Smoluchowski Equations for Agglomeration in Conditions of Variable Temperature and Pressure and a New Scaling of Rate Constants: Application to Nozzle-Beam Expansion.

The Smoluchowski equations provide a rigorous and efficient means for including multiple kinetic pathways when modeling coalescence growth systems. Originally written for a constant temperature and volume system, the equations must be modified if temperature and pressure vary during the coalescence time. In this paper, the equations are generalized, and adaptations appropriate to the situation presented by supersonic nozzle beam expansions are described. Given rate constants for all the cluster-cluster reactions, solution of the Smoluchowski equations would yield the abundances of clusters of all sizes at all times. This is unlikely, but we show that if these rate constants scale with the sizes of the reacting partners, the asymptotic (large size and large time) form of the cluster size distribution can be predicted. Experimentally determined distributions for He fit the predicted asymptotic distribution very well. Deviations between predicted and observed distributions allow identification of special cluster sizes that is, magic numbers. Furthermore, fitting an observed distribution to the theoretical form yields the base agglomeration cross section, from which all cluster-cluster rate constants may be obtained by scaling. Comparing the base cross section to measures of size and reactivity gives information about the coalescence process.

Scaling and the Smoluchowski equations.

The Smoluchowski equations, which describe coalescence growth, take into account combination reactions between a j-mer and a k-mer to form a (j+k)-mer, but not breakup of larger clusters to smaller ones. All combination reactions are assumed to be second order, with rate constants K(jk). The K(jk) are said to scale if K(lambda j,gamma k) = lambda(mu)gamma(nu)K(jk) for j < or = k. It can then be shown that, for large k, the number density or population of k-mers is given by Ak(a)e(-bk), where A is a normalization constant (a function of a, b, and time), a = -(mu+nu), and b(mu+nu-1) depends linearly on time. We prove this in a simple, transparent manner. We also discuss the origin of odd-even population oscillations for small k. A common scaling arises from the ballistic model, which assumes that the velocity of a k-mer is proportional to 1/square root of m(k) (Maxwell distribution), i.e., thermal equilibrium. This does not hold for the nascent distribution of clusters produced from monomers by reactive collisions. By direct calculation, invoking conservation of momentum in collisions, we show that, for this distribution, velocities are proportional to m(k)(-0.577). This leads to mu+nu = 0.090, intermediate between the ballistic (0.167) and diffusive (0.000) results. These results are discussed in light of the existence of systems in the experimental literature which apparently correspond to very negative values of mu+nu.

Application of scaling and kinetic equations to helium cluster size distributions: Homogeneous nucleation of a nearly ideal gas.

A previously published model of homogeneous nucleation [Villarica et al., J. Chem. Phys. 98, 4610 (1993)] based on the Smoluchowski [Phys. Z. 17, 557 (1916)] equations is used to simulate the experimentally measured size distributions of 4He clusters produced in free jet expansions. The model includes only binary collisions and does not consider evaporative effects, so that binary reactive collisions are rate limiting for formation of all cluster sizes despite the need for stabilization of nascent clusters. The model represents these data very well, accounting in some cases for nearly four orders of magnitude in variation in abundance over cluster sizes ranging up to nearly 100 atoms. The success of the model may be due to particularities of 4He clusters, i.e., their very low coalescence exothermicity, and to the low temperature of 6.7 K at which the data were collected.

Drug-RNA footprinting.

RNase I and RNase T1 can be used to obtain high-quality footprinting information for paromomycin binding to a 176-mer RNA from the packaging region of HIV-1 (LAI). Controls and scanning procedures are necessary for quantitation of autoradiographic data, so that footprinting plots showing cutting behavior as a function of drug concentration can be used to identify binding sites and regions of altered structure on the 176-mer. From the RNase I footprinting results the primary paromomycin binding sites on the 176-mer are on the main stem and on the stem of SL1, but noncontiguous sequences may be involved in the same binding event. Strong enhancements in cleavage with added drug are also observed, indicating drug-induced structural changes. Drug binding may cause linker regions between stem-loops of the 176-mer to change structure, possibly providing a site or sites for additional drug binding. Because drug binding changes the structure of the packaging region, which may alter its function, paromomycin analogs with enhanced specificity for HIV psi RNA have potential as a new class of agent for treating AIDS.

Binding of human immunodeficiency virus type 1 nucleocapsid protein to psi-RNA-SL3.

