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.     

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.     

The elastic rod model for DNA and its application to the tertiary structure of DNA minicircles in mononucleosomes.

Explicit solutions to the equations of equilibrium in the theory of the elastic rod model for DNA are employed to develop a procedure for finding the configuration that minimizes the elastic energy of a minicircle in a mononucleosome with specified values of the minicircle size N in base pairs, the extent w of wrapping of DNA about the histone core particle, the helical repeat h(0)b of the bound DNA, and the linking number Lk of the minicircle. The procedure permits a determination of the set Y(N, w, h(0)b) of integral values of Lk for which the minimum energy configuration does not involve self-contact, and graphs of writhe versus w are presented for such values of Lk. For the range of N of interest here, 330 < N < 370, the set Y(N, w, h(0)b) is of primary importance: when Lk is not in Y(N, w, h(0)b), the configurations compatible with Lk have elastic energies high enough to preclude the occurrence of an observable concentration of topoisomer Lk in an equilibrium distribution of topoisomers. Equilibrium distributions of Lk, calculated by setting differences in the free energy of the extranucleosomal loop equal to differences in equilibrium elastic energy, are found to be very close to Gaussian when computed under the assumption that w is fixed, but far from Gaussian when it is assumed that w fluctuates between two values. The theoretical results given suggest a method by which one may calculate DNA-histone binding energies from measured equilibrium distributions of Lk.     

Looping charged elastic rods: applications to protein-induced DNA loop formation

We analyze looping of thin charged elastic filaments under applied torques and end forces, using the solution of linear elasticity theory equations. In application to DNA, we account for its polyelectrolyte character and charge renormalization, calculating electrostatic energies stored in the loops. We argue that the standard theory of electrostatic persistence is only valid when the loop’s radius of curvature and close-contact distance are much larger than the Debye screening length. We predict that larger twist rates are required to trigger looping of charged rods as compared with neutral ones. We then analyze loop shapes formed on charged filaments of finite length, mimicking DNA looping by proteins with two DNA-binding domains. We find optimal loop shapes at different salt amounts, minimizing the sum of DNA elastic, DNA electrostatic, and protein elastic energies. We implement a simple model where intercharge repulsions do not affect the loop shape directly but can choose the energy-optimized shape from the allowed loop types. At low salt concentrations more open loops are favored due to enhanced repulsion of DNA charges, consistent with the results of computer simulations on formation of DNA loops by lac repressor. Then, we model the precise geometry of DNA binding by the lac tetramer and explore loop shapes, varying the confined DNA length and protein opening angle. The characteristics of complexes obtained, such as the total loop energy, stretching forces required to maintain its shape, and the reduction of electrostatic energy with increment of salt, are in good agreement with the outcomes of more elaborate numerical calculations for lac-repressor-induced DNA looping.     

Conformational analysis of stiff chiral polymers with end-constraints

We present a Lie-group-theoretic method for the kinematic and dynamic analysis of stiff chiral polymers with end constraints. The first is to determine the minimum energy conformations of stiff polymers with end constraints and the second is to perform normal mode analysis based on the determined minimum energy conformations. In this paper, we use concepts from the theory of Lie groups and principles of variational calculus to model such polymers as inextensible or extensible chiral elastic rods with coupling between stiffnesses. This method is general enough to include any stiffness and chirality parameters in the context of elastic filament models with the quadratic elastic potential energy function. As an application of this formulation, the analysis of DNA conformations is discussed. We demonstrate our method with examples of DNA conformations in which topological properties such as writhe, twist and linking number are calculated from the results of the proposed method. Given these minimum energy conformations, we describe how to perform the normal mode analysis. The results presented here build both on recent experimental work in which DNA mechanical properties have been measured and theoretical work in which the mechanics of non-chiral elastic rods has been studied.     

Bacterial protein HU dictates the morphology of DNA condensates produced by crowding agents and polyamines

Controlling the size and shape of DNA condensates is important in vivo and for the improvement of nonviral gene delivery. Here, we demonstrate that the morphology of DNA condensates, formed under a variety of conditions, is shifted completely from toroids to rods if the bacterial protein HU is present during condensation. HU is a non-sequence-specific DNA binding protein that sharply bends DNA, but alone does not condense DNA into densely packed particles. Less than one HU dimer per 225 bp of DNA is sufficient to completely control condensate morphology when DNA is condensed by spermidine. We propose that rods are favored in the presence of HU because rods contain sharply bent DNA, whereas toroids contain only smoothly bent DNA. The results presented illustrate the utility of naturally derived proteins for controlling the shape of DNA condensates formed in vitro. HU is a highly conserved protein in bacteria that is implicated in the compaction and shaping of nucleoid structure. However, the exact role of HU in chromosome compaction is not well understood. Our demonstration that HU governs DNA condensation in vitro also suggests a mechanism by which HU could act as an architectural protein for bacterial chromosome compaction and organization in vivo.     

