Discrete-State Kinetics Model for NMR-Based Analysis of Protein Translocation on DNA at Equilibrium

In the target DNA search process, sequence-specific DNA-binding proteins first nonspecifically bind to DNA and stochastically move from one site to another before reaching their targets. To rigorously assess how the translocation process influences NMR signals from proteins interacting with nonspecific DNA, we incorporated a discrete-state kinetic model for protein translocation on DNA into the McConnell equation. Using this equation, we simulated line shapes of NMR signals from proteins undergoing translocations on DNA through sliding, dissociation/reassociation, and intersegment transfer. Through this analysis, we validated an existing NMR approach for kinetic investigations of protein translocation on DNA, which utilizes NMR line shapes of two nonspecific DNA–protein complexes and their mixture. We found that, despite its use of simplistic two-state approximation neglecting the presence of many microscopic states, the previously proposed NMR approach provides accurate kinetic information on the intermolecular translocations of proteins between two DNA molecules. Interestingly, our results suggest that the same NMR approach can also provide qualitative information about the one-dimensional diffusion coefficient for proteins sliding on DNA

Temperature Dependence of Internal Motions of Protein Side-Chain NH₃⁺ Groups: Insight into Energy Barriers for Transient Breakage of Hydrogen Bonds

Although charged side chains play important roles in protein function, their dynamic properties are not well understood. Nuclear magnetic resonance methods for investigating the dynamics of lysine side-chain NH₃⁺ groups were established recently. Using this methodology, we have studied the temperature dependence of the internal motions of the lysine side-chain NH₃⁺ groups that form ion pairs with DNA phosphate groups in the HoxD9 homeodomain–DNA complex. For these NH₃⁺ groups, we determined order parameters and correlation times for bond rotations and reorientations at 15, 22, 28, and 35 °C. The order parameters were found to be virtually constant in this temperature range. In contrast, the bond-rotation correlation times of the NH₃⁺ groups were found to depend strongly on temperature. On the basis of transition state theory, the energy barriers for NH₃⁺ rotations were analyzed and compared to those for CH₃ rotations. Enthalpies of activation for NH₃⁺ rotations were found to be significantly higher than those for CH₃ rotations, which can be attributed to the requirement of hydrogen bond breakage. However, entropies of activation substantially reduce the overall free energies of activation for NH₃⁺ rotations to a level comparable to those for CH₃ rotations. This entropic reduction in energy barriers may accelerate molecular processes requiring hydrogen bond breakage and play a kinetically important role in protein function

Internal Motions of Basic Side Chains of the Antennapedia Homeodomain in the Free and DNA-Bound States

Basic side chains play crucial roles in protein–DNA interactions. In this study, using NMR spectroscopy, we investigated the dynamics of Arg and Lys side chains of the fruit fly Antennapedia homeodomain in the free state and in the complex with target DNA. We measured ¹⁵N relaxation for Arg and Lys side chains at two magnetic fields, from which generalized order parameters for the cationic groups were determined. Mobility of the R5 side chain, which makes hydrogen bonds with a thymine base in the DNA minor groove, was greatly dampened. Several Lys and Arg side chains that form intermolecular ion pairs with DNA phosphates were found to retain high mobility with the order parameter being <0.6 in the DNA-bound state. Interestingly, some of the interfacial cationic groups in the complex were more mobile than in the free protein. The retained or enhanced mobility of the Arg and Lys side chains in the complex should mitigate the overall loss of conformational entropy in the protein–DNA association and allow dynamic molecular recognition

Thermodynamic Additivity for Impacts of Base-Pair Substitutions on Association of the Egr‑1 Zinc-Finger Protein with DNA

The transcription factor Egr-1 specifically binds as a monomer to its 9 bp target DNA sequence, GCG­T­G­G­GCG, via three zinc fingers and plays important roles in the brain and cardiovascular systems. Using fluorescence-based competitive binding assays, we systematically analyzed the impacts of all possible single-nucleotide substitutions in the target DNA sequence and determined the change in binding free energy for each. Then, we measured the changes in binding free energy for sequences with multiple substitutions and compared them with the sum of the changes in binding free energy for each constituent single substitution. For the DNA variants with two or three nucleotide substitutions in the target sequence, we found excellent agreement between the measured and predicted changes in binding free energy. Interestingly, however, we found that this thermodynamic additivity broke down with a larger number of substitutions. For DNA sequences with four or more substitutions, the measured changes in binding free energy were significantly larger than predicted. On the basis of these results, we analyzed the occurrences of high-affinity sequences in the genome and found that the genome contains millions of such sequences that might functionally sequester Egr-1