The interaction of the nucleocapsid protein NCp7, from the pNL4-3 isolate of HIV-1, with psi-RNA-SL3, with the sequence 5'-GGACUAGCGGAGGCUAGUCC, was studied using non-denaturing gel electrophoresis. Two kinds of experiments were performed, using buffered solutions of radiolabeled RNA and unlabeled protein. In the 'dilution' experiments, the total RNA concentration, RT, was varied for a series of solutions, but kept equal to the total protein concentration, PT, In the 'titration' experiments, solutions having RT constant but with varying PT were analyzed. The solutions were electrophoresed and the autoradiographic spot intensities, proportional to the amounts of the different species present, were measured. The intensities were fit to a number of equilibrium models, differing in species stoichiometries, by finding the best values of the binding constants. It was shown that NCp7 protein and SL3 RNA combine to form at least two complexes. When PT is below approximately 10 microM, a complex that contains two RNAs and one protein forms. Increasing PT to approximately 100 microM causes the 2:1 complex to oligomerize, forming a species having eight RNAs and four proteins. For the dilution experiments, run at 5 degrees C at an ionic strength of 31 mM, we found K1 for the 2:1 complex is approximately 10(11) M(-2) and K2 for the 8:4 complex is approximately 10(16) M(-3). The titration experiments returned K1 approximately 10(7) M(-2) (poorly determined) and K2 approximately 10(19) M(-3). The analysis was complicated by the loss of RNA at higher protein concentrations, due to formation of an insoluble species containing both RNA and protein, which does not enter the gel. Correcting for this changes the calculated values of equilibrium constants, but not the molecularities determined by our analysis. The observation that a small complex can oligomerize to form a larger species is consistent with the fact that NCp7 organizes and condenses the genome in the virus particle.

Monomer-dimer equilibrium constants of RNA in the dimer initiation site of human immunodeficiency virus type 1.

The genome of the human immunodeficiency virus (HIV) exists as a dimer of two identical RNA molecules hydrogen bonded to each other near their 5' ends. The dimer, known to be important for viral infectivity, is formed by two monomers interacting through a stem-loop structure called the dimer initiation site (DIS). An initially formed intermediate, the "kissing" dimer, is unstable and rearranges to the stable, duplex form. In this report we use nondenaturing polyacrylamide gel electrophoresis to measure the monomer-dimer equilibrium constant of three RNA sequences, 41-, 27-, and 19-mers, located in the DIS of the MAL isolate of HIV-1. Experiments in which the RNA was equilibrated at various temperatures before electrophoresis revealed that interconversion is rapid for all the sequences, so that they reach equilibrium in the loading well of the gel at 5 degrees C before they enter the gel proper. However, interconversion kinetics in the gel are slow, so autoradiographic spot intensities can be used to measure the amounts of monomer and dimer present when the sample entered the gel. After correction for the amount of RNA added with the radiolabel and dilution of samples in the loading well of the gel, dimerization equilibrium constants were calculated from spot intensities. The calculated values of the dimerization constant K at 5 degrees C were approximately 10(5), approximately 10(6), and approximately 10(8) M(-1) for the 41-, 27-, and 19-mers, respectively, in solutions of ionic strength, I, of about 100 mM. The decrease in K by three orders of magnitude between the 19-mer and 41-mer is due in part to the change in rotational entropy of rodlike molecules on dimerization and in part to the increased conformational entropy of the monomers. As expected, increased ionic strength increases the dimerization constant for all three RNAs. For the 41-mer, however, K has a maximum value at I approximately 140 mM. The origin of the decrease in K for higher I is unknown but it may be due to formation of species (perhaps higher order oligomers) that do not enter the gel. The 41-mer exists in two dimeric forms assigned to the kissing and duplex dimers. The ratio of kissing to duplex form at 5 degrees C is 0.48 +/- 0.22 at I = 113 mM and 0.91 +/- 0.35 at I = 183 mM. The observed decrease in K with RNA length suggests that the dimerization constant of the packaging region of HIV-1 is small, < approximately 10(5) M(-1), implying that the nucleocapsid protein is important in promoting dimerization in the capsid of the virus.

Quantitation of ethidium-stained closed circular DNA in agarose gels.

The fluorescence of ethidium bromide (EB) bound to equimolar amounts of supercoiled form I and unstrained linear form III pBR322, SV40 and PM2 DNA in agarose gels has been measured by scanning a photographic negative of the gel with a microdensitometer. For SV40 and PM2 DNA, commonly used staining conditions cause both forms, i.e. linear and supercoiled, to fluoresce to the same extent. This obviates the need to use a correction factor for the fluorescence of form I DNA when measuring the amount of this form relative to the amounts of unstrained forms in agarose gels. In the case of PBR322 DNA, form I was found to fluoresce approximately 20% more than form III DNA.

