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We study a protein-DNA target search model with explicit DNA dynamics applicable to in vitro experiments. We show that the DNA dynamics plays a crucial role for the effectiveness of protein jumps between sites distant along the DNA contour but close in 3D space. A strongly binding protein that searches by 1D sliding and jumping alone, explores the search space less redundantly when the DNA dynamics is fast on the timescale of protein jumps than in the opposite frozen DNA limit. We characterize the crossover between these limits using simulations and scaling theory. We also rationalize the slow exploration in the frozen limit as a subtle interplay between long jumps and long trapping times of the protein in islands within random DNA configurations in solution.
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Much of the complexity observed in gene regulation originates from cooperative protein-DNA binding. While studies of the target search of proteins for their specific binding sites on the DNA have revealed design principles for the quantitative characteristics of protein-DNA interactions, no such principles are known for the cooperative interactions between DNA-binding proteins. We consider a simple theoretical model for two interacting transcription factor (TF) species, searching for and binding to two adjacent target sites hidden in the genomic background. We study the kinetic competition of a dimer search pathway and a monomer search pathway, as well as the steady-state regulation function mediated by the two TFs over a broad range of TF-TF interaction strengths. Using a transcriptional AND-logic as exemplary functional context, we identify the functionally desirable regime for the interaction. We find that both weak and very strong TF-TF interactions are favorable, albeit with different characteristics. However, there is also an unfavorable regime of intermediate interactions where the genetic response is prohibitively slow.
Statistics of Poincare recurrences is studied for the base-pair breathing dynamics of an all-atom DNA molecule in realistic aqueous environment with thousands of degrees of freedom. It is found that at least over five decades in time the decay of recurrences is described by an algebraic law with the Poincare exponent close to $beta=1.2$. This value is directly related to the correlation decay exponent $ u = beta -1$, which is close to $ uapprox 0.15$ observed in the time resolved Stokes shift experiments. By applying the virial theorem we analyse the chaotic dynamics in polynomial potentials and demonstrate analytically that exponent $beta=1.2$ is obtained assuming the dominance of dipole-dipole interactions in the relevant DNA dynamics. Molecular dynamics simulations also reveal the presence of strong low frequency noise with the exponent $eta=1.6$. We trace parallels with the chaotic dynamics of symplectic maps with a few degrees of freedom characterized by the Poincare exponent $beta sim 1.5$.
DNA surface-hybridization biosensors utilize the selective hybridization of target sequences in solution to surface-immobilized probes. In this process, the target is usually assumed to be in excess, so that its concentration does not significantly vary while hybridizing to the surface-bound probes. If the target is initially at low concentrations and/or if the number of probes is very large and have high affinity for the target, the DNA in solution may get depleted. In this paper we analyze the equilibrium and kinetics of hybridization of DNA biosensors in the case of strong target depletion, by extending the Langmuir adsorption model. We focus, in particular, on the detection of a small amount of a single-nucleotide mutant sequence (concentration $c_2$) in a solution, which differs by one or more nucleotides from an abundant wild-type sequence (concentration $c_1 gg c_2$). We show that depletion can give rise to a strongly-enhanced sensitivity of the biosensors. Using representative values of rate constants and hybridization free energies, we find that in the depletion regime one could detect relative concentrations $c_2/c_1$ that are up to three orders of magnitude smaller than in the conventional approach. The kinetics is surprisingly rich, and exhibits a non-monotonic adsorption with no counterpart in the no-depletion case. Finally, we show that, alongside enhanced detection sensitivity, this approach offers the possibility of sample enrichment, by substantially increasing the relative amount of the mutant over the wild-type sequence.
The success of DNA nanotechnology has been driven by the discovery of novel structural motifs with a wide range of shapes and uses. We present a comprehensive study of the T-motif, a 3-armed, planar, right-angled junction that has been used in the self-assembly of DNA polyhedra and periodic structures. The motif is formed through the interaction of a bulge loop in one duplex and a sticky end of another. The polarity of the sticky end has significant consequences for the thermodynamic and geometrical properties of the T-motif: different polarities create junctions spanning different grooves of the duplex. We compare experimental binding strengths with predictions of oxDNA, a coarse-grained model of DNA, for various loop sizes. We find that, although both sticky-end polarities can create stable junctions, junctions resulting from 5$$ sticky ends are stable over a wider range of bulge loop sizes. We highlight the importance of possible coaxial stacking interactions within the motif and investigate how each coaxial stacking interaction stabilises the structure and favours a particular geometry.
Problems of search and recognition appear over different scales in biological systems. In this review we focus on the challenges posed by interactions between proteins, in particular transcription factors, and DNA and possible mechanisms which allow for a fast and selective target location. Initially we argue that DNA-binding proteins can be classified, broadly, into three distinct classes which we illustrate using experimental data. Each class calls for a different search process and we discuss the possible application of different search mechanisms proposed over the years to each class. The main thrust of this review is a new mechanism which is based on barrier discrimination. We introduce the model and analyze in detail its consequences. It is shown that this mechanism applies to all classes of transcription factors and can lead to a fast and specific search. Moreover, it is shown that the mechanism has interesting transient features which allow for stability at the target despite rapid binding and unbinding of the transcription factor from the target.
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