Abstract
A simple model of temperature-increase-driven homo- or heteroduplex dissociation is analyzed. It features a temperature-independent association constant, and a dissociation constant that increases with temperature according to an Arrhenius law. The model is analytically tractable for quasiequilibrium conditions, for two special cases in the intermediate regime, and in the strongly irreversible regime. In the latter, the fraction of isolated components depends on temperature according to a Gumbel minimal value distribution. The model suggests a logarithmic dependence of the dissociation temperature on the rate of temperature increase. It further predicts that the dissociation occurs in a twice broader temperature interval for slow than fast temperature increase. Finally, the model points to a previously overlooked source of discrepancy between apparent van't Hoff and calorimetric enthalpies. Applied to short double stranded DNA, the model explains the dependence of the melting temperature on the rate of temperature increase, and the twice lower width of the melting transition in low salt compared to high salt conditions.
Highlights
Natural units for time and temperature are set by the inverse of the dissociation constant k = kdis(Tm ) and by HvH/4. With reference to these units, the rate of temperature increase can be expressed as a dimensionless parameter α: α= k
As α quantifies rates of temperature increase with reference to units of time and temperature set by material properties, it is possible to vary α for fixed heating rate by altering the dissociation constant k, a material property
It is assumed that dissociation is controlled by an Arrhenius law and counteracted by a temperature-independent association reaction
Summary
A simple model for temperature T controlled homo(A = B) or heteroduplex (A = B) dissociation or fission, applicable, for example, to DNA melting, is considered. The model treats dissociation as a single-step event controlled by an Arrhenius law and assumes that dissociation is counteracted by a temperature-independent association reaction. Let T denote the temperature, and Tm the temperature for which 50% of the homo- or heteroduplex is dissociated (“m” stands for “median”) under quasiequilibrium conditions. Use kdis(T ) for the temperature-dependent dissociation rate constant, k for the dissociation rate constant at temperature Tm, and kas for the association rate constant. R is the Boltzmann constant, and H the dissociation enthalpy. The above model can be summarized as follows: AB −k−dis−(T−)−=k−e−→ (T ) A + B,
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