Lac repressor-operator interaction: DNA length dependence

The interaction of the E. coli lac operon repressor with its operator DNA has been directly examined as a function of the length of operator-containing DNA. The apparent bimolecular association rate constants were calculated as ka = (kd/KD), where the dissociation equilibrium constant, KD and the dissociation rate constant, kd, were measured by nitrocellulose filter adsorption assays. The values obtained for the overall association rate constants are compared with theoretical association rate curves for specific mechanisms. Association of the repressor with short operator containing DNA fragments (less than 70 base pairs) occurs at rates expected of three-dimensional diffusion. Our data also imply that at longer DNA lengths a combination of three-dimensional diffusion with one-dimensional sliding along with hopping and/or intersegment transfer must be involved to facilitate the repressor operator association.     

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.     

Mobility of adsorbed proteins: a Brownian dynamics study

We simulate the adsorption of lysozyme on a solid surface, using Brownian dynamics simulations. A protein molecule is represented as a uniformly charged sphere and interacts with other molecules through screened Coulombic and double-layer forces. The simulation starts from an empty surface and attempts are made to introduce additional proteins at a fixed time interval that is inversely proportional to the bulk protein concentration. We examine the effect of ionic strength and bulk protein concentration on the adsorption kinetics over a range of surface coverages. The structure of the adsorbed layer is examined through snapshots of the configurations and quantitatively with the radial distribution function. We extract the surface diffusion coefficient from the mean square displacement. At high ionic strengths the Coulombic interaction is effectively shielded, leading to increased surface coverage. This effect is quantified with an effective particle radius. Clustering of the adsorbed molecules is promoted by high ionic strength and low bulk concentrations. We find that lateral protein mobility decreases with increasing surface coverage. The observed trends are consistent with previous theoretical and experimental studies.     

How Lac repressor finds lac operator in vitro.

Filter-binding and gel mobility shift assays were used to analyse the kinetics of the interaction of Lac repressor with lac operator. A comparison of the two techniques reveals that filter-binding assays with tetrameric Lac repressor have often been misinterpreted. It has been assumed that all complexes of Lac repressor and lac operator DNA bind with equal affinity to nitrocellulose filters. This assumption is wrong. Sandwich or loop complexes where two lac operators bind to one tetrameric Lac repressor are not or are only badly retained on nitrocellulose filters under normal conditions. Taking this into account, dimeric and tetrameric Lac repressor do not show any DNA-length dependence of their association and dissociation rate constants when they bind to DNA fragments smaller than 2455 base-pairs carrying a single symmetric ideal lac operator. A ninefold increased association rate to ideal lac operator on lambda DNA is observed for tetrameric but not dimeric Lac repressor. It is presumably due to intersegment transfer involving lac operator-like sequences.     

Dissociation of the lactose repressor-operator DNA complex: effects of size and sequence context of operator-containing DNA

The dissociation kinetics for repressor-32P-labeled operator DNA have been examined by adding unlabeled operator DNA to trap released repressor or by adding a small volume of concentrated salt solution to shift the Kd of repressor-operator interaction. The dissociation rate constant for pLA 322-8, an operator-containing derivative of pBR 322, was 2.4 X 10(-3) s-1 in 0.15 M KCl. The dissociation rate constant at 0.15 M KCl for both lambda plac and pIQ, each of which contain two pseudooperator sequences, was approximately 6 X 10(-4) s-1. Elimination of flanking nonspecific DNA sequences by use of a 40 base pair operator-containing DNA fragment yielded a dissociation rate constant of 9.3 X 10(-3) s-1. The size and salt dependences of the rate constants suggest that dissociation occurs as a multistep process. The data for all the DNAs examined are consistent with a sliding mechanism of facilitated diffusion to/from the operator site. The ability to form a ternary complex of two operators per repressor, determined by stoichiometry measurements, and the diminished dissociation rates in the presence of intramolecular nonspecific and pseudooperator DNA sites suggest the formation of an intramolecular ternary complex. The salt dependence of the dissociation rate constant for pLA 322-8 at high salt concentrations converges with that for a 40 base pair operator. The similarity in dissociation rate constants for pLA 322-8 and a 40 base pair operator fragment under these conditions indicates a common dissociation mechanism from a primary operator site on the repressor.     

