Loop energy in DNA

Thermal denaturation of fluctuating finite DNA chains: the role of bending rigidity in bubble nucleation

Statistical DNA models available in the literature are often effective models where the base-pair state only (unbroken or broken) is considered. Because of a decrease by a factor of 30 of the effective bending rigidity of a sequence of broken bonds, or bubble, compared to the double stranded state, the inclusion of the molecular conformational degrees of freedom in a more general mesoscopic model is needed. In this paper we do so by presenting a one-dimensional Ising model, which describes the internal base-pair states, coupled to a discrete wormlike chain model describing the chain configurations [J. Palmeri, M. Manghi, and N. Destainville, Phys. Rev. Lett. 99, 088103 (2007)]. This coupled model is exactly solved using a transfer matrix technique that presents an analogy with the path integral treatment of a quantum two-state diatomic molecule. When the chain fluctuations are integrated out, the denaturation transition temperature and width emerge naturally as an explicit function of the model parameters of a well defined Hamiltonian, revealing that the transition is driven by the difference in bending (entropy dominated) free energy between bubble and double-stranded segments. The calculated melting curve (fraction of open base pairs) is in good agreement with the experimental melting profile of poly(dA)-poly(dT) and, by inserting the experimentally known bending rigidities, leads to physically reasonable values for the bare Ising model parameters. Among the thermodynamical quantities explicitly calculated within this model are the internal, structural, and mechanical features of the DNA molecule, such as bubble correlation length and two distinct chain persistence lengths. The predicted variation of the mean-square radius as a function of temperature leads to a coherent explanation for the experimentally observed thermal viscosity transition. Finally, the influence of the DNA strand length is studied in detail, underlining the importance of finite size effects, even for DNA made of several thousand base pairs. Simple limiting formulas, useful for analyzing experiments, are given for the fraction of broken base pairs, Ising and chain correlation functions, effective persistence lengths, and chain mean-square radius, all as a function of temperature and DNA length.

Communication Between Noncontacting Macromolecules

Molecular interactions are the language that molecules use to communicate recognition, binding, and regulation, events central to biological control mechanisms. Traditionally, such interactions involve direct, atom-to-atom, noncovalent contacts, or indirect contacts bridged by relatively fixed solvent molecules. Here we discuss a third class of molecular communication that, to date, has received less experimental attention, namely solvent-mediated communication between noncontacting macromolecules. This form of communication can be understood in terms of fundamental, well-established principles (coupled equilibria and linkage thermodynamics) that govern interactions between individual polymers and their solutions. In contrast to simple solutions used in laboratory studies, biological systems contain a multitude of nominally noninteracting biopolymers within the same solution environment. The exquisite control of biological function requires some form of communication between many of these solution components, even in the absence of direct and/or indirect contacts. Such communication must be considered when describing potential mechanisms of biological regulation.

Counterion association with native and denatured nucleic acids: an experimental approach

