Electrostatic contributions to the binding free energy of the lambdacI repressor to DNA.

A model based on the nonlinear Poisson-Boltzmann (NLPB) equation is used to study the electrostatic contribution to the binding free energy of the lambdacI repressor to its operator DNA. In particular, we use the Poisson-Boltzmann model to calculate the pKa shift of individual ionizable amino acids upon binding. We find that three residues on each monomer, Glu34, Glu83, and the amino terminus, have significant changes in their pKa and titrate between pH 4 and 9. This information is then used to calculate the pH dependence of the binding free energy. We find that the calculated pH dependence of binding accurately reproduces the available experimental data over a range of physiological pH values. The NLPB equation is then used to develop an overall picture of the electrostatics of the lambdacI repressor-operator interaction. We find that long-range Coulombic forces associated with the highly charged nucleic acid provide a strong driving force for the interaction of the protein with the DNA. These favorable electrostatic interactions are opposed, however, by unfavorable changes in the solvation of both the protein and the DNA upon binding. Specifically, the formation of a protein-DNA complex removes both charged and polar groups at the binding interface from solvent while it displaces salt from around the nucleic acid. As a result, the electrostatic contribution to the lambdacI repressor-operator interaction opposes binding by approximately 73 kcal/mol at physiological salt concentrations and neutral pH. A variety of entropic terms also oppose binding. The major force driving the binding process appears to be release of interfacial water from the protein and DNA surfaces upon complexation and, possibly, enhanced packing interactions between the protein and DNA in the interface. When the various nonelectrostatic terms are described with simple models that have been applied previously to other binding processes, a general picture of protein/DNA association emerges in which binding is driven by the nonpolar interactions, whereas specificity results from electrostatic interactions that weaken binding but are necessary components of any protein/DNA complex.     

Interaction of effecting ligands with lac repressor and repressor-operator complex.

The equilibrium association constants for the binding of a wide variety of effecting ligands of the lac repressor were measured by equilibrium dialysis. Also, detailed investigations of the apparent rate of dissociation of repressor-operator comples as a function of ligand concentration were carried out for several inducers and anti-inducers. The affinity of repressor-ligand comples for operator DNA was evaluated from the specific rate constants at saturating concentrations of effecting ligand. By fitting the experimental data depicting the functional dependence of the rate of dissociation upon ligand concentrations to calculated curves, assuming simple models of the induction mechanism, the equilibrium association constant for the binding of effecting ligand to repressor-operator comples was determined. Inducers reduce the affinity of lac repressor for operator DNA by a factor of approximately 1000 under standard conditions; the extent of destabilization depends on Mg2+ ion concentration. Anti-inducers increase the affinity of repressor for operator at most a factor of five. Only one neutral ligand, which binds to repressor without altering the stability of repressor-operator comples, was found. No homotropic or heterotropic interactions in the binding of effecting ligands either to repressor or to repressor-operator complex are evident.     

Dynamics of repressor-operator recognition: the Tn10-encoded tetracycline resistance control

Binding of the Tet repressor to nonspecific and specific DNA leads to quenching of the Tet fluorescence by approximately 22% and approximately 35%, respectively. This effect is used for a direct, quantitative characterization of the binding equilibria and dynamics involved in the recognition of the operator by its repressor. From the dependence of the nonspecific binding constant on the ion concentration, it is concluded that nonspecific binding is almost completely driven by the entropy change resulting from the release of three to four Na+ ions from the double helix upon protein binding. Formation of the specific complex is driven by a higher entropy term resulting from the release of seven to eight Na+ ions and in addition by a free energy term of -33 kJ/mol from nonelectrostatic interactions, which are attributed to the specific contacts. The dynamics of the repressor-operator recognition are resolved by stopped-flow measurements at various salt concentrations and for different DNA chain lengths into two separate steps. The first step follows a second-order mechanism and results in an intermediate complex associated with formation of about three to four electrostatic contacts between protein and DNA; apparently, this complex is equivalent to the nonspecific complex. The existence of an intermediate is also indicated by experiments in mixed Na+-Mg2+ buffers, which can be described with high accuracy by competition of Mg2+ and protein. The intermediate complex is formed at a rate of 3 X 10(8) M-1 s-1 and is converted in the second reaction step to the specific complex with a rate constant of 6 X 10(4) s-1, which is almost independent of the salt concentration. Our interpretation and the parameters obtained from our model are confirmed by competition of nonspecific DNA with operator DNA for repressor binding. The observed maximal rate constant of 3 X 10(8) M-1 s-1 is very close to theoretical predictions for the association without a sliding mechanism. The very small dependence of the observed rate constants on the chain length shows that the Tet repressor is not able to slide over any substantial distance even at low salt concentrations. The question of a potential contribution from sliding under our experimental conditions is critically discussed. The absence of sliding in the case of the Tet repressor under physiological conditions is compared with the high sliding efficiency of the lac repressor and is discussed with respect to possible molecular mechanisms of sliding in relation to biological function.     