Formation of mixed disulfide adducts at cysteine-281 of the lactose repressor protein affects operator and inducer binding parameters

The lactose repressor protein has been modified with three sulfhydryl-specific reagents which form mixed disulfide adducts. Methyl methanethiosulfonate (MMTS) and 5,5'-dithiobis(2-nitrobenzoic acid) (DTNB) completely reacted with all three cysteine residues, whereas only partial reaction was observed with didansylcystine. Cysteines-107 and -140 reacted stoichiometrically with MMTS and DTNB, while Cys-281 was modified only at higher molar ratios. Didansylcystine reacted primarily with cysteines-107 and -140. Affinity of MMTS-modified repressor for 40 base pair operator DNA was decreased 30-fold compared to unmodified repressor, and this decrease correlated with modification of cysteine-281. DTNB-modified repressor bound operator DNA with a 50-fold weaker affinity than unmodified repressor. Modification of the lac repressor with didanylcystine decreased operator binding only 4-fold, and nonspecific DNA binding increased 3-fold compared to unmodified repressor. No change in the inducer equilibrium binding constant was observed following modification with any of these reagents. In contrast, inducer association and dissociation rate constants were decreased approximately 50-fold for repressor completely modified with MMTS or DTNB, while didansylcystine had minimal effect on inducer binding kinetics. Correlation between modification of Cys-281 and the observed decrease in rate constants indicates that this region of the protein regulates the accessibility of the sugar binding site. The parallel between the increase in the Kd for repressor binding to operator, the altered rate constant for inducer binding, and modification of cysteine-281 suggests that this region of the protein is crucially involved in the function of the repressor protein.     

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.     

Energetics of Shaker K channels block by inactivation peptides

A synthetic peptide of the NH2-terminal inactivation domain of the ShB channel blocks Shaker channels which have an NH2-terminal deletion and mimics many of the characteristics of the intramolecular inactivation reaction. To investigate the role of electrostatic interactions in both peptide block and the inactivation process we measured the kinetics of block of macroscopic currents recorded from the intact ShB channel, and from ShB delta 6-46 channels in the presence of peptides, at different ionic strengths. The rate of inactivation and the association rate constants (k(on)) for the ShB peptides decreased with increasing ionic strength. k(on) for a more positively charged peptide was more steeply dependent on ionic strength consistent with a simple electrostatic mechanism of enhanced diffusion. This suggests that a rate limiting step in the inactivation process is the diffusion of the NH2-terminal domain towards the pore. The dissociation rates (k(off)) were insensitive to ionic strength. The temperature dependence of k(on) for the ShB peptide was very high, (Q10 = 5.0 +/- 0.58), whereas k(off) was relatively temperature insensitive (Q10 approximately 1.1). The results suggest that at higher temperatures the proportion of time either the peptide or channel spends in the correct conformation for binding is increased. There were two components to the time course of recovery from block by the ShB peptide, indicating two distinct blocked states, one of which has similar kinetics and dependence on external K+ concentration as the inactivated state of ShB. The other is voltage- dependent and at -120 mV is very unstable. Increasing the net charge on the peptide did not increase sensitivity to knock-off by external K+. We propose that the free peptide, having fewer constraints than the tethered NH2-terminal domain binds to a similar site on the channel in at least two different conformations.     

Thermal denaturation of engineered tet repressor proteins and their complexes with tet operator and tetracycline studied by temperature gradient gel electrophoresis

The effects of Trp to Phe exchanges in the Tet repressor on the thermal stability of the proteins and their complexes with operator DNA and inducer have been studied by temperature gradient polyacrylamide gel electrophoresis. The denaturation temperatures obtained by this method are compared with the results from temperature-dependent fluorescence and binding activities of the proteins. It is established that exchanging the interior Trp75 to Phe reduces the thermal stability of the Tet repressor by 8 degrees C while exchanging the exterior Trp43 to Phe has no effect on the stability of the protein. Binding of the inducer tetracycline increases the thermal stability of wild-type and Trp43 to Phe mutant Tet repressors by 5 degrees C, while the ones with the Trp75 to Phe mutation are stabilized by 10 degrees C. The stabilizing effect of operator binding is 20 degrees C in the Trp75 to Phe mutant and only 9 degrees C in the ones with the Trp43 to Phe exchange. In addition to the denaturation temperatures, the gel mobility shifts observed in temperature gradient gel electrophoresis reveal also information about the intermediates of the denaturation reaction. The free proteins and their complexes with the inducer tetracycline exhibit monophasic transitions upon denaturation. The operator complexes of wild-type and Trp75 to Phe mutant repressors denature in more complex reactions. At low temperature they exhibit a stoichiometry of two repressor dimers per tandem tet operator DNA. Upon elevating the temperature they form complexes with only one repressor dimer per DNA fragment. When the temperature is further increased the double-stranded DNA begins to melt from one end resulting in a complex with partially single-stranded DNA which exists only in a narrow temperature range. Finally, the denatured protein and single-stranded DNA are formed at high temperature. The associated mobility shifts are analyzed by changing the ionic strength and characterizing multiphasic melting of a pure DNA fragment by temperature gradient gel electrophoresis.     

