global minimum, the paths of the flexible connecting DNA segments are determined through a numerical solution of the equations of equilibrium for torsionally relaxed elastic rods. The minimal energy forms reveal how protein binding and spacing and plasmid size differentially affect folding and offer new insights into experimental minichromosome systems.     

Effects of DNA sequence and conformation on nucleosome formation

A simple theoretical analysis of the free energy balance controlling nucleosome formation shows that the specific effects of different DNA sequences and/or conformations observed in vitro are mainly due to their different elastic properties. A calculation of the elastic free energy required to fold DNA on histone octamers yields quantitative results rationalizing the experimental findings provided that: (i) the average helical repeat of DNA on nucleosomes is greater than 10.2 bp per turn, and (ii) poly[dG.dC] adopts an A-type conformation.     

Flexibility of Acanthamoeba myosin rod minifilaments.

Previous electric birefringence experiments have shown that the actin-activated Mg2+-ATPase activity of Acanthamoeba myosin II correlates with the ability of minifilaments to cycle between flexible and stiff conformations. The cooperative transition between conformations was shown to depend on Mg2+ concentration, on ATP binding, and on the state of phosphorylation of three serines in the C-terminal end of the heavy chains. Since the junction between the heavy meromyosin (HMM) and light meromyosin (LMM) regions is expected to disrupt the alpha-helical coiled-coil structure of the rod, this region was anticipated to be the flexible site. We have now cloned and expressed the wild-type rod (residues 849-1509 of the full-length heavy chain) and rods mutated within the junction in order to test this. The sedimentation and electric birefringence properties of minifilaments formed by rods and by native myosin II are strikingly similar. In particular, the Mg2+-dependent flexible-to-stiff transitions of native myosin II and wild-type rod minifilaments are virtually superimposable. Mutations within the junction between the HMM and LMM regions of the rod modulate the ability of Mg2+ to stabilize the stiff conformation. Less Mg2+ is required to induce minifilament stiffening if proline-1244 is replaced with alanine. Deleting the entire junction region (25 amino acids) results in a even greater decrease in the Mg2+ concentration necessary for the transition. The HMM-LMM junction does indeed seem to act as a Mg2+-dependent flexible hinge.     

Vibrations-determined properties of green fluorescent protein

The physicochemical characteristics of the green fluorescent protein (GFP), including the thermodynamic properties (entropy, enthalpy, Gibbs' free energy, heat capacity), normal mode vibrations, and atomic fluctuations, were investigated. The Gaussian 03 computational chemistry program was employed for normal mode analysis using the AMBER force field. The thermodynamic parameters and atomic fluctuations were then calculated from the vibrational eigenvalues (frequencies) and eigenvectors. The regions of highest rigidity were shown to be the beta-sheet barrel with the central alpha-helix, which bears the chromophore. The most flexible parts of the GFP molecule were the outlying loops that cover the top and bottom of the beta-barrel. This way, the balance between rigidity and flexibility is maintained, which is the optimal relationship for protein stability in terms of Gibbs' free energy. This dual-schemed structure satisfies the requirements for GFP function. In this sense, the structure of GFP resembles a nanoscale drum: a stiff cylinder with flexible vibrating end(s).     

Investigating energy‐based pool structure selection in the structure ensemble modeling with experimental distance constraints: The example from a multidomain protein Pub1

The structural variations of multidomain proteins with flexible parts mediate many biological processes, and a structure ensemble can be determined by selecting a weighted combination of representative structures from a simulated structure pool, producing the best fit to experimental constraints such as interatomic distance. In this study, a hybrid structure‐based and physics‐based atomistic force field with an efficient sampling strategy is adopted to simulate a model di‐domain protein against experimental paramagnetic relaxation enhancement (PRE) data that correspond to distance constraints. The molecular dynamics simulations produce a wide range of conformations depicted on a protein energy landscape. Subsequently, a conformational ensemble recovered with low‐energy structures and the minimum‐size restraint is identified in good agreement with experimental PRE rates, and the result is also supported by chemical shift perturbations and small‐angle X‐ray scattering data. It is illustrated that the regularizations of energy and ensemble‐size prevent an arbitrary interpretation of protein conformations. Moreover, energy is found to serve as a critical control to refine the structure pool and prevent data overfitting, because the absence of energy regularization exposes ensemble construction to the noise from high‐energy structures and causes a more ambiguous representation of protein conformations. Finally, we perform structure‐ensemble optimizations with a topology‐based structure pool, to enhance the understanding on the ensemble results from different sources of pool candidates.     

