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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.


The physical equivalences in probing interactions of molecular recognition.(A) A specific ligand binding to different receptors, P1∼Pn represent the different receptor proteins with the associated binding sites. (B) Different interactions through different atomic contacts of a specific pair of ligand-receptor complex, M1∼Mn represent the different interactions with different set of contacts located at the different binding sites of a specific receptor. (C) A specific receptor binding to different ligands, N1∼Nn represent the different ligands with different sequences.
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pcbi.1004212.g001: The physical equivalences in probing interactions of molecular recognition.(A) A specific ligand binding to different receptors, P1∼Pn represent the different receptor proteins with the associated binding sites. (B) Different interactions through different atomic contacts of a specific pair of ligand-receptor complex, M1∼Mn represent the different interactions with different set of contacts located at the different binding sites of a specific receptor. (C) A specific receptor binding to different ligands, N1∼Nn represent the different ligands with different sequences.

Mentions: Experiments on random sequence protein folding [11] and protein design [12], have implied the statistical distributions of physical observable. Experimental and computational studies on biomolecular binding have also shown evidences of distribution of physical relevant quantities such as binding equilibrium constants K [13–18]. Since Log K is proportional to the free energy difference between the native and non-native states termed as the stability or affinity, this infers that the free energy also has a distribution. The experimental features on binding indicate that the appropriate physical variable is the free energy of binding of ligands to the receptor, not the energy. The similar situation also appears for random sequence protein folding and protein design. As a result, the free energy stability or affinity for each specific sequence of ligand can be obtained. Certain values of the affinity appear more often than others. The free energies therefore are distributed. When we discuss about the distribution of the free energies, we mean the sampling of different free binding energies from the different ligands with different sequences binding to the same receptor. The binding free energy of each individual ligand to a specific receptor can be calculated and measured directly from the experiments (through the equilibrium constant measurements). Collecting the free energies from different ligands binding to the same receptor, we can find the distributions of the free energy. The similar procedure applies to the statistics of specificity, equilibrium constants and kinetics for different ligands binding to the same receptor protein. We mainly focus on the statistics of the different ligands binding to the same receptor protein in this study. By exploring the sequence space of ligands, one also equivalently goes through the interactions and conformation space under the ergodicity condition. Here, we describe a physical hypothesis based on a thought experiment (see the Fig 1) [19–21]. Imagine we connect all the different receptors by linkers (for example, connecting N terminus of a protein and C terminus of another by glycines), then the whole universe of receptors now becomes one giant protein. When the receptor protein is large enough, probing the interactions of binding through different parts (binding sites/pockets) of the same receptor protein (panel B) and probing the interactions through the sequences (different receptors in panel A or different ligands in panel C) should be equivalent. The quantitative issue is how large the receptor protein should be in order to see the above mentioned approximate equivalence. Since the protein folds have been estimated to be on the order of a thousand [22], the actual number of the interactions via the atomic contacts of the ligands with the receptors is finite and enumerable. In other words, a large but finite size protein may already contain most of the interactions encountered for ligand binding. Under the assumption of large receptor protein (large enough to effectively represent the sequences of the diverse receptor universe), obviously searching for all the binding sites or pockets of a particular finite size protein is equivalent to searching for the whole universe of the receptors. Therefore, in this case, probing interactions can be reached approximately equivalently by the following three approaches: (1) multiple ligands binding to the same receptor, or (2) multiple receptors binding to the same ligand, or (3) a ligand binding to a receptor exploring the different binding sites (modes). This hypothesis has been tested and validated for specificity of Cox-2/Cox-1 receptor-ligand complexes [21]. In other words, the statistical properties through the exploration of sequence space of different ligands with the same receptor is equivalent of searching through the conformational or structural space for a particular ligand receptor pair. Although the free energy is in general a complicated function of interactions and entropy, combinatorial library of ligands and database of small molecules provide us a great opportunity to study the interactions and underlying principles of binding. In the free energy distribution, the native (strongest) binding state(mode) should appear in the lowest end of the tail where the density of these binding states becomes discrete.