Studies on the binding of FMN by apoflavodoxin from Peptostreptococcus elsdenii, pH and NaCl concentration dependence.

1. The pH and ionic strength dependence of the interaction of FMN with apoflavodoxin has been studied by fluorometry in the pH region 2-5, at 22 degrees C. 2. The rate constant of dissociation and the dissociation constant were experimentally determined; the rate constants of association were claculated at a given pH value. These constants depend on the ionic strength. The plots of these constants against the square root of the ionic strength are straight. 3. Our data have been interpreted in terms of the Br?nsted theory, which relates chemical reaction rates to ionic strength. The data indicate that the apoenzyme reaches its maximum net positive charge at pH 2.0-2.6. The calculated net charge in this pH region is between 11 and 12 and is in agreement with the theoretical value of 12 as deduced from the primary structure of the protein. The isoelectric point of the holoenzyme is about 4. 4. The rate constant of association extrapolated to zero ionic strength is 3.2-10(5)M-1-s-1 and is pH-independent. 5. The rate constant of dissociation and the dissociation constant extrapolated to zero ionic strength depend on the pH. The results are explained by assuming that there are two protein ionizations with a pK value of 3.4; these ionizing groups are possibly close to the FMN binding site.     

The trajectory of a stiff rod in a curved potential energy trough. An initial result for short nucleosomal rods

The equilibrium trajectory of the axis of a rod subject to an externally imposed curved potential energy trough tends to conform to the shape of the curved trough, but also tends to be straight because of elastic resistance to bending. The actual path of the axis is a balance between the two extremes. We consider a potential energy trough centered along a circular arc of radius R. For a rod of small length compared to R, we show that the axis at equilibrium forms an arc of a circle of radius greater than R. The value of the radius of the axial path depends on the relative values of the Hooke's Law bending constant for the rod and the depth and width of the trough. Motivation for the calculation is provided by nucleosomal DNA, which conforms to the surface of a roughly cylindrical histone core at physiological ionic strength, but is observed to unwind into a partially extended conformation at very low ionic strength. We suggest that the rigidity to bending of short DNA segments becomes sufficiently great at low ionic strength to overcome attractive interactions with the histone surface. Alternately, of course, if during the cell cycle mutually attractive forces between DNA and histone core are weakened at constant ionic strength, the same type of unfolding would be expected to occur as the strength of the DNA-histone contacts drops below the level required to overcome elastic resistance to bending of the DNA rod.     

Two-photon excitation and photolysis by pulsed laser illumination modelled by spatially non-uniform reactions with simultaneous diffusion