DAPI binding to the DNA minor groove: a continuum solvent analysis

A continuum solvent model based on the generalized Born (GB) or finite-difference Poisson-Boltzmann (FDPB) approaches has been employed to compare the binding of 4'-6-diamidine-2-phenyl indole (DAPI) to the minor groove of various DNA sequences. Qualitative agreement between the results of GB and FDPB approaches as well as between calculated and experimentally observed trends regarding the sequence specificity of DAPI binding to B-DNA was obtained. Calculated binding energies were decomposed into various contributions to solvation and DNA-ligand interaction. DNA conformational adaptation was found to make a favorable contribution to the calculated total interaction energy but did not change the DAPI binding affinity ranking of different DNA sequences. The calculations indicate that closed complex formation is mainly driven by nonpolar contributions and was found to be disfavored electrostatically due to a desolvation penalty that outbalances the attractive Coulomb interaction. The calculated penalty was larger for DAPI binding to GC-rich sequences compared with AT-rich target sequences and generally larger for the FDPB vs the GB continuum model. A radial interaction profile for DAPI at different distances from the DNA minor groove revealed an electrostatic energy minimum a few Angstroms farther away from the closed binding geometry. The calculated electrostatic interaction up to this distance is attractive and it may stabilize a nonspecific binding arrangement.     

Anatomy of specific interactions between lambda repressor and operator DNA

Recognition of specific DNA sequences by proteins is essential for regulation of gene expression. To fully understand the recognition mechanism, it is necessary to understand not only the structure of the specific protein-DNA interactions but also the energetics. We therefore performed a computer analysis in which a phage DNA-binding protein, lambda repressor, was used to examine the changes in binding free energy (DeltaDeltaG) and its energy components caused by single base mutations. We then determined which of the calculated energy components best correlated with the experimental data. The experimental DeltaDeltaG values were well reproduced by the calculations. Component analysis revealed that the electrostatic and hydrogen bond energies were most strongly correlated with the experimental data. Among the 51 single base-substitution mutants examined, positive DeltaDeltaG values, corresponding to weakened binding, were caused by the loss of favorable electrostatic interactions and hydrogen bonds, the introduction of steric collisions and electrostatic repulsion, the loss of favorable interactions with a thymine methyl group, and the increase of unfavorable hydration energy from isolated DNA. This analysis also showed distinct patterns of recognition at A-T and G-C positions, as different combinations of energy components were involved in DeltaDeltaG caused by the two substitution types. We have thus been able to identify the energy components that most strongly correlate with sequence-dependent DeltaDeltaG and determine their contribution to the specificity of DNA sequence recognition by the lambda repressor. Application of this method to other systems should provide additional insight into the molecular mechanism of protein-DNA recognition.     

基于分子模拟的离子交换层析中静电相互作用研究

将分子模拟方法引入到蛋白质离子交换层析中的静电相互作用研究。选用蛋清溶菌酶和牛胰凝乳蛋白酶为模型蛋白质,阳离子交换吸附剂SP Sepharose FF等为模型层析介质。从蛋白质数据库(PDB)中获得蛋白质三维结构数据,分析了介质孔径和配基分布,以点电荷模拟离子交换层析介质的功能配基,构筑了蛋白质-介质配基模拟表面体系。采用MCCE、Delphi和GRASP等程序包进行了分子模拟计算,考察了作用方向、作用距离、盐浓度、pH等对蛋白质和模拟配基平面间静电相互作用的影响。结果表明,宏观的层析平衡常数与微观分子模拟计算的相互作用能量参数间存在良好的线性关系。     

