1.4 The B-A transition of DNA double helices
1.4.3 B-A transition is cooperative
Cooperative processes are observed in polymers. If a process consists of a series of equivalent reaction steps, it can undergo a cooperative process. A process is referred as cooperative, if it is carried out at once by a group of reaction steps rather than by individual reactions. Cooperative conformational transitions are of great importance in the understanding of biological processes such as enzyme regulation, synthesis and denaturation of nucleic acids and proteins etc. The formation of an α-helix from a disordered polypeptide, which is a cooperative transition, is one of the most studied transitions in polypeptides. Depending on various factors such as temperature, solvent, pH and salt concentration, polypeptides exist in a state of either
random coils or of the more highly ordered α- helix. The transitions between the two conformations are usually quite sharp, which is characteristic of a cooperative phenomenon. Moreover, the rate of forming a helix from the random coil state is very fast, generally occurring within 10-5 to 10-7sec, and is independent of the length of the polypeptide chain. In contrast, the rate of unravelling is strongly size dependent (Creighton, 1983).
A cooperative transition is reflected by a sharp transition curve. If the transition is a non-cooperative one or if the chain length is below the cooperative length, a broad transition curve will be obtained. The B-A transition is found to have a relatively narrow transition curve, which indicates that this transition might be cooperative. If the B-A transition is cooperative, the base pairs will take part as a group. For this reason within a transition interval, a long DNA molecule is subdivided into alternating parts of B- and A- conformations (Krylov et al., 1990). Then there will be two types of junction points A/B or B/A, which are specific boundary conformation, probably different from both A-and B-conformations. The boundary concentration is maximal at a half transition point, i.e., at an alcohol content where there are equal A- and fractions. At this point the difference between the A- and B-form free energies is equal to zero. Hence the relative concentration of boundaries is determined solely by the free energy of boundary Fj.
[A/B]/[DNA] = exp (-Fj/RT)
where, [A/B] is the concentration of A/B junction, [DNA] is the concentration of DNA, R is the universal gas constant and T is the temperature.
The inverse value, evidently an average distance between neighbouring boundaries at the transition point is called the cooperativity length ν:
ν = exp (Fj/RT) or Fj = RT ln ν
So the higher is the boundary energy, the more cooperative the transition is, and the transition curve will have less width.
Ivanov and Krylov (1992) described three independent methods to show the cooperative character of B-A transition and determined the cooperative length of this transition. In the first method, ligands, which binds specifically with either B for or A form is used. The theory of co-operative transitions in the presence of ligands, developed by Frank-Kamenetskii and Karapetyan (1972) for helix – coil transition, was used to determine the cooperativity length. According to this theory, the
cooperative length ν0 can be determined using the formula, ν0 = (4/∆a) clim0 (δat)2 / (cδ∆a)
where, ∆a is the width of the transition curve without ligands, δat is the shift of the mid point of transition in the presence of a concentration of ligands, c, expressed as the number of ligands per base pair and δ∆a is the change in the width of the transition. The condition for the selection of ligands is that the ligand binding constant of one of the DNA forms is at least 10 times higher than that of the other one or the widening between the two curves should be two times larger than the shift of the transition point. Netropsin, which stabilizes B-form, and spermine which stabilizes A-form, were used as the ligand. Using these ligands, the cooperative length was found to be 10-30 base pairs (Ivanov et al., 1974; Minyat et al., 1979).
The second method was based on the phase diagram of A, B, and coil forms. Poly [d(A-T)] was used as the model system and the change in enthalpy of the polynucleotide melting was determined by calorimetry. The slope of the A-coil and B-coil branches in the vicinity of the triple point was obtained from the phase diagram. Using these parameters and the width of the B-A transition for poly [d(A-T)], a cooperative length of 30 base pair for B-A transition was obtained. (Ivanov et al., 1983,1985).
The drawback of the first method was the use of a foreign compound, whose size is comparable to the cooperativity length of the B-A transition. This problem was overcame by doing experiments with short fragments, where the length of the fragment is equal to or less than that of the cooperative length. Here the duplex will undergo the transition in an all-or-none principle, that is, without B-A junctions.
B-A transition was followed in four self-complementary decadeoxyduplexes and found that all transitions have the same width of about 6% in terms of relative humidity. Using this transition width and the free energy parameters obtained from phase diagrams a cooperative length B-A transition was found to be approximately 16 base pairs.
The accuracy of these independent determinations is not very high. But all of them provided similar values and this confirms that the cooperative length of B-A transition is in the range of 10-30 base pairs. For comparison, helix to coil transition in DNA is characterized by a cooperativity length ν = 102 pairs (Frank-Kamenetskii, 1974), for B to Z transition ν = 10-25 base pairs (Ivanov and Minyat, 1981; Ivanov et
al., 1983).
But molecular dynamics simulation studies showing the B-A transition occurring within a few nanoseconds and the absence of any significant activation barrier suggested by Dickerson et al (2001) using a continuum of X-ray structures between B and A forms speaks against the cooperativity of B-A transition. Therefore, there is an ambiguity about the cooperative nature of B-A transition. To arrive at a conclusion about the cooperativity of B-A transition, the width of the transition for different chain lengths should be followed. For chain lengths above the cooperative length, a narrow transition range will be observed. Reasonable awareness about the time constants of this transition can reveal some idea about the cooperative nature of the B-A transition. It is expected that chain lengths above the cooperative length will undergo the transition at the same rate, whereas for those below the cooperative length, a noticeable retardation will be observed.