Dynamic Equilibria of Short-Range Electrostatic Interactions at Molecular Interfaces of Protein–DNA Complexes

Intermolecular ion pairs (salt bridges) are crucial for protein–DNA association. For two protein–DNA complexes, we demonstrate that the ion pairs of protein side-chain NH₃⁺ and DNA phosphate groups undergo dynamic transitions between distinct states in which the charged moieties are either in direct contact or separated by water. While the crystal structures of the complexes show only the solvent-separated ion pair (SIP) state for some interfacial lysine side chains, our NMR hydrogen-bond scalar coupling data clearly indicate the presence of the contact ion pair (CIP) state for the same residues. The 0.6-μs molecular dynamics (MD) simulations confirm dynamic transitions between the CIP and SIP states. This behavior is consistent with our NMR order parameters and scalar coupling data for the lysine side chains. Using the MD trajectories, we also analyze the free energies of the CIP–SIP equilibria. This work illustrates the dynamic nature of short-range electrostatic interactions in DNA recognition by proteins

Residence Times of Molecular Complexes in Solution from NMR Data of Intermolecular Hydrogen-Bond Scalar Coupling

The residence times of molecular complexes in solution are important for understanding biomolecular functions and drug actions. We show that NMR data of intermolecular hydrogen-bond scalar couplings can yield information on the residence times of molecular complexes in solution. The molecular exchange of binding partners via the breakage and reformation of a complex causes self-decoupling of intermolecular hydrogen-bond scalar couplings, and this self-decoupling effect depends on the residence time of the complex. For protein–DNA complexes, we investigated the salt concentration dependence of intermolecular hydrogen-bond scalar couplings between the protein side-chain ¹⁵N and DNA phosphate ³¹P nuclei, from which the residence times were analyzed. The results were consistent with those obtained by ¹⁵N_<i>z</i>-exchange spectroscopy. This self-decoupling-based kinetic analysis is unique in that it does not require any different signatures for the states involved in the exchange, whereas such conditions are crucial for kinetic analyses by typical NMR and other methods

Direct Observation of the Ion-Pair Dynamics at a Protein–DNA Interface by NMR Spectroscopy

Ion pairing is one of the most fundamental chemical interactions and is essential for molecular recognition by biological macromolecules. From an experimental standpoint, very little is known to date about ion-pair dynamics in biological macromolecular systems. Absorption, infrared, and Raman spectroscopic methods were previously used to characterize dynamic properties of ion pairs, but these methods can be applied only to small compounds. Here, using NMR ¹⁵N relaxation and hydrogen-bond scalar ¹⁵N–³¹P <i>J</i>-couplings (^<i>h3</i><i>J</i>_NP), we have investigated the dynamics of the ion pairs between lysine side-chain NH₃⁺ amino groups and DNA phosphate groups at the molecular interface of the HoxD9 homeodomain–DNA complex. We have determined the order parameters and the correlation times for C–N bond rotation and reorientation of the lysine NH₃⁺ groups. Our data indicate that the NH₃⁺ groups in the intermolecular ion pairs are highly dynamic at the protein–DNA interface, which should lower the entropic costs for protein–DNA association. Judging from the C–N bond-rotation correlation times along with experimental and quantum-chemically derived ^<i>h3</i><i>J</i>_NP hydrogen-bond scalar couplings, it seems that breakage of hydrogen bonds in the ion pairs occurs on a sub-nanosecond time scale. Interestingly, the oxygen-to-sulfur substitution in a DNA phosphate group was found to enhance the mobility of the NH₃⁺ group in the intermolecular ion pair. This can partially account for the affinity enhancement of the protein–DNA association by the oxygen-to-sulfur substitution, which is a previously observed but poorly understood phenomenon