Electrostatic interactions in a peptide--RNA complex

Parallel experimental measurements and theoretical calculations have been used to investigate the energetics of electrostatic interactions in the complex formed between a 22 residue, alpha-helical peptide from the N protein of phage lambda and its cognate 19 nucleotide box B RNA hairpin. Salt-dependent free energies were measured for both peptide folding from coil to helix and peptide binding to RNA, and from these the salt-dependence of binding pre-folded, helical peptide to RNA was determined ( partial differential (DeltaG degrees (dock))/ partial differential log[KCl]=5.98(+/-0.21)kcal/mol). (A folding transition taking place in the RNA hairpin loop was shown to have a negligible dependence on salt concentration.) The non-linear Poisson-Boltzmann equation was used to calculate the same salt dependence of the binding free energy as 5.87(+/-0.22)kcal/mol, in excellent agreement with the measured value. Close agreement between experimental measurements and calculations was also obtained for two variant peptides in which either a basic or acidic residue was replaced with an uncharged residue, and for an RNA variant with a deletion of a single loop nucleotide. The calculations suggest that the strength of electrostatic interactions between a peptide residue and RNA varies considerably with environment, but that all 12 positive and negative N peptide charges contribute significantly to the electrostatic free energy of RNA binding, even at distances up to 11A from backbone phosphate groups. Calculations also show that the net release of ions that accompanies complex formation originates from rearrangements of both peptide and RNA ion atmospheres, and includes accumulation of ions in some regions of the complex as well as displacement of cations and anions from the ion atmospheres of the RNA and peptide, respectively.     

Analysis of trp repressor-operator interaction by filter binding.

A filter binding assay was developed that allows measurement of specific binding of trp repressor to operator DNA. The most important feature of this procedure is the concentration and type of salt present in the binding buffer. Using this assay the dissociation constant of the repressor-operator complex was determined to be 2.6 X 10(-9) M, and 1.34 repressor dimers were found to be bound to each operator-containing DNA molecule. These values agree with those obtained by more complex methods. The dissociation constant of the repressor for the corepressor L-tryptophan in the presence of operator DNA was shown to be 2.5 X 10(-5) M. A synthetic 48 bp operator fragment was used to determine the repressor-operator dissociation constant in the presence of tryptophan or tryptophan analogs which have higher or lower affinities for aporepressor. The rate of dissociation of repressor from operator DNA also was determined. Our findings indicate that dissociation is influenced by the concentration of tryptophan or tryptophan analogs and suggest that release of the corepressor may be the first step in dissociation of the repressor-operator complex.     

A novel stable RNA pentaloop that interacts specifically with a motif peptide of lambda-N protein

To achieve a novel specific peptide-nucleic acid binding model, we designed an in vitro selection procedure to decrease the energetic contribution of the electrostatic interaction in the total binding energy and to increase the contribution of hydrogen bonding and pi-pi stacking. After the selection of hairpin-loop RNAs that specifically bound to a model peptide of lambda N protein (N peptide), a new thermostable pentaloop RNA motif (N binding thermostable RNA hairpin: NTS RNA) was revealed. The obtained NTS RNA was able to bind to the N peptide with superior specificity to the boxB RNA, which is the naturally occurring partner of the lambda N protein.     

Electrostatic fixed charge distribution in the RBC-glycocalyx and their influence upon the total free interaction energy

On the basis of a recently developed biophysical model of cell-cell interaction, including electrostatic, electrodynamic, steric and bonding/bridging interaction energies the influence of different fixed charge (dissociated groups of the glycocalyx) density distributions in red blood cell (RBC) glycocalyces on the total free interaction energy was investigated. An analytical equation of electrostatic free energy on the basis of the linear Poisson-Boltzmann approach taking into account arbitrary distributions of fixed glycocalyx charges was obtained and corresponding free electrostatic energies of three example distributions were calculated. The electrodynamic, steric and bonding/bridging energies were computed as usual. It was shown that the free energy as a function of interaction distances strongly depends on the charge distribution and, correspondingly, the "weight" of this energy term in the total free interaction energy balance equation. Generally, it can be stated that as more charges are assumed to be fixed in the outer layer of RBC glycocalyx as more important becomes the electrostatic energy in contrast to the remaining three terms.     