Helicase from hepatitis C virus,energetics of DNA binding

The ability of a helicase to bind single-stranded nucleic acid is critical for nucleic acid unwinding. The helicase from the hepatitis C virus, NS3 protein, binds to the 3'-DNA or the RNA strand during unwinding. As a step to understand the mechanism of unwinding, DNA binding properties of the helicase domain of NS3 (NS3h) were investigated by fluorimetric binding equilibrium titrations. The global analysis of the binding data by a combinatorial approach was done using MATLAB. NS3h interactions with single-stranded DNA (ssDNA) are 300-1000-fold tighter relative to duplex DNA. The NS3h protein binds to ssDNA less than 15 nt in length with a stoichiometry of one protein per DNA. The minimal ssDNA binding site of NS3h helicase was determined to be 8 nucleotides with the microscopic K(d) of 2-4 nm or an observed free energy of -50 kJ/mol. These NS3h-DNA interactions are highly sensitive to salt, and the K(d) increases 4 times when the NaCl concentration is doubled. Multiple HCV helicase proteins bind to ssDNA >15 nucleotides in length, with an apparent occluded site of 8-11 nucleotides. The DNA binding data indicate that the interactions of multiple NS3h protein molecules with long ssDNA are both noncooperative and sequence-independent. We discuss the DNA binding properties of HCV helicase in relation to other superfamily 1 and 2 helicases. These studies provide the basis to investigate the DNA binding interactions with the unwinding substrate and their modulation by the ATPase activity of HCV helicase.     

The role of polymer nanolayer architecture on the separation performance of anion-exchange membrane adsorbers: I. Protein separations

This contribution describes the preparation of strong anion-exchange membranes with higher protein binding capacities than the best commercial resins. Quaternary amine (Q-type) anion-exchange membranes were prepared by grafting polyelectrolyte nanolayers from the surfaces of macroporous membrane supports. A focus of this study was to better understand the role of polymer nanolayer architecture on protein binding. Membranes were prepared with different polymer chain graft densities using a newly developed surface-initiated polymerization protocol designed to provide uniform and variable chain spacing. Bovine serum albumin and immunoglobulin G were used to measure binding capacities of proteins with different size. Dynamic binding capacities of IgG were measured to evaluate the impact of polymer chain density on the accessibility of large size protein to binding sites within the polyelectrolyte nanolayer under flow conditions. The dynamic binding capacity of IgG increased nearly linearly with increasing polymer chain density, which suggests that the spacing between polymer chains is sufficient for IgG to access binding sites all along the grafted polymer chains. Furthermore, the high dynamic binding capacity of IgG (>130 mg/mL) was independent of linear flow velocity, which suggests that the mass transfer of IgG molecules to the binding sites occurs primarily via convection. Overall, this research provides clear evidence that the dynamic binding capacities of large biologics can be higher for well-designed macroporous membrane adsorbers than commercial membrane or resin ion-exchange products. Specifically, using controlled polymerization leads to anion-exchange membrane adsorbers with high binding capacities that are independent of flow rate, enabling high throughput. Results of this work should help to accelerate the broader implementation of membrane adsorbers in bioprocess purification steps.     

FRET-based analysis of protein-nucleic acid interactions by genetically incorporating a fluorescent amino acid

Protein–nucleic acid interaction is an important process in many biological phenomena. In this study, a fluorescence resonance energy transfer (FRET)-based protein–DNA binding assay has been developed, in which a fluorescent amino acid is genetically incorporated into a DNA-binding protein. A coumarin-containing amino acid was incorporated into a DNA-binding protein, and the mutant protein specifically produced a FRET signal upon binding to its cognate DNA labeled with a fluorophore. The protein–DNA binding affinity was then measured under equilibrium conditions. This method is advantageous for studying protein-nucleic acid interactions, because it is performed under equilibrium conditions, technically easy, and applicable to any nucleic acid-binding protein.     

Statistical thermodynamic analysis of peptide and protein insertion into lipid membranes.

