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Comparative Study
. 2006;34(19):5638-49.
doi: 10.1093/nar/gkl683. Epub 2006 Oct 11.

Indirect readout: detection of optimized subsequences and calculation of relative binding affinities using different DNA elastic potentials

Nils B Becker  1 , Lars Wolff, Ralf Everaers
Affiliations
Comparative Study

Indirect readout: detection of optimized subsequences and calculation of relative binding affinities using different DNA elastic potentials

Nils B Becker et al. Nucleic Acids Res. 2006.

Abstract

Essential biological processes require that proteins bind to a set of specific DNA sites with tuned relative affinities. We focus on the indirect readout mechanism and discuss its theoretical description in relation to the present understanding of DNA elasticity on the rigid base pair level. Combining existing parametrizations of elastic potentials for DNA, we derive elastic free energies directly related to competitive binding experiments, and propose a computationally inexpensive local marker for elastically optimized subsequences in protein-DNA co-crystals. We test our approach in an application to the bacteriophage 434 repressor. In agreement with known results we find that indirect readout dominates at the central, non-contacted bases of the binding site. Elastic optimization involves all deformation modes and is mainly due to the adapted equilibrium structure of the operator, while sequence-dependent elasticity plays a minor role. These qualitative observations are robust with respect to current parametrization uncertainties. Predictions for relative affinities mediated by indirect readout depend sensitively on the chosen parametrization. Their quantitative comparison with experimental data allows for a critical evaluation of DNA elastic potentials and of the correspondence between crystal and solution structures. The software written for the presented analysis is included as Supplementary Data.

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Figures

Figure 1
Figure 1
Representation of 434 repressor–OR3 complex structure (4). The outer 5 + 5 and the inner 4 bp are shaded differently. Together they form the 14 bp binding site. The OR sequences are indicated.
Figure 2
Figure 2
Elastic energy E along OR1, 2, 3. A 3 bps window was used. The elastic energy and parametrization uncertainty per bps are shown in units of kBT. The top curve shows the full elastic energy, while partial energies are shown subsequently shifted down by 2 kBT for clarity.
Figure 3
Figure 3
Elastic optimization in 434 repressor structures OR1, 2, 3. Deformation energy E and free energy F, first and second rows. Z-scores of mean (green) and minimum (gray), third row. The fourth row shows the sequence potential G together with the random G level. All energies are given in kBT. E and F are per bps while G is per bp. The moving window length is 3 bps. Error bars indicate parametrization uncertainty, and lighter shading marks the inner 4 bp.
Figure 4
Figure 4
Histograms of the free energy per bps of mutated sequences, in kBT units. All possible mutations inside a 5 bps window were generated, around bps 3, 7 and 11 from left to right. The structure is OR2, and the MD parameter set combined with P-DNA equilibrium values is used. The vertical line indicates the F value of the native sequence.
Figure 5
Figure 5
Elastic energy (E) and sequence free energy (G) in the OR1 structure, using the MP potential. The moving window lengths 1, 2 and 3 bps are shown with short, long and no dashes, respectively. E and G are given per bps and per bp, respectively.
Figure 6
Figure 6
Similarity to elastic consensus for native subsequences in the OR complexes. Information (gray) and scaled native probability (green) are shown for 1, 2 and 4 bp subsequences, from top to bottom.
Figure 7
Figure 7
Sequence potential G for OR1, 2, 3. The curves show the fully sequence-dependent potential, the potential with averaged equilibrium values ξ0, and the potential with averaged stiffness matrix S, from top to bottom and shifted in 2 kBT steps. The zero line corresponds to random sequences.
Figure 8
Figure 8
Sequence potential G along OR1, 2, 3, analogous to Figure 2. The partial free energies are shifted down by 2 kBT successively for clarity, and each one is shown together with the level of random probability. A 3 bps moving window was used.
Figure 9
Figure 9
Elastic energy E and sequence free energy G in the OR2 complex, for all parametrizations used. Full and partial energies are shown, with color coding and offsets as in Figures 2 and 8.
Figure 10
Figure 10
Computed deformation free energy differences versus measured log affinity differences. From left to right, we used ΔF values for all structures and parametrizations (AVG), the OR3 structure and all parametrizations (OR3), all structures and the MP parametrization (MP) and OR3 together with MP (MP, OR3). Error bars indicate the spread in ΔF, and the line indicates equality.
Figure 11
Figure 11
Computed deformation free energy differences versus measured log affinity differences, for all combinations of crystal structure and employed parametrization, see also Figure 10. Linear correlation coefficients (upper number) and the RMSD from the line βΔF=Δlogc1/2 (lower number) are inset.
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