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The universal statistical distributions of the affinity, equilibrium constants, kinetics and specificity in biomolecular recognition.

Zheng X, Wang J - PLoS Comput. Biol. (2015)

Bottom Line: The results of the analytical studies are confirmed by the microscopic flexible docking simulations.Our study provides new insights into the statistical nature of thermodynamics, kinetics and function from different ligands binding with a specific receptor or equivalently specific ligand binding with different receptors.The elucidation of distributions of the kinetics and free energy has guiding roles in studying biomolecular recognition and function through small-molecule evolution and chemical genetics.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, ChangChun, Jilin, P.R. China.

ABSTRACT
We uncovered the universal statistical laws for the biomolecular recognition/binding process. We quantified the statistical energy landscapes for binding, from which we can characterize the distributions of the binding free energy (affinity), the equilibrium constants, the kinetics and the specificity by exploring the different ligands binding with a particular receptor. The results of the analytical studies are confirmed by the microscopic flexible docking simulations. The distribution of binding affinity is Gaussian around the mean and becomes exponential near the tail. The equilibrium constants of the binding follow a log-normal distribution around the mean and a power law distribution in the tail. The intrinsic specificity for biomolecular recognition measures the degree of discrimination of native versus non-native binding and the optimization of which becomes the maximization of the ratio of the free energy gap between the native state and the average of non-native states versus the roughness measured by the variance of the free energy landscape around its mean. The intrinsic specificity obeys a Gaussian distribution near the mean and an exponential distribution near the tail. Furthermore, the kinetics of binding follows a log-normal distribution near the mean and a power law distribution at the tail. Our study provides new insights into the statistical nature of thermodynamics, kinetics and function from different ligands binding with a specific receptor or equivalently specific ligand binding with different receptors. The elucidation of distributions of the kinetics and free energy has guiding roles in studying biomolecular recognition and function through small-molecule evolution and chemical genetics.

No MeSH data available.


Related in: MedlinePlus

Three representative ligands analyzed in the docking simulations.The left panels of (A), (B) and (C) show the one dimensional projection of binding free energy landscape to RMSD with high, medium and low ISR with similar affinity as well as the corresponding structures of the different ligands, where the docked pose with the most stable affinity or the strongest binding state is chosen as the reference structure to calculate the RMSDs; the Autodock score function is used to evaluate the interaction energies between the ligand and the receptor. (high:fork structure, medium:near-linear structure, low:linear structure);the right panels of them show the corresponding binding energy spectrum for each, the sparse part of the spectrum implies there are fewer states, and dense part of the spectrum implies there are more states. (D) show the kinetic time for binding for the above three different ISRs. The upper black line represents the predicted kinetic timeoff and the under black line represents the predicted kinetic timeon. The vertical axis represents the calculated kinetic time.
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pcbi.1004212.g010: Three representative ligands analyzed in the docking simulations.The left panels of (A), (B) and (C) show the one dimensional projection of binding free energy landscape to RMSD with high, medium and low ISR with similar affinity as well as the corresponding structures of the different ligands, where the docked pose with the most stable affinity or the strongest binding state is chosen as the reference structure to calculate the RMSDs; the Autodock score function is used to evaluate the interaction energies between the ligand and the receptor. (high:fork structure, medium:near-linear structure, low:linear structure);the right panels of them show the corresponding binding energy spectrum for each, the sparse part of the spectrum implies there are fewer states, and dense part of the spectrum implies there are more states. (D) show the kinetic time for binding for the above three different ISRs. The upper black line represents the predicted kinetic timeoff and the under black line represents the predicted kinetic timeon. The vertical axis represents the calculated kinetic time.

Mentions: In Fig 10A–10C, we also show the one dimensional projection of binding free energy landscape to RMSD with different ligands with different intrinsic specificity characterized by ISR. Different free energy landscapes give different free energy barrier heights between the non-native and native states. This leads to different kinetics for binding(Figs 2 and 10D). As we can see the large intrinsic specificity characterized by high ISR gives smaller free energy barrier and lower ISR gives higher barrier. There is also a structural correspondence shown in the figure for different ligands. The ligands with the fork structure have high structural specificity and faster kinetics, and ligands without the fork structure have low specificity and slower kinetics. We plot the free energy barrier height and the kinetic time for binding of these three cases as shown in Fig 10D. By exploring the different off rates Timeoff and on rates Timeon of binding for three ligands, we found that the ligand with higher ISR has faster on rate and slower off rate. In other words, the ligand has longer residence time for binding. In contrast, the ligand with lower ISR has slower on rate and faster off rate with shorter residence time. In a word, we found indeed that the large ISR leads to lower barrier height and faster kinetics. This implies that the kinetics is determined by the intrinsic specificity which is determined by the competition of the slope of the landscape towards the native state and the roughness of the landscape, not just by the affinity alone as conventionally people would have thought. There are recently growing experimental evidences of the similar affinity but completely different kinetic accessibility [53, 54].