A Novel Constraint for Thermodynamically Designing DNA Sequences

Biotechnological and biomolecular advances have introduced novel uses for DNA such as DNA computing, storage, and encryption. For these applications, DNA sequence design requires maximal desired (and minimal undesired) hybridizations, which are the product of a single new DNA strand from 2 single DNA strands. Here, we propose a novel constraint to design DNA sequences based on thermodynamic properties. Existing constraints for DNA design are based on the Hamming distance, a constraint that does not address the thermodynamic properties of the DNA sequence. Using a unique, improved genetic algorithm, we designed DNA sequence sets which satisfy different distance constraints and employ a free energy gap based on a minimum free energy (MFE) to gauge DNA sequences based on set thermodynamic properties. When compared to the best constraints of the Hamming distance, our method yielded better thermodynamic qualities. We then used our improved genetic algorithm to obtain lower-bound DNA sequence sets. Here, we discuss the effects of novel constraint parameters on the free energy gap.     

Force-extension formula for the worm-like chain model from a variational principle

Stiff polymers, such as single-stranded DNA, unstructured RNA and cellulose, are all basically extremely long rods with relatively short repeating monomers. The simplest model for describing such stiff polymers is called the freely jointed chain model, which treats a molecule as a chain of perfectly rigid subunits of orientationally independent statistical segments, joined together by perfectly flexible hinges. A more realistic model that incorporates the entropic elasticity of a molecule, called the worm-like chain model, has been proposed by assuming that each monomer resists the bending force. Some force-extension formulae for the worm-like chain model have been previously found in terms of interpolation and numerical solutions resulting from statistical mechanics. In this paper, however, we adopt a variational principle to seek the minimum energy configuration of a stretched molecule by incorporating all the possible orientations of each monomer under thermal equilibrium, i.e., constant temperature. We determine a force-extension formula for the worm-like chain model analytically. We find that our formula suggests new terms such as the free energy and the cut-off force of a molecule, which define a clear transition from the entropic regime to the enthalpic regime and the fracture of the molecule, respectively. In addition, we predict two possible phase changes for a stretched molecule, i.e., from a super-helix to a soliton and then from a soliton to a vertical twisted line. We show theoretically that a molecule must undergo at least one phase change before it is fully stretched into its total contour length. This new formula is used to fit recent experimental data and shows a good agreement with some current literature that uses a statistical approach. Finally, an instability analysis is adopted to investigate the sensitivity of the new formula subject to small changes in temperature.     

Modeling protein conformational changes by iterative fitting of distance constraints using reoriented normal modes

Recently we have developed a normal-modes-based algorithm that predicts the direction of protein conformational changes given the initial state crystal structure together with a small number of pairwise distance constraints for the end state. Here we significantly extend this method to accurately model both the direction and amplitude of protein conformational changes. The new protocol implements a multisteps search in the conformational space that is driven by iteratively minimizing the error of fitting the given distance constraints and simultaneously enforcing the restraint of low elastic energy. At each step, an incremental structural displacement is computed as a linear combination of the lowest 10 normal modes derived from an elastic network model, whose eigenvectors are reorientated to correct for the distortions caused by the structural displacements in the previous steps. We test this method on a list of 16 pairs of protein structures for which relatively large conformational changes are observed (root mean square deviation >3 angstroms), using up to 10 pairwise distance constraints selected by a fluctuation analysis of the initial state structures. This method has achieved a near-optimal performance in almost all cases, and in many cases the final structural models lie within root mean square deviation of 1 approximately 2 angstroms from the native end state structures.     

Stereochemical effects of non-ionic methylphosphonates on nucleotide conformations.

The preferred conformations of deoxyribo and ribonucleoside 3'-methylphosphonates are analysed by minimizing the conformational energy as a function of all the major parameters including the sugar ring for both the S- and R-isomers. The results show that neither the substitution nor the nature of the diastereomer affects significantly the preferred conformations compared to the naturally occurring nucleoside 3'-phosphates. The preferred range of C3'-O3' bond torsions or the phase angles of pseudorotation (P) of the sugar are unaffected. The chiral substitution on the phosphate always adopts a conformation distal to the secondary C3' carbon atom in the minimum energy conformational state. Further, it introduces certain restrictions on the preferred range of P-O3' torsions depending on the methylphosphonate configuration. Methylphosphonate, especially the S-isomer, renders the normal gauche- range of P-O3' bond torsions responsible for the stacked helical duplexes to be energetically unfavourable besides introducing a high energy barrier between trans and gauche conformations. Therefore it is suggested that duplexes with S-methylphosphonate may favour extended phosphodiester conformations. These factors explain the observed lower melting temperature as well as the downfield shifts in the 31P signals in duplexes containing the S-isomer.     

The role of shape in determining molecular motions

We examined the role of molecular shape in determining the patterns of low-frequency deformational motions of biological macromolecules. The low-frequency subspace of eigenvectors in normal mode analysis was found to be robustly similar upon randomization of the Hessian matrix elements as long as the structure of the matrix is maintained, which indicates that the global shape of molecules plays a more dominant role in determining the highly anisotropic low-frequency motions than the absolute values of stiffness and directionality of local interactions. The results provided a quantitative foundation for the validity of elastic normal mode analysis.     