Kinetics of cleavage of intra- and extracellular simian virus 40 DNA with the enediyne anticancer drug C-1027.

A kinetic analysis of cleavage of simian virus DNA (SV40 DNA) inside and outside green monkey BSC-1 cells by the enediyne-protein antibiotic C-1027 and its free chromophore is described. Information on rate constants was obtained by fitting populations of forms I (closed circular DNA), II (nicked circular DNA) and III (linear DNA) SV40 DNA as a function of drug concentration to a kinetic model which includes: cutting of form I to give form II with rate constant k1, cutting of form I to give form III with rate constant K4, and cutting of form II to give form III with rate constant k2. The ratio of single-strand (ss) to double-strand (ds) cutting for the holoantibiotic and the free chromophore, k1/k4, is approximately 1.8 for extracellular SV40 DNA. For intracellular DNA and extracellular DNA which has been post-treated with putrescine, ds cutting is much more probable, with k4 about four times as large as k1. This observation suggests that amine groups present in the cell are able to convert abasic sites opposite an ss break into a ds break in SV40 chromatin. The overall rate of cleavage of form-I DNA inside the cell is much larger than the rate outside, the sum k1 + k4 being about three times as large for intracellular DNA as for extracellular DNA.

Kinetic analysis of drug cleavage of closed-circular DNA.

Various cleavage agents interact with circular double-stranded DNA molecules to convert the closed-circular form (form-I) to the open-circular (form-II) and linear (form-III) forms, and ultimately to small DNA fragments. The various cutting processes which take place in the DNA pool are here analyzed kinetically, and, by solving the kinetic equations, expressions are derived for the amounts of the closed-circular, open-circular, and linear forms of DNA as a function of reaction time and concentration of cleavage agent. Conversions between subspecies of forms II and III, differing in numbers of internal cuts, are taken into account. The only assumption required to solve the kinetic equations is that the concentration of cleavage agent obeys [D] = D0 f(t) where the function of time f(t) is independent of D0, the initial concentration of cleavage agent. By choosing parameters in the expressions for the calculated amounts of forms I, II and III to give the best fit to the measured amounts, one obtains information about the rates and rate constants for the conversions. The rate constants in turn give important information about the specificity and mechanism of action of the cleavage agents. The analysis is applied to the cleavage of pBR322, SV-40 and PM2 DNAs by DNase I, Fe-EDTA, and the antitumor agents calicheamicin and bleomycin. Cleavage rate constants are derived and discussed for these systems.

Cleavage of DNA by the insulin-mimetic compound, NH4[VO(O2)2(phen)].

The kinetics and mechanism of cleavage of DNA by the insulin-mimetic peroxo-vanadate NH4[VO(O2)2(phen)], pV, are described. In the presence of low energy UV radiation or biologically common reducing agents, pV decomposes into the monomer, dimer, and tetramer of vanadate and an uncharacterized compound of V4+ as shown by 51V NMR, ESR, and absorption spectra. The rate of photodecomposition of pV is reduced in the presence of calf thymus DNA, indicating that a decomposition product of the peroxo-vanadate, that is important in the destruction pathway of the complex, is interacting with DNA. This species, probably a short-lived complex of V4+, may also be responsible for the observed catalytic decomposition of pV in the absence of DNA by ascorbate. If closed circular pBR322 DNA is present when the peroxo-vanadate is destroyed by either UV radiation or reducing agents, the polymer may have its sugar-phosphate backbone broken. Closed circular DNA (form I) is converted into nicked circular DNA (form II) and linear DNA (form III). The amounts of the various forms produced as a function of irradiation time and peroxo-vanadate concentration were fit to a kinetic model to derive rate constants for the conversions. The kinetic analysis shows that pV is a single-strand nicking agent which exhibits some base and/or sequence preference. Furthermore, the pH dependences of the rates for conversion of form I to form II and for conversion of form II to form III are different, indicating that the nature of the chemistry at the site of cleavage on DNA influences further cutting by activated pV. Reduced amounts of DNA breakage in the presence of various salts and metal binding ligands indicate that a short-lived reactive complex of V4+, not the V4+ species detected by ESR at long irradiation times, is important in the cleavage process. The susceptibility of pV to decomposition by biologically common reducing agents suggests that metabolites of the agent, and not the compound itself, are responsible for its insulin-mimetic effects.

