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note
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This simplifying assumption may be more realistic for other complexes, such as the lambda cI repressor, which are thought to be more rigid than LacI.
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51
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33845765076
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Again, this idealization may be more literally appropriate for other repressors, such as lambda cI.
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Again, this idealization may be more literally appropriate for other repressors, such as lambda cI.
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Recall that we are assuming that the DNA is permanently bound to the protein. More generally we need to account for the fact that protein-DNA binding generally unwinds the DNA; for example in lac the unwinding is nearly one radian. The work done by external torsional stress against this rotation effectively modifies the binding constant relative to the value appropriate for isolated operator fragments.
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Note that the external torque Mext need not equal M3 at the points si, sf, because the coupler can exert torque on the DNA.
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note
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The twist stiffness given here is smaller than the value found in single-molecule studies. Widom and Cloutier found that this small value was needed to fit their data on cyclization of short DNA, and proposed that it was an effective value reflecting a nonlinear breakdown of elasticity under high strain. Previous authors also found that a significant, though less dramatic, reduction of the value of twist stiffess was needed to fit cyclization of longer DNA. In the present work we found that a reduced effective twist stiffness was needed to get the required magnitude of the peak-to-valley energy change in Fig. 1; however, Saiz and Vilar have argued that the existence of multiple looping geometries can also reduce this modulation.
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