Physical constraints and functional characteristics of transcription factor-DNA interaction - PubMed (original) (raw)
Physical constraints and functional characteristics of transcription factor-DNA interaction
Ulrich Gerland et al. Proc Natl Acad Sci U S A. 2002.
Abstract
We study theoretical "design principles" for transcription factor (TF)-DNA interaction in bacteria, focusing particularly on the statistical interaction of the TFs with the genomic background (i.e., the genome without the target sites). We introduce and motivate the concept of programmability, i.e., the ability to set the threshold concentration for TF binding over a wide range merely by mutating the binding sequence of a target site. This functional demand, together with physical constraints arising from the thermodynamics and kinetics of TF-DNA interaction, leads us to a narrow range of "optimal" interaction parameters. We find that this parameter set agrees well with experimental data for the interaction parameters of a few exemplary prokaryotic TFs, which indicates that TF-DNA interaction is indeed programmable. We suggest further experiments to test whether this is a general feature for a large class of TFs.
Figures
Fig 1.
For the purpose of TF binding, the genome may be treated as random DNA plus functional target site(s). (A) Histogram of the specific binding energies for Cro [solid line] on the E. coli genome together with the average histogram (circles) for Cro on random nucleotide sequences (synthesized with the same length and single-nucleotide frequencies as the E. coli genome; normalization for both histograms such that maximum is at N). Except for statistical fluctuations at the low-energy end, the histograms are indistinguishable from each other. The approximate position of the threshold energy for nonspecific binding _E_ns is indicated as the thin dashed line. (B) Energy landscape for Cro on the bacteriophage λ DNA. The landscape appears to be random, e.g., no “funnel” guides the TF to the target site. The spatial correlation function of the landscape (not shown) decays quickly to zero beyond the scale of L = 17 for this case. Random-energy landscapes are found also for the other two TFs with known energy matrices (not shown).
Fig 2.
(A) Schematic illustration of the search dynamics: a TF (represented by a solid ellipse) moves among genomic DNA (lines) via a combination of 1D (along the genome) and 3D (hopping between nearby segments) diffusion as illustrated by the arrows. The open circles indicate the potential kinetic traps, which are sites that are preferred by the TF in a random background. (B) Dependence of the chemical potential μ on the number n of TFs in a cell for Mnt, Cro, and λ repressor obtained by directly solving and inverting the defining equation (Eq. 13). The comparison with the dashed line μ = k_B_T ln n shows that μ(n) is sufficiently well described by the simple expression (Eq. 13) over the regime 1 < n < 1,000.
Fig 3.
(A) Plot of the region where (ɛ,L) ≤ 1. The boundary L*(ɛ) for N = 107 is indicated by the solid line (see text). The dashed line ln(N)/[ln ζ−1(ɛ) − ɛ/(1 + _e_ɛ/3)] indicates the onset of the glass transition in the random-energy model where the annealed approximation breaks down. As argued in the text, the desired parameter regime is close to = 1 such that the annealed approximation is justified. (B) The binding threshold ñ as a function of the total number of mismatches r of the target-sequence s→t from the best binder s→* at different parameter combinations (ɛ,L).
Fig 4.
Graphical construction of the background free energy _F_b and other quantities used in the text.
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