Normal-modes-based prediction of protein conformational changes guided by distance constraints

Based on the elastic network model, we develop a novel method that predicts the conformational change of a protein complex given its initial-state crystal structure together with a small set of pairwise distance constraints for the end state. The predicted conformational change, which is a linear combination of multiple low-frequency normal modes that are solved from the elastic network model, is computed as a response displacement induced by a perturbation to the system Hamiltonian that incorporates the given distance constraints. For a list of test cases, we find that the computed response displacement overlaps significantly with the measured conformational changes, when only a handful of pairwise constraints are used (相似文献   

Modulating DNA configuration by interfacial traction: an elastic rod model to characterize DNA folding and unfolding

As a continuum model of DNA, a thin elastic rod subjected to interfacial interactions is used to investigate the equilibrium configuration of DNA in intracellular solution. The interfacial traction between the rod and the solution environment is derived in detail. Kirchhoff’s theory of elastic rods is used to analyze the equilibrium configuration of a DNA segment under the action of the interfacial traction. The influences of the interfacial energy factor and bending stiffness on the toroidal spool formation of the DNA segment are discussed. The results show that the equilibrium configuration of DNA is mainly determined by competition between the interfacial energy and elastic strain energy of the DNA itself, and the interfacial traction is one of the forces that drives DNA folding and unfolding.     

Dissimilar kinetic behavior of electrically manipulated single- and double-stranded DNA tethered to a gold surface

We report on the electrical manipulation of single- and double-stranded oligodeoxynucleotides that are end tethered to gold surfaces in electrolyte solution. The response to alternating repulsive and attractive electric surface fields is studied by time-resolved fluorescence measurements, revealing markedly distinct dynamics for the flexible single-stranded and stiff double-stranded DNA, respectively. Hydrodynamic simulations rationalize this finding and disclose two different kinetic mechanisms: stiff polymers undergo rotation around the anchoring pivot point; flexible polymers, on the other hand, are pulled onto the attracting surface segment by segment.     

Refinement of the thrombin-bound structure of a hirudin peptide by a restrained electrostatically driven Monte Carlo method.

Energy refinement of the structure of a linear peptide, hirudin56-65, bound to thrombin was carried out using a conformational search method in combination with restrained minimization. Five conformations originated from nmr data and distance geometry calculations having a similar global folding pattern but quite different backbone conformations were used as the starting structures. As a result of this approach, a series of low-energy conformations compatible with a set of upper and lower bounds of interproton distances determined from transferred nuclear Overhauser effects were found. A comparison among the lowest energy conformations of each run showed that the combination of energy refinement plus distance constraints led to a very well-defined structure for both the backbone and the side chains of the last 7 residues of the polypeptide. Furthermore, the low-energy conformations generated with this technique contain a segment of 3(10)-helix involving the last 5 residues at the COOH terminal end.     

Synthesis of poly(phenylacetylene)s containing chiral phenylethyl carbamate residues as coated-type CSPs with high solvent tolerability

Two novel helical poly(phenylacetylene) derivatives containing chiral phenylethyl carbamate residues in the end of each side chain ( PPA-S and PPA-R ) were synthesized by polymerization of the corresponding phenylacetylene monomers using Rh(nbd)BPh₄ as a catalyst in DMF. The enantioseparation properties of the polymers were evaluated as coated-type chiral stationary phases (CSPs) for high-performance liquid chromatography (HPLC). Under the same chromatographic conditions, PPA-S and PPA-R showed different enantioseparation properties, indicating that the different interactions between the analytes and the polymers, which result from the different chiral phenylethyl carbamate groups in the end of each side chains. Racemates 1 , 7 , and 8 could be better resolved on PPA-S , while racemate 6 was separated on PPA-R more efficiently. In addition, the coated-type CSPs showed good solvent tolerability and could work without any damage by introducing the polar solvents, such as CHCl₃ and THF, in eluent. Moreover, some racemates could be better resolved on these coated-type CSPs with the addition of THF to the eluent.     

Structural basis of hierarchical multiple substates of a protein. III: Side chain and main chain local conformations

An analysis is carried out of differences in the minimum energy conformations obtained in the previous paper by energy minimization starting from conformations sampled by a Monte Carlo simulation of conformational fluctuations in the native state of a globular protein, bovine pancreatic trypsin inhibitor. Main conformational differences in each pair of energy minima are found usually localized in several side chains and in a few local main chain segments. Such side chains and local main chain segments are found to take a few distinct local conformations in the minimum energy conformations. Energy minimum conformations can thus be described in terms of combinations of these multiple local conformations.