The melting temperature of the poly(dA) . poly(dT) double helix is exquisitely sensitive to salt concentration, and the helix-to-coil transition is sharp. Modern calorimetric instrumentation allows this transition to be detected and characterized with high precision at extremely low duplex concentrations. We have taken advantage of these properties to show that this duplex can be used as a sensitive probe to detect and to characterize the influence of other solutes on solution properties. We demonstrate how the temperature associated with poly(dA) . poly(dT) melting can be used to define the change in bulk solution cation concentration imparted by the presence of other duplex and triplex solutes, in both their native and denatured states. We use this information to critically evaluate features of counterion condensation theory, as well as to illustrate "crosstalk" between different, non-contacting solute molecules. Specifically, we probe the melting of a synthetic homopolymer, poly(dA) . poly(dT), in the presence of excess genomic salmon sperm DNA, or in the presence of one of two synthetic RNA polymers (the poly(rA) . poly(rU) duplex or the poly(rU) . poly(rA) . poly(rU) triplex). We find that these additions cause a shift in the melting temperature of poly(dA) . poly(dT), which is proportional to the concentration of the added polymer and dependent on its conformational state (B versus A, native versus denatured, and triplex versus duplex). To a first approximation, the magnitude of the observed tm shift does not depend significantly on whether the added polymer is RNA or DNA, but it does depend on the number of strands making up the helix of the added polymer. We ascribe the observed changes in melting temperature of poly(dA) . poly(dT) to the increase in ionic strength of the bulk solution brought about by the presence of the added nucleic acid and its associated counterions. We refer to this communication between non-contacting biopolymers in solution as solvent-mediated crosstalk. By comparison with a known standard curve of tm versus log[Na+] for poly(dA) . poly(dT), we estimate the magnitude of the apparent change in ionic strength resulting from the presence of the bulk nucleic acid, and we compare these results with predictions from theory. We find that current theoretical considerations correctly predict the direction of the t(m) shift (the melting temperature increases), while overestimating its magnitude. Specifically, we observe an apparent increase in ionic strength equal to 5% of the concentration of the added duplex DNA or RNA (in mol phosphate), and an additional apparent increase of about 9.5 % of the nucleic acid concentration (mol phosphate) upon denaturation of the added DNA or RNA, yielding a total apparent increase of 14.5 %. For the poly(rU) . poly(rA) . poly(rU) triplex, the total apparent increase in ionic strength corresponds to about 13.6% of the amount of added triplex (moles phosphate). The effect we observe is due to coupled equilibria between the solute molecules mediated by modulations in cation concentration induced by the presence and/or the transition of one of the solute molecules. We note that our results are general, so one can use a different solute probe sensitive to proton binding to characterize subtle changes in solution pH induced by the presence of another solute in solution. We discuss some of the broader implications of these measurements/results in terms of nucleic acid melting in multicomponent systems, in terms of probing counterion environments, and in terms of potential regulatory mechanisms.

Communication between noncontacting macromolecules

We present a quantitative experimental demonstration of solvent-mediated communication between noncontacting biopolymers. We show that changes in the activity of a solvent component brought about by a conformational change in one biopolymer can result in changes in the physical properties of a second noncontacting biopolymer present in solution. Specifically, we show that the release of protons on denaturation of a donor polymer (in this case, a four-stranded DNA tetraplex, iDNA) modulates the melting temperature of a noncontacting, acceptor polymer [in this case poly(A)]. In addition to such proton-mediated cross talk, we also demonstrate counterion-mediated cross talk between noncontacting biopolymers. Specifically, we show that counterion association/release on denaturation of native salmon sperm DNA (the donor polymer) can modulate the melting temperature of poly(dA) x poly(dT) (the acceptor polymer). Taken together, these two examples demonstrate how poly(A) and poly(dA) x poly(dT) can serve as molecular probes that report the pH and free salt concentrations in solution, respectively. Further, we demonstrate how such through-solvent dialogue between biopolymers that do not directly interact can be used to evaluate (in a model-free manner) association/dissociation reactions of solvent components (e.g., protons, sodium cations) with one of the two biopolymers. We propose that such through-solution dialogue is a general property of all biopolymers. As a result, such solvent-mediated cross talk should be considered when assessing reactions of multicomponent systems such as those that exist in essentially all biological processes.

Thermal stability of DNA

Tij and Delta Hij for stacking of pair i upon j in DNA have been obtained over the range 0.034-0.114 M Na+from high-resolution melting curves of well-behaved synthetic tandemly repeating inserts in recombinant pN/MCS plasmids. Results are consistent with neighbor-pair thermodynamic additivity, where the stability constant, sij , for different domains of length N depend quantitatively on the product of stability constants for each individual pair in domains, sijN . Unit transition enthalpies with average errors less than +/-5%, were determined by analysis of two-state equilibria associated with the melting of internal domains and verified from variations of Tij with [Na+]. Enthalpies increase with Tij , in close agreement with the empirical function: Delta Hij = 52.78@ Tij - 9489, and in parallel with a smaller increase in Delta Sij . Delta Hij and Delta Sij are in good agreement with the results of an extensive compilation of published Delta Hcal and Delta Scal for synthetic and natural DNAs. Neighbor-pair additivity was also observed for (dA@dT)-tracts at melting temperatures; no evidence could be detected of the familiar and unusual structural features that characterize tracts at lower temperatures. The energetic effects of loops were determined from the melting behavior of repeating inserts installed between (G+C)-rich barrier domains in the pN/MCS plasmids. A unique set of values for the cooperativity, loop exponent and stiffness parameters were found applicable to internal domains of all sizes and sequences. Statistical mechanical curves calculated with values of Tij([Na+]) , Delta Hij and these loop parameters are in good agreement with observation.