Sequence-specific DNA-protein interaction: the lac represser

A model is proposed for lac repressor-lac operator binding which accounts for the tetrameric subunit structure of the lac repressor and for factors involved in the strength, specificity and regulation of repressor-operator interaction. The model employs a π-helix in the amino terminal 25 residues of the lac repressor whereby three tyrosine residues of each subunit intercalate between base pairs of the lac operator. For the outer palindromic sequences of the operator, base specificity is provided by amino acids adjacent to the carboxyl sides of the tyrosine residues of two of the subunits. The inner palindromic sequences which bind the other two subunits form stems of hairpin loops in the operator. Base specificity for these two subunits is provided by amino acids adjacent to the amino sides of the tyrosine residues. In addition to 12 intercalated tyrosine residues, the model provides for a total of at least eight electrostatic interactions and ten sequence-specific hydrogen bonds.     

Interaction of tight binding repressors with lac operators. An analysis by DNA-footprinting

To increase our understanding of protein-DNA interaction in general, and in particular that of lac repressor with lac operator, we have investigated the interaction of tight binding (Itb) repressors with wild type (WT) operator and Oc operators. Nine Oc and a WT operator were cloned and sequenced. Three different Oc and an O+ were then chosen for the footprint analysis of six Itb repressors and WT repressor. Distinct protection patterns for the various repressor-operator pairs were observed at low repressor concentrations whereas, at high repressor concentrations, a stretch of 24 bases of the lower strand of the four different operators was protected in most cases. This protection pattern at high repressor concentration was almost completely redundant for all repressor-operator pairs, in spite of the fact that the affinities of the various pairs differed by more than three orders of magnitude. Two exceptions to this general observation were the two tight binding repressors R67 and R78a. These had been mapped in a region that codes for amino acid residues involved in subunit interaction. The two repressors showed reduced protection of O+ and of some Oc operators at the 3' (right) end of the lower strand. Dimethylsulfoxide, which is known to increase the affinity of O+ for repressor, did not increase the number of bases protected by WT repressor on the lower strand of O+. The footprinting results presented here clearly demonstrate that lac repressor can maximally protect about 24 bases of the lower strand of the operator and that the number and kind of interactions occurring in this region determine the strength of the repressor-operator interaction.     

Poisson-Boltzmann calculations of nonspecific salt effects on protein-protein binding free energies

The salt dependence of the binding free energy of five protein-protein hetero-dimers and two homo-dimers/tetramers was calculated from numerical solutions to the Poisson-Boltzmann equation. Overall, the agreement with experimental values is very good. In all cases except one involving the highly charged lactoglobulin homo-dimer, increasing the salt concentration is found both experimentally and theoretically to decrease the binding affinity. To clarify the source of salt effects, the salt-dependent free energy of binding is partitioned into screening terms and to self-energy terms that involve the interaction of the charge distribution of a monomer with its own ion atmosphere. In six of the seven complexes studied, screening makes the largest contribution but self-energy effects can also be significant. The calculated salt effects are found to be insensitive to force-field parameters and to the internal dielectric constant assigned to the monomers. Nonlinearities due to high charge densities, which are extremely important in the binding of proteins to negatively charged membrane surfaces and to nucleic acids, make much smaller contributions to the protein-protein complexes studied here, with the exception of highly charged lactoglobulin dimers. Our results indicate that the Poisson-Boltzmann equation captures much of the physical basis of the nonspecific salt dependence of protein-protein complexation.     

Thermodynamic analysis of the lactose repressor-operator DNA interaction

Kinetic and equilibrium constants for lactose repressor-operator DNA interaction have been examined as a function of salt concentration, size and sequence context of the operator DNA, and temperature. Significant salt effects were observed on kinetic and equilibrium parameters for pLA 322-8, an operator-containing derivative of pBR 322, and pIQ, an operator and pseudooperator-containing derivative of pBR 322. The association rate constant and equilibrium constant for the 40 base pair operator fragment were also salt dependent. Data for all the DNAs were consistent with a sliding mechanism for repressor-operator association/dissociation [Berg, O. G., & Blomberg, C. (1978) Biophys. Chem. 8, 271-280]. Calculation of the number of ionic interactions based on salt dependence yielded a value of approximately 8 for repressor binding to pIQ and pLA 322-8 vs. approximately 6 for the repressor-40 base pair fragment. These data and the differences in binding parameters for the plasmids vs. the 40 base pair operator are consistent with the formation of an intramolecular ternary complex in the plasmid DNAs. Unusual biphasic temperature dependence was observed in the equilibrium and dissociation rate constants for pLA 322-8, pIQ, and the 40 base pair fragment. These observations coupled with a discontinuity found in the inducer association rate constant as a function of temperature suggest a structural change in the protein. The large positive entropy contributions associated with repressor binding to all the DNAs examined provide the significant driving force for the reaction and are consistent with involvement of ionic and apolar interactions in complex formation.     