A statistical thermodynamic approach is used to analyze the various contributions to the free energy change associated with the insertion of proteins and protein fragments into lipid bilayers. The partition coefficient that determines the equilibrium distribution of proteins between the membrane and the solution is expressed as the ratio between the partition functions of the protein in the two phases. It is shown that when all of the relevant degrees of freedom (i.e., those that change their character upon insertion into the membrane) can be treated classically, the partition coefficient is fully determined by the ratio of the configurational integrals and thus does not involve any mass-dependent factors, a conclusion that is also valid for related processes such as protein adsorption on a membrane surface or substrate binding to proteins. The partition coefficient, and hence the transfer free energy, depend only on the potential energy of the protein in the membrane. Expressing this potential as a sum of a "static" term, corresponding to the equilibrium (minimal free energy) configuration of the protein in the membrane, and a "dynamical" term representing fluctuations around the equilibrium configuration, we show that the static term contains the "solvation" and "lipid perturbation" contributions to the transfer free energy. The dynamical term is responsible for the "immobilization" free energy, reflecting the loss of translational and rotational entropy of the protein upon incorporation into the membrane. Based on a recent molecular theory of lipid-protein interactions, the lipid perturbation and immobilization contributions are then expressed in terms of the elastic deformation free energy resulting from the perturbation of the lipid environment by the foreign (protein) inclusion. The model is formulated for cylindrically shaped proteins, and numerical estimates are given for the insertion of an alpha-helical peptide into a lipid bilayer. The immobilization free energy is shown to be considerably smaller than in previous estimates of this quantity, and the origin of the difference is discussed in detail.     

A computational and cellular solids approach to the stiffness-based design of bone scaffolds

We derive a cellular solids approach to the design of bone scaffolds for stiffness and pore size. Specifically, we focus on scaffolds made of stacked, alternating, orthogonal layers of hydroxyapatite rods, such as those obtained via micro-robotic deposition, and aim to determine the rod diameter, spacing and overlap required to obtain specified elastic moduli and pore size. To validate and calibrate the cellular solids model, we employ a finite element model and determine the effective scaffold moduli via numerical homogenization. In order to perform an efficient, automated execution of the numerical studies, we employ a geometry projection method so that analyses corresponding to different scaffold dimensions can be performed on a fixed, non-conforming mesh. Based on the developed model, we provide design charts to aid in the selection of rod diameter, spacing and overlap to be used in the robotic deposition to attain desired elastic moduli and pore size.     

Packaging double-helical DNA into viral capsids: structures, forces, and energetics

Small, icosahedral double-stranded DNA bacteriophage pack their genomes tightly into preformed protein capsids using an ATP-driven motor. Coarse-grain molecular-mechanics models provide a detailed picture of DNA packaging in bacteriophage, revealing how conformation depends on capsid size and shape, and the presence or absence of a protein core. The forces that oppose packaging have large contributions from both electrostatic repulsions and the entropic penalty of confining the DNA into the capsid, whereas elastic deformations make only a modest contribution. The elastic deformation energy is very sensitive to the final conformation, whereas the electrostatic and entropic penalties are not, so the packaged DNA favors conformations that minimize the bending energy.     

Stability of molecular adhesion mediated by confined polymer repellers and ligand-receptor bonds

Experiments have shown that stable adhesion of a variety of animal cells on substrates prepared with precisely controlled ligand distribution can be formed only if the ligand spacing is below 58 nm. To explain this phenomenon, here we propose a confined polymer model to study the stability of molecular adhesion mediated by polymer repellers and ligand-receptor bonds. In this model, both repellers and binders are treated as wormlike chains confined in a nanoslit, and the stability of adhesion is considered as a competition between attractive interactions of ligand-receptor binding and repulsive forces due to the size mismatch between repellers and binders. The force on each ligand-receptor bond is calculated from the confined polymer model, and the classic model of Bell is used to describe the association/dissociation reactions of ligand-receptor bonds. The calculated equilibrium bond distribution shows that there exists a critical ligand density for stable adhesion, corresponding to a critical ligand spacing which agrees not only qualitatively but also quantitatively with the experimental observation. In the case of stable adhesion, the model predicts an equilibrium separation between adhesion surfaces below 60% of the contour length of the ligand-receptor bonds.     

Heme reactivity of hemoglobins. Azide and fluoride binding equilibria of free and mercuriated ferri-gamma chains.

The free gamma chains, isolated from human foetal hemoglobin, are stable when oxidized and thus suitable for ligand binding and subunit equilibrium studies. The metaquo-ferri chains, with cysteine-F9 in the free state II ag gamma SH) possess several properties which are different from those of their p-mercuribenzoate derivative (III aq gammaSHgR); these are: stronger binding of a high-field ligand (N3- minus), altered spin equilibrium and an altered subunit equilibrium. A quantitative assessment of the free energy changes associated with all individual steps involved in changing the metaquo chains to their azide derivatives has been made. The results show that the higher apparent reactivity of III ag gammaSH (compared to IIIaq gammaSHgR) for the azide ion is not solely due to compensatory effects arising from differences of subunit dissociation or of spin equilibrium: other process(es) occurring in the ligand binding site have to be considered.     

