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. 2008 Aug;95(3):1151-6.
doi: 10.1529/biophysj.108.129825. Epub 2008 May 2.

Are DNA transcription factor proteins maxwellian demons?

Longhua Hu  1 , Alexander Y Grosberg, Robijn Bruinsma
Affiliations

Are DNA transcription factor proteins maxwellian demons?

Longhua Hu et al. Biophys J. 2008 Aug.

Abstract

Transcription factor (TF) proteins rapidly locate unique target sites on long genomic DNA molecules--and bind to them--during gene regulation. The search mechanism is known to involve a combination of three-dimensional diffusion through the bulk of the cell and one-dimensional sliding diffusion along the DNA. It is believed that the surprisingly high target binding rates of TF proteins relies on conformational fluctuations of the protein between a mobile state that is insensitive to the DNA sequence and an immobile state that is sequence-sensitive. Since TFs are not able to consume free energy during their search to obtain DNA sequence information, the Second Law of Thermodynamics must impose a strict limit on the efficiency of passive search mechanisms. In this article, we use a simple model for the protein conformational fluctuations to obtain the shortest binding time consistent with thermodynamics. The binding time is minimized if the spectrum of conformational fluctuations that take place during the search is impedance-matched to the large-scale conformational change that takes place at the target site. For parameter values appropriate for bacterial TF, this minimum binding time is within an order-of-magnitude of a limiting binding time corresponding to an idealized protein with instant target recognition. Numerical estimates suggest that typical bacteria operate in this regime of optimized conformational fluctuations.

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Figures

FIGURE 1
FIGURE 1
Schematic representation of the model. A protein moving diffusively through the cell volume (a) is adsorbed on genomic DNA (b) where it adopts one of two conformations: + and −. In the +conformation it is loosely associated with the DNA and can move by one-dimensional diffusion along the DNA chain (b) while in the −conformation (c) it is tightly associated with the DNA and is immobile. After returning to the +state, it restarts the sliding motion. The protein also can desorb from the chain (d) and return to three-dimensional diffusive motion. After a number of such cycles, the protein lands in the antenna region within a distance λ of the target binding site (e). After reaching the target site by one-dimensional diffusion it can undergo a large-scale irreversible conformational transition to the final bound state if it is in the −state (f).
FIGURE 2
FIGURE 2
Contour plots of the transport enhancement factor A as a function of the equilibrium constant K and the occupation probability ratio μ of the + over −states for D1 = 10−9 cm2/s, D3 = 3 × 10−7 cm2/s, a = 0.34 nm, b = 5 nm, φ = 0.01, and Ω = 3 × 103 Hz. There is a shallow maximum at ∼μ = 0.1 and K = 10−3. The ratio of the transport enhancement factor at this maximum, Aopt, and the thermodynamic limiting enhancement factor, A∞, equals 0.193. (Upper inset) Dependence of the ratio Aopt/A∞ on the dimensionless binding rate ω. (Lower inset) Enhancement factor A against μ at the value of K corresponding to the maximum of the main figure.
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