Chemically and photochemically initiated DNA cleavage by an insulin-mimetic bisperoxovanadium complex.

Chemically and photochemically induced cleavage of DNA by the insulin-mimetic compound NH4[VO(O2)2-(1,10-phenanthroline)], bpV(phen), have been studied. 51V NMR and absorption indicate that photoirradiation with low energy UV light of aqueous solutions containing bpV(phen) leads to the conversion of the compound to simple vanadates. Photoillumination of the compound in the presence of supercoiled pBR322 DNA results in cutting of the plasmid to produce nicked circular and linear DNA. Quantitative analysis of agarose gel data shows that bpV(phen) is a single strand nicking agent exhibiting sequence and/or base specificity.

Quantitative footprinting analysis.

This review outlines the steps for obtaining relative binding constants for drugs from footprinting data. After correcting the autoradiographic spot intensities for differing amounts of radioactive DNA loaded into the lanes of a sequencing gel, footprinting plots, showing individual spot intensities as a function of drug concentration, are constructed. The initial relative slopes of footprinting plots are proportional to the binding constant of the drug for its DNA site. Slopes of plots outside of drug binding sites can be used to identify locations of altered DNA structure. It illustrates the power of quantitative footprinting analysis by analyzing the binding of the antiviral agent netropsin to a 139-base pair restriction fragment in the presence of the antitumor agent actinomycin D. While two netropsin binding regions are unaffected by actinomycin D a third region experiences enhanced binding in the presence of the antitumor agent.

Interaction of cationic porphyrins with DNA.

Utilizing linear dichroism (LD), circular dichroism (CD), and fluorescence energy transfer, the binding geometries of a series of Co(3+)-porphyrins and their free ligands were examined. The compounds studied were Co-meso-tetrakis(N-methylpyridinium-4-yl)porphyrin (CoTMPyP) and its free ligand (H2-TMPyP), Co-meso-tetrakis(N-n-butylpyridinium-4-yl)porphyrin (CoTBPyP) and its free ligand (H2TBPyP), and Co-meso-tetrakis(N-n-octylpyridinium-4-yl)porphyrin (CoTOPyP). The two non-metalloporphyrins exhibit negative LD, having angles of roughly 75 degrees relative to the DNA helix axis. They also display negative CD and a significant contact energy transfer from the DNA bases. On the other hand, the three metalloporphyrins display orientation angles of roughly 45 degrees between the porphyrin plane and the helix axis of DNA. Furthermore, they exhibit positive CD and no contact energy transfer from DNA bases. These observations show that the metalloporphyrins are not intercalated whereas non-metalloporphyrins having four freely rotating meso-aryl groups intercalate between the base pairs of DNA. In the presence of KHSO5, the cobalt porphyrins cleave closed circular PM2 DNA in a single strand manner, i.e., a single activation event on the porphyrin leads to a break in one of the DNA strands. A kinetic analysis of the cleavage data revealed that cleavage rates are in the order CoTMPyP > CoTBPyP > CoTOPyP with the difference being due to different DNA affinities rather than differences in cleavage rate-constants. Based on these and earlier observations, the metalloporphyrins appear bound to a partially melted region of DNA.

Quantitative footprinting analysis of the chromomycin A3--DNA interaction.

Chromomycin A3 (CHR) binding to the duplex d(CAAGTCTGGCCATCAGTC).d(GACTGATGGCCAGACTTG) has been studied using quantitative footprinting methods. Previous NMR studies indicated CHR binds as a dimer in the minor groove. Analysis of autoradiographic spot intensities derived from DNase I cleavage of the 18-mer in the presence of various amounts of CHR revealed that the drug binds as a dimer to the sequence 5'-TGGCCA-3',3'-ACCGGT-5' in the 18-mer with a binding constant of (2.7 +/- 1.4) x 10(7) M-1. Footprinting and fluorescence data indicate that the dimerization constant for the drug in solution is approximately 10(5) M-1. Since it has been suggested that CHR binding alters DNA to the A configuration, quantitative footprinting studies using dimethyl sulfate, which alkylates at N-7 of guanine in the major groove, were also carried out. Apparently, any drug-induced alteration in DNA structure does not affect cleavage by DMS enough to be observed by these experiments.

Site-specific binding constants for actinomycin D on DNA determined from footprinting studies.

