Dynamics of DNA melting

Modelling Asymmetric Unemployment Dynamics: The Logarithmic-Harmonic Potential Approach

Asymmetric behaviour has been documented in unemployment rates which increase quickly in recessions but decline relatively slowly during expansions. To model such asymmetric dynamics, this paper provides a rigorous derivation of the asymmetric mean-reverting fundamental dynamics governing the unemployment rate based on a model of a simple labour supply and demand (fundamental) relationship, and shows that the fundamental dynamics is a unique choice following the Rayleigh process. By analogy, such a fundamental can be considered as a one-dimensional overdamped Brownian particle moving in a logarithmic–harmonic potential well, and a simple prototype of stochastic heat engines. The solution of the model equation illustrates that the unemployment rate rises faster with more flattened potential well of the fundamental, more ample labour supply, and less anchored expectation of the unemployment rate, suggesting asymmetric unemployment rate dynamics in recessions and expansions. We perform explicit calibration of both the unemployment rate and fundamental dynamics, confirming the validity of our model for the fundamental dynamics.

A least microenvironmental uncertainty principle (LEUP) as a generative model of collective cell migration mechanisms

Collective migration is commonly observed in groups of migrating cells, in the form of swarms or aggregates. Mechanistic models have proven very useful in understanding collective cell migration. Such models, either explicitly consider the forces involved in the interaction and movement of individuals or phenomenologically define rules which mimic the observed behavior of cells. However, mechanisms leading to collective migration are varied and specific to the type of cells involved. Additionally, the precise and complete dynamics of many important chemomechanical factors influencing cell movement, from signalling pathways to substrate sensing, are typically either too complex or largely unknown. The question is how to make quantitative/qualitative predictions of collective behavior without exact mechanistic knowledge. Here we propose the least microenvironmental uncertainty principle (LEUP) that may serve as a generative model of collective migration without precise incorporation of full mechanistic details. Using statistical physics tools, we show that the famous Vicsek model is a special case of LEUP. Finally, to test the biological applicability of our theory, we apply LEUP to construct a model of the collective behavior of spherical Serratia marcescens bacteria, where the underlying migration mechanisms remain elusive.

Freezing Transition in the Barrier Crossing Rate of a Diffusing Particle

We study the decay rate θ(a) that characterizes the late time exponential decay of the first-passage probability density F_{a}(t|0)∼e^{-θ(a)t} of a diffusing particle in a one dimensional confining potential U(x), starting from the origin, to a position located at a>0. For general confining potential U(x) we show that θ(a), a measure of the barrier (located at a) crossing rate, has three distinct behaviors as a function of a, depending on the tail of U(x) as x→-∞. In particular, for potentials behaving as U(x)∼|x| when x→-∞, we show that a novel freezing transition occurs at a critical value a=a_{c}, i.e., θ(a) increases monotonically as a decreases till a_{c}, and for a≤a_{c} it freezes to θ(a)=θ(a_{c}). Our results are established using a general mapping to a quantum problem and by exact solution in three representative cases, supported by numerical simulations. We show that the freezing transition occurs when in the associated quantum problem, the gap between the ground state (bound) and the continuum of scattering states vanishes.

DNA breathing dynamics under periodic forcing: Study of several distribution functions of relevant Brownian functionals

In this paper, we study DNA breathing dynamics in the presence of an external periodic force by proposing and inspecting several probability distribution functions (PDFs) of relevant Brownian functionals which specify the bubble lifetime, reactivity, and average size. We model the bubble dynamics process by an overdamped Langevin equation of broken base pairs on the Poland-Scheraga free energy landscape. Introducing an effective time-independent description for timescales larger than T[over ̃]=2π/ω (where ω is the frequency of external periodic force) and using an elegant backward Fokker-Planck method we derive closed form expressions of several PDFs associated with such stochastic processes. For instance, with an initial bubble size of x_{0}, we derive the following analytical expressions: (i) the PDF P(t_{f}|x_{0}) of the first passage time t_{f} which specifies the lifetime of the DNA breathing process, (ii) the PDF P(A|x_{0}) of the area A until the first passage time, and it provides much valuable information about the average bubble size and reactivity of the process, and (iii) the PDF P(M) associated with the maximum bubble size M of the breathing process before complete denaturation. Our analysis is limited to two limits: (a) large bubble size and (b) small bubble size. We further confirm our analytical predictions by computing the same PDFs with direct numerical simulations of the corresponding Langevin equations. We obtain very good agreement of our theoretical predictions with the numerically simulated results. Finally, several nontrivial scaling behaviors in the asymptotic limits for the above-mentioned PDFs are predicted, which can be verified further from experimental observation. Our main conclusion is that the large bubble dynamics is unaffected by the rapidly oscillating force, but the small bubble dynamics is significantly affected by the same periodic force.

ssDNA Pairing Accuracy Increases When Abasic Sites Divide Nucleotides into Small Groups

Accurate sequence dependent pairing of single-stranded DNA (ssDNA) molecules plays an important role in gene chips, DNA origami, and polymerase chain reactions. In many assays accurate pairing depends on mismatched sequences melting at lower temperatures than matched sequences; however, for sequences longer than ~10 nucleotides, single mismatches and correct matches have melting temperature differences of less than 3°C. We demonstrate that appropriately grouping of 35 bases in ssDNA using abasic sites increases the difference between the melting temperature of correct bases and the melting temperature of mismatched base pairings. Importantly, in the presence of appropriately spaced abasic sites mismatches near one end of a long dsDNA destabilize the annealing at the other end much more effectively than in systems without the abasic sites, suggesting that the dsDNA melts more uniformly in the presence of appropriately spaced abasic sites. In sum, the presence of appropriately spaced abasic sites allows temperature to more accurately discriminate correct base pairings from incorrect ones.

Approach to equilibrium of diffusion in a logarithmic potential

The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is given by two distinct scaling forms, corresponding to a diffusive (x∼t(1/2)) and a subdiffusive (x∼t(γ) with a given γ<1/2) length scale, respectively, (ii) the overall scaling function is selected by the initial condition, and (iii) depending on the tail of the initial condition, the scaling exponent that characterizes the scaling function is found to exhibit a transition from a continuously varying to a fixed value.

DNA breathing dynamics: analytic results for distribution functions of relevant Brownian functionals

We investigate DNA breathing dynamics by suggesting and examining several Brownian functionals associated with bubble lifetime and reactivity. Bubble dynamics is described as an overdamped random walk in the number of broken base pairs. The walk takes place on the Poland-Scheraga free-energy landscape. We suggest several probability distribution functions that characterize the breathing process, and adopt the recently studied backward Fokker-Planck method and the path decomposition method as elegant and flexible tools for deriving these distributions. In particular, for a bubble of an initial size x₀, we derive analytical expressions for (i) the distribution P(t{f}|x₀) of the first-passage time t{f}, characterizing the bubble lifetime, (ii) the distribution P(A|x₀) of the area A until the first-passage time, providing information about the effective reactivity of the bubble to processes within the DNA, (iii) the distribution P(M) of the maximum bubble size M attained before the first-passage time, and (iv) the joint probability distribution P(M,t{m}) of the maximum bubble size M and the time t{m} of its occurrence before the first-passage time. These distributions are analyzed in the limit of small and large bubble sizes. We supplement our analytical predictions with direct numericalsimulations of the related Langevin equation, and obtain a very good agreement in the appropriate limits. The nontrivial scaling behavior of the various quantities analyzed here can, in principle, be explored experimentally.