Two-photon absorption in the focus of a pulsed laser has the potential for localized photolysis of caged compounds, generating high concentrations of neurotransmitters, hormones and messengers. The concentrations of cage, intermediates and products in the femtolitre focal volume depend on reaction rates and diffusional exchange with the external volume. This problem of reaction with diffusion was analysed with analytical and numerical methods to determine simple relations between parameters useful in the design and interpretation of experiments. The diffraction-limited laser spot is approximated well by a sphere, radius A, in diffusional exchange with either an infinite uniform medium, representing extracellular photolysis, or within a non-permeable sphere, a "cell" of radius B, representing intracellular photolysis. Photolysis is modelled as sequential irreversible reactions, with either the excitation step alone, rate constant k(e), or with a subsequent "dark" reaction, rate constant k(p). For extracellular photolysis, steady-state depletion of a cage averaged in a spherical spot increases hyperbolically with k(e) with half-maximum depletion at k(e) = K0.5 = 2.5 D/A2, where D is the diffusion coefficient. With measured parameters for spot size A = 0.3 microm and diffusion D = 800 microm2/s, K0.5 = 22,200 s(-1). The optimal exposure for localized photolysis is the characteristic diffusion time tau = A2/D, 113 micros in this example, and is the time taken to reach 57% of steady state in the diffusion-limited case. In the two-step model, with excitation and "dark" reaction steps, rate constants both exceeding K0.5 are necessary to generate 50% of maximal product concentration in the illuminated volume. High concentrations of photolysis products depend particularly on a high excitation rate constant (k(e) > K0.5), and localization of the products requires fast dark reactions (k(p) > K0.5). If products diffuse faster than the cage, their steady-state concentrations are decreased, and concentration transients may occur. For localized intracellular photolysis, the duration of exposure that generates product concentration at the cell boundary, B, less than 10% of the spot concentration should be shorter than 0.043(B/A)3tau, and is determined by diffusion.     

The reaction between cytochrome c1 and cytochrome c

The kinetics of electron transfer between the isolated enzymes of cytochrome c1 and cytochrome c have been investigated using the stopped-flow technique. The reaction between ferrocytochrome c1 and ferricytochrome c is fast; the second-order rate constant (k1) is 3.0 . 10(7) M-1 . s-1 at low ionic strength (I = 223 mM, 10 degrees C). The value of this rate constant decreases to 1.8 . 10(5) M-1 . s-1 upon increasing the ionic strength to 1.13 M. The ionic strength dependence of the electron transfer between cytochrome c1 and cytochrome c implies the involvement of electrostatic interactions in the reaction between both cytochromes. In addition to a general influence of ionic strength, specific anion effects are found for phosphate, chloride and morpholinosulphonate. These anions appear to inhibit the reaction between cytochrome c1 and cytochrome c by binding of these anions to the cytochrome c molecule. Such a phenomenon is not observed for cacodylate. At an ionic strength of 1.02 M, the second-order rate constants for the reaction between ferrocytochrome c1 and ferricytochrome c and the reverse reaction are k1 = 2.4 . 10(5) M-1 . s-1 and k-1 = 3.3 . 10(5) M-1 . s-1, respectively (450 mM potassium phosphate, pH 7.0, 1% Tween 20, 10 degrees C). The 'equilibrium' constant calculated from the rate constants (0.73) is equal to the constant determined from equilibrium studies. Moreover, it is shown that at this ionic strength, the concentrations of intermediary complexes are very low and that the value of the equilibrium constant is independent of ionic strength. These data can be fitted into the following simple reaction scheme: cytochrome c2+1 + cytochrome c3+ in equilibrium or formed from cytochrome c3+1 + cytochrome c2+.     

Association kinetics with coupled diffusion: III. Ionic-strength dependence of the lac repressor-operator association

The repressor- operator association is treated in a model where the represser molecule can find its specific binding site the operator, on a large DNA chain by performing a one-dimensional diffusion along the chain. The ionic-strength depen deuce is calculated by introducing a screened electrostatic potential around the DNA chain and coupling the free diffusion of the represser in this potential to the proposed one-dimensional diffusion along the chain. The main influence on the association rate comes from the competitive binding of ions to the unspecific DNA sites. It is also demonstrated that during the time that the represser is bound in a global sense, the diffusion along the chain will be made up of a strictly one-dimensional motion over fairly short distances, interspersed with many local dissociations during which the repressor in essence is free in solution.     

Role of electrostatics in the interaction between cytochrome f and plastocyanin of the cyanobacterium Phormidium laminosum

The role of charged residues on the surface of plastocyanin from the cyanobacterium Phormidium laminosum in the reaction with soluble cytochrome f in vitro was studied using site-directed mutagenesis. The charge on each of five residues on the eastern face of plastocyanin was neutralized and/or inverted, and the effect of the mutation on midpoint potentials was determined. The dependence of the overall rate constant of reaction, k(2), on ionic strength was investigated using stopped-flow spectrophotometry. Removing negative charges (D44A or D45A) accelerated the reaction and increased the dependence on ionic strength, whereas removing positive charges slowed it down. Two mutations (K46A, K53A) each almost completely abolished any influence of ionic strength on k(2), and three mutations (R93A, R93Q, R93E) each converted electrostatic attraction into repulsion. At low ionic strength, wild type and all mutants showed an inhibition which might be due to changes in the interaction radius as a consequence of ionic strength dependence of the Debye length or to effects on the rate constant of electron transfer, k(et). The study shows that the electrostatics of the interaction between plastocyanin and cytochrome f of P. laminosum in vitro are not optimized for k(2). Whereas electrostatics are the major contributor to k(2) in plants [Kannt, A., et al. (1996) Biochim. Biophys. Acta 1277, 115-126], this role is taken by nonpolar interactions in the cyanobacterium, leading to a remarkably high rate at infinite ionic strength (3.2 x 10(7) M(-1) s(-1)).     

