Equilibrium Statistical Physics

Plischke, Michael; Bergersen, B.

doi:10.1142/2247

Cited by 182 publications

(269 citation statements)

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“…4) one can conclude that the above quantities diverge as |K c (2) − K| −γ when approaching the critical point. Within the statistical error the value of the exponent γ agrees with those found for the twodimensional Ising model (γ = 7/4) [50][51][52]. These numerical data suggest that the robustness of the Ising universality class is not disturbed by an additional coordinated strategy pair in the corresponding four-strategy evolutionary game.…”

Section: B Monte Carlo Simulationssupporting

confidence: 80%

Evolutionary games combining two or three pair coordinations on a square lattice

Király

Szabó

2017

Phys. Rev. E

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We study multiagent logit-rule-driven evolutionary games on a square lattice whose pair interactions are composed of a maximal number of nonoverlapping elementary coordination games describing Ising-type interactions between just two of the available strategies. Using Monte Carlo simulations we investigate the macroscopic noise-level-dependent behavior of the two-and three-pair games and the critical properties of the continuous phase transtitions these systems exhibit. The four-strategy game is shown to be equivalent to a system that consists of two independent and identical Ising models.

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Section: B Monte Carlo Simulationssupporting

confidence: 80%

Evolutionary games combining two or three pair coordinations on a square lattice

Király

Szabó

2017

Phys. Rev. E

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“…S1). The notion of the correlation scale in our sequence design is qualitatively analogous to the correlation length of the one-dimensional Ising model (20), or analogous to the frequency of the nearest-neighbor base sequences in DNA (21). All DNA sequences in our experimental design have identical nucleotide content, and all of them have an identical specific motif in the center of the sequence, flanked by the nonconsensus background.…”

Section: Resultsmentioning

confidence: 99%

Protein−DNA binding in the absence of specific base-pair recognition

Afek

Schipper

Horton

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

103

134

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Until now, it has been reasonably assumed that specific base-pair recognition is the only mechanism controlling the specificity of transcription factor (TF)−DNA binding. Contrary to this assumption, here we show that nonspecific DNA sequences possessing certain repeat symmetries, when present outside of specific TF binding sites (TFBSs), statistically control TF−DNA binding preferences. We used highthroughput protein−DNA binding assays to measure the binding levels and free energies of binding for several human TFs to tens of thousands of short DNA sequences with varying repeat symmetries. Based on statistical mechanics modeling, we identify a new protein−DNA binding mechanism induced by DNA sequence symmetry in the absence of specific base-pair recognition, and experimentally demonstrate that this mechanism indeed governs protein−DNA binding preferences. protein−DNA binding is an important biophysical mechanism operating in a living cell (1). This seminal work makes it possible to interpret experiments that measured how transcription factors (TFs) search for their specific target sites flanked by nonconsensus sequence elements (1-10). A specific consensus motif is a short DNA sequence, typically 6-20 base pairs (bp), that possesses an enhanced binding affinity for a particular TF. For example, the sequence CACGTG represents the specific consensus motif for the human protein Max used in this study (Fig. 1). The process of establishing specific, consensus protein−DNA binding requires the formation of precise geometrical fit between the protein and its consensus DNA motif, accompanied by the formation of specific hydrogen and electrostatic contacts at the protein−DNA binding interface (6, 7) ( Fig. 1). In addition to binding to their consensus DNA motifs, transcription factors can also bind, albeit with lower affinity, to DNA regions lacking any consensus motifs. The term "nonspecific protein−DNA binding" (6) is typically used to describe these weaker interactions. Von Hippel and Berg suggested classifying nonspecific protein−DNA binding into two related mechanisms (6). The first mechanism includes protein binding to its mutated specific motifs that retain some residual, reduced specificity. The second mechanism is largely DNA sequence independent, and it involves electrostatic binding modulated by the overall DNA geometry (6). Despite significant experimental progress, molecular mechanisms responsible for these two types of nonspecific binding remain poorly understood, and the free energy of nonspecific protein−DNA binding has not been systematically characterized (11)(12)(13)(14). The interplay between consensus and nonconsensus DNA sequence elements emerges as a dominant factor that governs protein−DNA binding preferences. However, this interplay is also poorly understood (15, 16). Until now, it has been reasonably assumed that specific (consensus) base-pair recognition must control the genome-wide specificity of TF−DNA binding.Contrary to this assumption, here we identify a general mechanism for protein−DNA bi...

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“…We study the three-dimensional Ising model on a simple cubic lattice with nearest-neighbor interactions. 2,3,16 We study lattices of size L ϫ L ϫ W. For our calculations of the nucleation rate, we consider a lattice with one wall that favors the spin-up phase and one wall that favors the spindown phase. These walls are flat and the wall that favors the spin-up phase is the z = 0 plane.…”

Section: Model and Simulation Techniquementioning

confidence: 99%

“…2,3 There, neighboring spins interact with a coupling of J and feel a bulk field h. At a wall that favors the spin-up phase, the spins feel a surface field h s . This is in addition to h and acts only on spins immediately adjacent to the wall.…”

Section: Model and Simulation Techniquementioning

confidence: 99%

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Continuity of the nucleation of bulk and surface phases

Sear

2008

The Journal of Chemical Physics

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Nucleation of a new bulk phase is almost always heterogeneous: It occurs at a surface. Nucleation of a new surface phase also occurs at a surface of course. We study nucleation in an Ising model with both bulk and surface ͑prewetting͒ transitions. We find no clear distinction between nucleation of the bulk and surface phases. As the bulk transition is crossed, the phase that is nucleating changes from being a new surface phase to being a new bulk phase. However, neither the nucleation rate nor the nucleus itself changes discontinuously. It appears that because the nucleus is only approximately two spins high, it is oblivious to the fact that on one side of the bulk transition it will grow to form a thick wetting layer, while on the other side it will grow to form a bulk phase of limitless thickness. The phase diagram of hard spheres at a hard wall is analogous to that of our model. Therefore, we suggest that the nucleation of the crystal phase of hard spheres at a hard wall may also be indistinguishable from that associated with a prefreezing surface transition.

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Equilibrium Statistical Physics

Cited by 182 publications

References 0 publications

Evolutionary games combining two or three pair coordinations on a square lattice

Evolutionary games combining two or three pair coordinations on a square lattice

Protein−DNA binding in the absence of specific base-pair recognition

Continuity of the nucleation of bulk and surface phases

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