Parallel-stranded DNA under topological stress: rearrangement of (dA)15.(dT)15 to a d(A.A.T)n triplex

DNA oligonucleotides with appropriate sequences can form a stable duplex in which the two strands are paired in a parallel orientation instead of as the conventional antiparallel double helix of B-DNA. In parallel-stranded DNA (ps-DNA) base pairing is noncanonical with the glycosidic bonds in a trans orientation. The two grooves are equivalent. We have synthesized DNA duplexes consisting of a central parallel-stranded (dA)15.(dT)15 tract flanked by normal antiparallel regions, and ligated them into the pUC18 plasmid. The effect of negative supercoiling on the covalently closed circular molecules was studied by two-dimensional agarose gel electrophoresis and by chemical modification with OsO4-pyridine (Os,py) and diethylpyrocarbonate (DEPC). The following results were obtained: (i) The ps insert, and by inference ps-DNA in general, adopts a right handed helical form. (ii) Upon increasing the negative superhelix density (-sigma) to greater than 0.03 the 15 bp ps insert undergoes a major transition leading to a relaxation corresponding to a reduction in twist of approximately 2.5 helical turns. The transition free surgery is approximately kcal/mol. (iii) The chemical modification pattern of the resulting structure suggests that the purine strand folds back and associates with the pyrimidine strand, forming a novel intramolecular triplex structure consisting of d(A.A.T) base triplets. A model for the triplex conformation is proposed and its thermodynamic properties are analyzed by statistical mechanics.

Parallel-stranded DNA under topological stress: rearrangement of (dA)15.(dT)15 to a d(A.A.T)n triplex

DNA oligonucleotides with appropriate sequences can form a stable duplex in which the two strands are paired in a parallel orientation instead of as the conventional antiparallel double helix of B-DNA. In parallel-stranded DNA (ps-DNA) base pairing is noncanonical with the glycosidic bonds in a trans orientation. The two grooves are equivalent. We have synthesized DNA duplexes consisting of a central parallel-stranded (dA)15.(dT)15 tract flanked by normal antiparallel regions, and ligated them into the pUC18 plasmid. The effect of negative supercoiling on the covalently closed circular molecules was studied by two-dimensional agarose gel electrophoresis and by chemical modification with OsO4-pyridine (Os,py) and diethylpyrocarbonate (DEPC). The following results were obtained: (i) The ps insert, and by inference ps-DNA in general, adopts a right handed helical form. (ii) Upon increasing the negative superhelix density (-sigma) to greater than 0.03 the 15 bp ps insert undergoes a major transition leading to a relaxation corresponding to a reduction in twist of approximately 2.5 helical turns. The transition free surgery is approximately kcal/mol. (iii) The chemical modification pattern of the resulting structure suggests that the purine strand folds back and associates with the pyrimidine strand, forming a novel intramolecular triplex structure consisting of d(A.A.T) base triplets. A model for the triplex conformation is proposed and its thermodynamic properties are analyzed by statistical mechanics.

Electrostatic forces at helix-coil boundaries in DNA

The Tm of internal loop-forming (dA.dT)N domains in pBR322 DNA has been measured over a tenfold range of [Na+]. The slopes SN = dTm/d log [Na+] are linear and decrease in magnitude with decreasing loop size N, signaling a reduction in Na+ released during the transition of these domains to the coil state. Values of SN decrease linearly with increasing N-1 in accordance with the expectation of a simple model for the occurrence of a gradient of long-range electrostatic forces at helix-coil boundaries, and extrapolate almost precisely to the value of S infinity observed for (dA.dT) infinity. These results indicate (1) less counterion is released per phosphate residue from the finite loop than from the infinite-sized loop, and (2) the difference in binding is constant for each boundary formed and independent of the size of the loop within the range examined: approximately 350 base pair (bp) greater than N greater than 71 bp. The slope of the dependence of SN on N-1 indicates the region of higher charge density at the boundary extends at least 18 A into the coil and probably 40-50 A before dropping to a value characteristic of the unperturbed coil. The free energy for excess counterion binding at boundaries can be expressed by -delta G/RT = 10.47 log[Na+] + 5.234 When the loop entropy function in a statistical mechanical algorithm for the dissociation of DNA is weighted by this quantity, calculated Tm are seen to vary by only +/- 0.09 degrees C from observed.