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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.


Funneled energy landscape of the biomolecular binding.Panel (A) shows the energy landscape of the receptor-ligand binding with a funneled shape towards the native state. Panel (B) shows the density of states of the ligand binding landscape. The intrinsic specificity ratio , where energy gap δE and energy roughness ΔE and size of the binding funnel measured by the entropy S are shown respectively. Panel (C) shows the free energy landscape of ligand binding, cartoon showing of receptor/ligand complex corresponds to the different binding states. The affinity measured by the free energy difference between the native binding state and unbound states are shown as ΔG. It can also be measured by the equilibrium constant K where ΔG = −RTlnK. Panel (D) shows the energy landscape and free energy profiles on different reaction coordinates.
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pcbi.1004212.g002: Funneled energy landscape of the biomolecular binding.Panel (A) shows the energy landscape of the receptor-ligand binding with a funneled shape towards the native state. Panel (B) shows the density of states of the ligand binding landscape. The intrinsic specificity ratio , where energy gap δE and energy roughness ΔE and size of the binding funnel measured by the entropy S are shown respectively. Panel (C) shows the free energy landscape of ligand binding, cartoon showing of receptor/ligand complex corresponds to the different binding states. The affinity measured by the free energy difference between the native binding state and unbound states are shown as ΔG. It can also be measured by the equilibrium constant K where ΔG = −RTlnK. Panel (D) shows the energy landscape and free energy profiles on different reaction coordinates.

Mentions: The conventional specificity refers to the discrimination of binding affinities between a specific ligand with different receptors. However, it is challenge to go through the whole universe of receptors to determine the binding specificity due to the lack of the full information. From the above equilvalence discussions in terms of probing the interactions of molecular recognition, another way of quantify the specificity is to find the discrimination in binding affinities of a ligand binding with different binding sites of a receptor. This is referred to the intrinsic specificity. Under large protein assumption, the intrinsic specificity and conventional specificity should be equivalent. The supporting evidence was illustrated in the Cox-2/Cox-1 binding with ligands [19–21]. Both affinity and specificity are crucial for determining the molecular recognition. An optimal quantitative criterion for the intrinsic specificity in discriminating the native from the non-native states for the best binding sequences is found to be the maximization of the intrinsic specificity ratio (ISR) of the energy gap between the energies of the native state and the average of the other states versus roughness or fluctuation modularized by the entropy or size of underlying binding energy landscape [19, 20], see panel B of Fig 2 for the density of states of binding. This implies that the underlying binding landscape is funneled towards the native state. This is not surprising since the driving force of the binding is the same as folding, the hydrophobic interactions. The folding can be seen as self binding and binding can be viewed as folding with multiple domains without the linkages between the domains. Therefore, one expects that the resulting binding energy landscape should have a funneled shape towards the native state to guarantee the stability and intrinsic specificity as well as the kinetic speed of recognition against the bumps or wiggles along the binding paths. (see panel A,C of Fig 2). This is in parallel to the protein folding studies where similar optimal criterion for folding has been used to design fast folding protein sequences [23–25]. Different ligands or small molecules will have different specificity for binding with a specific receptor. Therefore, the intrinsic specificity(ISR) should also have a statistical distribution. This reflects different degrees of binding specificity. There is a small group of high specificity ligands among all the available ones. This is rare and lies in the high end tail of the distribution of specificity.


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

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

Funneled energy landscape of the biomolecular binding.Panel (A) shows the energy landscape of the receptor-ligand binding with a funneled shape towards the native state. Panel (B) shows the density of states of the ligand binding landscape. The intrinsic specificity ratio , where energy gap δE and energy roughness ΔE and size of the binding funnel measured by the entropy S are shown respectively. Panel (C) shows the free energy landscape of ligand binding, cartoon showing of receptor/ligand complex corresponds to the different binding states. The affinity measured by the free energy difference between the native binding state and unbound states are shown as ΔG. It can also be measured by the equilibrium constant K where ΔG = −RTlnK. Panel (D) shows the energy landscape and free energy profiles on different reaction coordinates.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi.1004212.g002: Funneled energy landscape of the biomolecular binding.Panel (A) shows the energy landscape of the receptor-ligand binding with a funneled shape towards the native state. Panel (B) shows the density of states of the ligand binding landscape. The intrinsic specificity ratio , where energy gap δE and energy roughness ΔE and size of the binding funnel measured by the entropy S are shown respectively. Panel (C) shows the free energy landscape of ligand binding, cartoon showing of receptor/ligand complex corresponds to the different binding states. The affinity measured by the free energy difference between the native binding state and unbound states are shown as ΔG. It can also be measured by the equilibrium constant K where ΔG = −RTlnK. Panel (D) shows the energy landscape and free energy profiles on different reaction coordinates.
Mentions: The conventional specificity refers to the discrimination of binding affinities between a specific ligand with different receptors. However, it is challenge to go through the whole universe of receptors to determine the binding specificity due to the lack of the full information. From the above equilvalence discussions in terms of probing the interactions of molecular recognition, another way of quantify the specificity is to find the discrimination in binding affinities of a ligand binding with different binding sites of a receptor. This is referred to the intrinsic specificity. Under large protein assumption, the intrinsic specificity and conventional specificity should be equivalent. The supporting evidence was illustrated in the Cox-2/Cox-1 binding with ligands [19–21]. Both affinity and specificity are crucial for determining the molecular recognition. An optimal quantitative criterion for the intrinsic specificity in discriminating the native from the non-native states for the best binding sequences is found to be the maximization of the intrinsic specificity ratio (ISR) of the energy gap between the energies of the native state and the average of the other states versus roughness or fluctuation modularized by the entropy or size of underlying binding energy landscape [19, 20], see panel B of Fig 2 for the density of states of binding. This implies that the underlying binding landscape is funneled towards the native state. This is not surprising since the driving force of the binding is the same as folding, the hydrophobic interactions. The folding can be seen as self binding and binding can be viewed as folding with multiple domains without the linkages between the domains. Therefore, one expects that the resulting binding energy landscape should have a funneled shape towards the native state to guarantee the stability and intrinsic specificity as well as the kinetic speed of recognition against the bumps or wiggles along the binding paths. (see panel A,C of Fig 2). This is in parallel to the protein folding studies where similar optimal criterion for folding has been used to design fast folding protein sequences [23–25]. Different ligands or small molecules will have different specificity for binding with a specific receptor. Therefore, the intrinsic specificity(ISR) should also have a statistical distribution. This reflects different degrees of binding specificity. There is a small group of high specificity ligands among all the available ones. This is rare and lies in the high end tail of the distribution of specificity.

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.