An elastic rod model to evaluate effects of ionic concentration on equilibrium configuration of DNA in salt solution

As a coarse-gained model, a super-thin elastic rod subjected to interfacial interactions is used to investigate the condensation of DNA in a multivalent salt solution. The interfacial traction between the rod and the solution environment is determined in terms of the Young–Laplace equation. Kirchhoff’s theory of elastic rod is used to analyze the equilibrium configuration of a DNA chain under the action of the interfacial traction. Two models are established to characterize the change of the interfacial traction and elastic modulus of DNA with the ionic concentration of the salt solution, respectively. The influences of the ionic concentration on the equilibrium configuration of DNA are discussed. The results show that the condensation 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 forces that drive DNA condensation. With the change of concentration, the DNA segments will undergo a series of alteration from the original configuration to the condensed configuration, and the spiral-shape appearing in the condensed configuration of DNA is independent of the original configuration.     

Energetics of hydrophobic matching in lipid-protein interactions

Lipid chain length modulates the activity of transmembrane proteins by mismatch between the hydrophobic span of the protein and that of the lipid membrane. Relative binding affinities of lipids with different chain lengths are used to estimate the excess free energy of lipid-protein interaction that arises from hydrophobic mismatch. For a wide range of integral proteins and peptides, the energy cost is much less than the elastic penalty of fully stretching or compressing the lipid chains to achieve complete hydrophobic matching. The chain length dependences of the free energies of lipid association are described by a model that combines elastic chain extension with a free energy term that depends linearly on the extent of residual mismatch. The excess free energy densities involved lie in the region of 0.5-2.0 k_BT.nm⁻². Values of this size could arise from exposure of hydrophobic groups to polar portions of the lipid or protein, but not directly to water, or alternatively from changes in tilt of the transmembrane helices that are energetically comparable to those activating mechanosensitive channels. The influence of hydrophobic mismatch on dimerization of transmembrane helices and their transfer between lipid vesicles, and on shifts in chain-melting transitions of lipid bilayers by incorporated proteins, is analyzed by using the same thermodynamic model. Segmental order parameters confirm that elastic lipid chain distortions are insufficient to compensate fully for the mismatch, but the dependence on chain length with tryptophan-anchored peptides requires that the free energy density of hydrophobic mismatch should increase with increasing extent of mismatch.     

Visualization of RecA protein and its complexes with DNA by quick-freeze/deep-etch electron microscopy

Freeze-etch electron microscopy of pure RecA protein aggregates, as well as of RecA protein complexes on single-stranded and double-stranded DNA formed with various nucleotides, has permitted a clearer discrimination between the two different helical polymers that this protein forms. Both are continuous, single-start, right-handed helices; however, the form observed when ATP or non-hydrolyzable ATP analogs are present has a pitch of 9.5 nm and a diameter of 10 nm, while the other form, observed in the absence of ATP or its analogs, or in the presence of ADP, has a pitch of 6 nm and a diameter of 12 nm. The former "long pitch" helix is found only when RecA protein is bound to DNA. The latter "short pitch" helix is also observed in pure RecA protein polymers (also termed rods) and in the needle-like paracrystals of RecA protein that form in the presence of magnesium or spermidine ions, representing bundles of rods closely packed in register. Addition of ATP or non-hydrolyzable ATP analogs in the absence of DNA dissociates the pure RecA protein crystals, as well as individual helical rods, into short curvilinear chains of attached monomers. These chains typically form closed, circular rings of 7(+/- 1) protein monomers, similar in construction to a single turn of the RecA protein helix, but significantly broader in diameter. The role of ATP in interconverting the various polymeric forms of RecA protein is discussed within the context that ATP functions as a reversible allosteric effector of RecA protein, much as it mediates reversible conformational changes in other vectoral motor proteins such as myosin, dynein, kinesin and the 70,000 Mr "heat shock" ATPases. We discuss how cyclic conversions back and forth between the short- and long-pitch conformations of RecA protein could mediate in reversible single-stranded and double-stranded DNA interactions during the search for homology.     

Expectation maximization algorithm for identifying protein-binding sites with variable lengths from unaligned DNA fragments.

An Expectation Maximization algorithm for identification of DNA binding sites is presented. The approach predicts the location of binding regions while allowing variable length spacers within the sites. In addition to predicting the most likely spacer length for a set of DNA fragments, the method identifies individual sites that differ in spacer size. No alignment of DNA sequences is necessary. The method is illustrated by application to 231 Escherichia coli DNA fragments known to contain promoters with variable spacings between their consensus regions. Maximum-likelihood tests of the differences between the spacing classes indicate that the consensus regions of the spacing classes are not distinct. Further tests suggest that several positions within the spacing region may contribute to promoter specificity.