We report site-specific binding constants for the intercalating anticancer drug actinomycin D (Act-D), binding to a 139-base-pair restriction fragment from pBR 322 DNA. The binding constants are derived from analysis of footprinting experiments, in which the radiolabeled 139-mer is cleaved using DNase I, the cleavage products undergo gel electrophoresis, and, from the gel autoradiogram, spot intensities, proportional to amounts of cleaved fragments, are measured. A bound drug prevents DNase I from cleaving at approximately 7 bonds, leading to decreased amounts of corresponding fragments. With the radiolabel on the 3' end of the noncoding strand (A-label), we measured relative amounts of 54 cleavage products at 25 Act-D concentrations. For cleavage of the 139-mer with the label on the 3' end of the coding strand (G-label), relative amounts of 43 cleavage products at 11 Act-D concentrations were measured. These measurements give information about approximately 120 base pairs of the restriction fragment (approximately 12 turns of the DNA helix); in this region, 14 strong and weak Act-D binding sites were identified. The model used to interpret the footprinting plots is derived in detail. Binding constants for 14 sites on the fragment are obtained simultaneously. It is important to take into account the effect of drug binding at its various sites on the local concentration of probe elsewhere. It is also necessary to include in the model weak as well as strong Act-D sites on the carrier DNA which is present, since the carrier DNA controls the free-drug concentration. As expected, the strongest sites are those with the sequence (all sequences are 5'----3') GC, with TGCT having the highest binding constant, 6.4 x 10(6) M-1. Sites having the sequence GC preceded by G are weak binding sites, having binding constants approximately 1 order of magnitude lower than those of the strong sites. Also, the non-GC-containing sequences CCG and CCC bind Act-D with a binding constant comparable to those of the weak GGC sites. The analysis may reveal drug-induced structural changes on the DNA, which are discussed in terms of the mechanism of Act-D binding.

Structural changes and enhancements in DNase I footprinting experiments.

In footprinting experiments, an increase in DNA cleavage with addition of ligand to a system may be due to a ligand-induced structural change. Ligand binding also enhances cleavage by displacing the cleavage agent from ligand-binding sites, thus increasing its concentration elsewhere. The theory and characteristics of this mass-action enhancement are given, and it is shown how it may be recognized. Results of DNase I footprinting of small oligomers, with actinomycin D as ligand, are analyzed to reveal which enhancements are due to mass action, and which can reasonably be ascribed to structural changes. Patterns in the footprinting plots from our experiments on actinomycin D binding to a 139-base-pair DNA fragment (with DNase I as a probe) are studied in the same way. The likely origins of these patterns are discussed, as are enhancements occurring with other probes commonly used in footprinting experiments.

Thermodynamic data from drug-DNA footprinting experiments.

Sequence-dependent thermodynamic quantities for the antiviral agent netropsin and a related bis(N-methylimidazole) dipeptide, lexitropsin, have been determined by DNase I footprinting techniques. The primary data are autoradiographic spot intensities derived from 10 footprinting experiments carried out in the temperature range 0-45 degrees C. After exclusion effects due to overlapped drug sites on DNA and redistribution phenomena associated with the enzyme were accounted for, sequence-dependent binding constants for the two ligands were calculated. Our approach does not require an independent determination of the free drug concentration, which is calculated, with individual site binding constants, by using only footprinting data. The temperature dependence of the binding constants for netropsin implied that the binding enthalpies for all the sites but one on a 139 base pair restriction fragment of pBR 322 DNA are exothermic. Their values roughly correlate with the free energies of binding, which are smaller for sites including a 5'-TA-3' sequence. The binding enthalpies for the lexitropsin to all its sites were exothermic and more negative than those of netropsin. This may be due to the greater ability of the lexitropsin, when compared to netropsin, to form hydrogen bonds with sites on DNA. The binding constants of the lexitropsin toward its GC interaction sequences were much lower than those of netropsin, as can be explained by the reduced charge of the former ligand. Although it is difficult to determine the specific origin of the thermodynamic effects measured, comparison between netropsin and the lexitropsin suggests that the degree of solvation in the minor groove of DNA may be a factor influencing the entropy of the binding process.

Quantitative footprinting analysis. Binding to a single site.

The theory for measuring ligand binding constants from footprinting autoradiographic data associated with a single binding site is derived. If the ligand and DNA cleavage agent compete for a common site, the spot intensities are not proportional to the amount of DNA not blocked by ligand. The analysis of a single site is experimentally illustrated by using results for the anticancer drug actinomycin D interacting with the duplex d(TAGCGCTA)2 as probed with the hydrolytic enzyme DNase I.