Electron transfer between flavodoxin semiquinone and c-type cytochromes: correlations between electrostatically corrected rate constants, redox potentials, and surface topologies

We have measured the ionic strength dependence of the rate constants for electron transfer from the semiquinone of Clostridium pasteurianum flavodoxin to 12 c-type cytochromes and several inorganic oxidants using stopped-flow methodology. The experimental data were fit quite well by an electrostatic model that represents the interaction domains as parallel disks with a point charge equal to the charge within this region of the protein. The analysis provides an evaluation of the electrostatic interaction energy and the rate constant at infinite ionic strength (k affinity). The electrostatic charge on the oxidant within the interaction site can be obtained from the electrostatic energy, and for most of those reactants for which structures are available, the results are in good agreement with expectation. The k affinity values were found to correlate with redox potential differences, as expected from the theory of adiabatic (or nonadiabatic) outer-sphere electron-transfer reactions. Deviations from the theoretical curves are interpreted in terms of the influence of surface topology on reaction rate constants. In general, we find that electrostatic effects, steric influences, and redox potential all exert a much larger effect on reaction rate constants for the flavodoxin-cytochrome system than has been previously observed for free flavin-cytochrome interactions. The implications of this for determining biological specificity are discussed.     

Stoichiometry of lac repressor binding to nonspecific DNA: three different complexes form

The stoichiometry of lac repressor binding to nonspecific DNA was investigated by three different techniques. Four molecules of the fluorescent probe 5,5'-bis(8-anilino-1-naphthalenesulfonate) [bis(ANS)] bind to each repressor subunit with an average dissociation constant of 20 microM. Nonspecific DNA displaces most of this bound bis(ANS), reducing the fluorescence. Titrations of repressor with nonspecific DNA monitored with high [bis(ANS)] (5-15 microM) had end points at 8 base pairs per repressor. Lower [bis(ANS)] (0.1-1 microM) resulted in end points at either 15 or 26 base pairs per repressor, depending on the ionic strength. These end points correspond to complexes containing approximately one, two, or four repressors per 28 base pairs. Boundary sedimentation velocity experiments with saturating amounts of repressor revealed that five repressors can bind to 28 base pairs. By monitoring the circular dichroism as DNA was added to repressor, the sequential appearance of complexes containing approximately four, two, and one repressors per 28 base pairs was observed. The inability of repressor cores or iodinated repressor to bind to complexes containing one or two repressors per 28 base pairs implies that all of the repressors directly contact the DNA in the complex containing four repressors per 28 base pairs. It is proposed that while two subunits of each repressor contact the DNA in complexes containing one or two repressors per 28 base pairs, only one subunit of each repressor contacts the DNA in the complex with four repressors per 28 base pairs. These results suggest a novel mechanism for the one-dimensional diffusion of repressor along DNA.     

External diffusion in solid-phase immunoassays

Calculations are presented describing the influence of external diffusion in the kinetics of solid-phase immunoassays. The analysis is concerned with systems where one reactant is immobilized at the surface of a sphere of arbitrary radius. The solution for a plane surface is found as a limiting case. The factors determining whether the reaction is diffusion or reaction controlled are found to be sphere radius, surface concentration of binding sites, forward reaction rate and diffusion constant of reacting species. Means of determining whether the reaction is diffusion or reaction controlled from observable quantities are described. When applied to heterogeneous antibody-antigen binding it is found that normally the binding to cell-size spheres is not limited by external diffusion. However, when applied to solid-phase assays with high surface concentrations of binding sites immobilized at plane surfaces or macroscopic spheres the binding is found to be diffusion limited. The importance of a mass transfer analysis in this case is also discussed.