The universal statistical distributions of the affinity, equilibrium constants, kinetics and specificity in biomolecular recognition.

Zheng X, Wang J - PLoS Comput. Biol. (2015)

Three representative ligands analyzed in the docking simulations.The left panels of (A), (B) and (C) show the one dimensional projection of binding free energy landscape to RMSD with high, medium and low ISR with similar affinity as well as the corresponding structures of the different ligands, where the docked pose with the most stable affinity or the strongest binding state is chosen as the reference structure to calculate the RMSDs; the Autodock score function is used to evaluate the interaction energies between the ligand and the receptor. (high:fork structure, medium:near-linear structure, low:linear structure);the right panels of them show the corresponding binding energy spectrum for each, the sparse part of the spectrum implies there are fewer states, and dense part of the spectrum implies there are more states. (D) show the kinetic time for binding for the above three different ISRs. The upper black line represents the predicted kinetic timeoff and the under black line represents the predicted kinetic timeon. The vertical axis represents the calculated kinetic time.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4401658&req=5

pcbi.1004212.g010: Three representative ligands analyzed in the docking simulations.The left panels of (A), (B) and (C) show the one dimensional projection of binding free energy landscape to RMSD with high, medium and low ISR with similar affinity as well as the corresponding structures of the different ligands, where the docked pose with the most stable affinity or the strongest binding state is chosen as the reference structure to calculate the RMSDs; the Autodock score function is used to evaluate the interaction energies between the ligand and the receptor. (high:fork structure, medium:near-linear structure, low:linear structure);the right panels of them show the corresponding binding energy spectrum for each, the sparse part of the spectrum implies there are fewer states, and dense part of the spectrum implies there are more states. (D) show the kinetic time for binding for the above three different ISRs. The upper black line represents the predicted kinetic timeoff and the under black line represents the predicted kinetic timeon. The vertical axis represents the calculated kinetic time.
Mentions: In Fig 10A–10C, we also show the one dimensional projection of binding free energy landscape to RMSD with different ligands with different intrinsic specificity characterized by ISR. Different free energy landscapes give different free energy barrier heights between the non-native and native states. This leads to different kinetics for binding(Figs 2 and 10D). As we can see the large intrinsic specificity characterized by high ISR gives smaller free energy barrier and lower ISR gives higher barrier. There is also a structural correspondence shown in the figure for different ligands. The ligands with the fork structure have high structural specificity and faster kinetics, and ligands without the fork structure have low specificity and slower kinetics. We plot the free energy barrier height and the kinetic time for binding of these three cases as shown in Fig 10D. By exploring the different off rates Timeoff and on rates Timeon of binding for three ligands, we found that the ligand with higher ISR has faster on rate and slower off rate. In other words, the ligand has longer residence time for binding. In contrast, the ligand with lower ISR has slower on rate and faster off rate with shorter residence time. In a word, we found indeed that the large ISR leads to lower barrier height and faster kinetics. This implies that the kinetics is determined by the intrinsic specificity which is determined by the competition of the slope of the landscape towards the native state and the roughness of the landscape, not just by the affinity alone as conventionally people would have thought. There are recently growing experimental evidences of the similar affinity but completely different kinetic accessibility [53, 54].

Bottom Line: The results of the analytical studies are confirmed by the microscopic flexible docking simulations.Our study provides new insights into the statistical nature of thermodynamics, kinetics and function from different ligands binding with a specific receptor or equivalently specific ligand binding with different receptors.The elucidation of distributions of the kinetics and free energy has guiding roles in studying biomolecular recognition and function through small-molecule evolution and chemical genetics.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, ChangChun, Jilin, P.R. China.

ABSTRACT
We uncovered the universal statistical laws for the biomolecular recognition/binding process. We quantified the statistical energy landscapes for binding, from which we can characterize the distributions of the binding free energy (affinity), the equilibrium constants, the kinetics and the specificity by exploring the different ligands binding with a particular receptor. The results of the analytical studies are confirmed by the microscopic flexible docking simulations. The distribution of binding affinity is Gaussian around the mean and becomes exponential near the tail. The equilibrium constants of the binding follow a log-normal distribution around the mean and a power law distribution in the tail. The intrinsic specificity for biomolecular recognition measures the degree of discrimination of native versus non-native binding and the optimization of which becomes the maximization of the ratio of the free energy gap between the native state and the average of non-native states versus the roughness measured by the variance of the free energy landscape around its mean. The intrinsic specificity obeys a Gaussian distribution near the mean and an exponential distribution near the tail. Furthermore, the kinetics of binding follows a log-normal distribution near the mean and a power law distribution at the tail. Our study provides new insights into the statistical nature of thermodynamics, kinetics and function from different ligands binding with a specific receptor or equivalently specific ligand binding with different receptors. The elucidation of distributions of the kinetics and free energy has guiding roles in studying biomolecular recognition and function through small-molecule evolution and chemical genetics.

No MeSH data available.


Related in: MedlinePlus