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

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

The physical equivalences in probing interactions of molecular recognition.(A) A specific ligand binding to different receptors, P1∼Pn represent the different receptor proteins with the associated binding sites. (B) Different interactions through different atomic contacts of a specific pair of ligand-receptor complex, M1∼Mn represent the different interactions with different set of contacts located at the different binding sites of a specific receptor. (C) A specific receptor binding to different ligands, N1∼Nn represent the different ligands with different sequences.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi.1004212.g001: The physical equivalences in probing interactions of molecular recognition.(A) A specific ligand binding to different receptors, P1∼Pn represent the different receptor proteins with the associated binding sites. (B) Different interactions through different atomic contacts of a specific pair of ligand-receptor complex, M1∼Mn represent the different interactions with different set of contacts located at the different binding sites of a specific receptor. (C) A specific receptor binding to different ligands, N1∼Nn represent the different ligands with different sequences.
Mentions: Experiments on random sequence protein folding [11] and protein design [12], have implied the statistical distributions of physical observable. Experimental and computational studies on biomolecular binding have also shown evidences of distribution of physical relevant quantities such as binding equilibrium constants K [13–18]. Since Log K is proportional to the free energy difference between the native and non-native states termed as the stability or affinity, this infers that the free energy also has a distribution. The experimental features on binding indicate that the appropriate physical variable is the free energy of binding of ligands to the receptor, not the energy. The similar situation also appears for random sequence protein folding and protein design. As a result, the free energy stability or affinity for each specific sequence of ligand can be obtained. Certain values of the affinity appear more often than others. The free energies therefore are distributed. When we discuss about the distribution of the free energies, we mean the sampling of different free binding energies from the different ligands with different sequences binding to the same receptor. The binding free energy of each individual ligand to a specific receptor can be calculated and measured directly from the experiments (through the equilibrium constant measurements). Collecting the free energies from different ligands binding to the same receptor, we can find the distributions of the free energy. The similar procedure applies to the statistics of specificity, equilibrium constants and kinetics for different ligands binding to the same receptor protein. We mainly focus on the statistics of the different ligands binding to the same receptor protein in this study. By exploring the sequence space of ligands, one also equivalently goes through the interactions and conformation space under the ergodicity condition. Here, we describe a physical hypothesis based on a thought experiment (see the Fig 1) [19–21]. Imagine we connect all the different receptors by linkers (for example, connecting N terminus of a protein and C terminus of another by glycines), then the whole universe of receptors now becomes one giant protein. When the receptor protein is large enough, probing the interactions of binding through different parts (binding sites/pockets) of the same receptor protein (panel B) and probing the interactions through the sequences (different receptors in panel A or different ligands in panel C) should be equivalent. The quantitative issue is how large the receptor protein should be in order to see the above mentioned approximate equivalence. Since the protein folds have been estimated to be on the order of a thousand [22], the actual number of the interactions via the atomic contacts of the ligands with the receptors is finite and enumerable. In other words, a large but finite size protein may already contain most of the interactions encountered for ligand binding. Under the assumption of large receptor protein (large enough to effectively represent the sequences of the diverse receptor universe), obviously searching for all the binding sites or pockets of a particular finite size protein is equivalent to searching for the whole universe of the receptors. Therefore, in this case, probing interactions can be reached approximately equivalently by the following three approaches: (1) multiple ligands binding to the same receptor, or (2) multiple receptors binding to the same ligand, or (3) a ligand binding to a receptor exploring the different binding sites (modes). This hypothesis has been tested and validated for specificity of Cox-2/Cox-1 receptor-ligand complexes [21]. In other words, the statistical properties through the exploration of sequence space of different ligands with the same receptor is equivalent of searching through the conformational or structural space for a particular ligand receptor pair. Although the free energy is in general a complicated function of interactions and entropy, combinatorial library of ligands and database of small molecules provide us a great opportunity to study the interactions and underlying principles of binding. In the free energy distribution, the native (strongest) binding state(mode) should appear in the lowest end of the tail where the density of these binding states becomes discrete.

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.