Binding and bending of the lambda replication origin by the phage O protein.

We have characterized the binding of lambda phage replication initiation protein O to the phage origin of replication. The minimal DNA segment required for O binding is the single iteron, a 19-bp sequence of hyphenated dyad symmetry that is repeated with variations four times in the origin. The isolated amino terminus of O protein is also sufficient to bind DNA. Electrophoretic studies show that the amino terminus of O protein induces bending of a single iteron. The DNA-protein interaction was characterized by ethylation interference, dimethyl sulfate protection and neocarzinostatin footprinting. Points of DNA-protein contact are largely concentrated in two areas symmetrically disposed with respect to the dyad symmetry of the iteron. This suggests the protein interacts as a dimer with half sites in the DNA. However, a few non-symmetrical contacts are found, indicating that O protein may distort the helix. This may correlate with the bending effects demonstrated electrophoretically. Cylindrical DNA projections were used to model O protein binding to the lambda origin and compare it with the lambda repressor-operator interaction. Whereas bound repressor nearly encircles the DNA in the major groove, O protein leaves the major groove on the opposite side exposed.     

Electrostatic contribution to the bending of DNA

A model is derived that accounts for the short-range electrostatic contribution to the bending of DNA molecule in solution and in complexes with proteins in terms of the non-linear Poisson-Boltzmann equation. We defined that the short-range electrostatic interactions depend on the changes of the polyion surface charge density under deformation, while the long-range interactions depend on the bending-induced changes in distances between each two points along the polyion axis. After an appropriate simplification of the Poisson-Boltzmann equation, the short-range term is calculated separately giving the lower limit for the electrostatic contribution to the DNA persistence length. The result is compared with the theoretical approaches developed earlier [M. Fixman, J. Chem. Phys. 76 (1982) 6346; M. Le Bret, J. Chem. Phys. 76 (1982) 6243] and with the experimental data. The conclusion is made that the results of Fixman-Le Bret, which took into account both types of the electrostatic interactions for a uniformly bent polyion, give the upper limit for the electrostatic persistence length at low ionic strength, and the actual behavior of the DNA persistence length lies between two theoretical limits. Only the short-range term is significant at moderate-to-high ionic strength where our results coincide with the predictions of Fixman-Le Bret. The bending of DNA on the protein surface that is accompanied by an asymmetric neutralization of the DNA charge is also analyzed. In this case, the electrostatic bending energy gives a significant favorite contribution to the total bending energy of DNA. Important implications to the mechanisms of DNA-protein interactions, particularly in the nucleosome particle, are discussed.     

On the role of electrostatic interactions in the design of protein-protein interfaces

Here, the methods of continuum electrostatics are used to investigate the contribution of electrostatic interactions to the binding of four protein-protein complexes; barnase-barstar, human growth hormone and its receptor, subtype N9 influenza virus neuraminidase and the NC41 antibody, the Ras binding domain (RBD) of kinase cRaf and a Ras homologue Rap1A. In two of the four complexes electrostatics are found to strongly oppose binding (hormone-receptor and neuraminidase-antibody complexes), in one case the net effect is close to zero (barnase-barstar) and in one case electrostatics provides a significant driving force favoring binding (RBD-Rap1A). In order to help understand the wide range of electrostatic contributions that were calculated, the electrostatic free energy was partitioned into contributions of individual charged and polar residues, salt bridges and networks involving salt bridges and hydrogen bonds. Although there is no one structural feature that accounts for the differences between the four interfaces, the extent to which the desolvation of buried charges is compensated by the formation of hydrogen bonds and ion pairs appears to be an important factor. Structural features that are correlated with contribution of an individual residue to stability are also discussed. These include partial burial of a charged group in the free monomer, the formation of networks involving charged and polar amino acids, and the formation of partially exposed ion-pairs. The total electrostatic contribution to binding is found to be inversely correlated with buried total and non-polar surface area. This suggests that different interfaces can be designed to exploit electrostatic and hydrophobic forces in very different ways.