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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 entropy S(E) as a function of energy for the random energy model.The curve is entropy S(E) = ln[n(E)], where n(E) is the density of states with energy E from the spectrum, Ec is the corresponding energy of the trapping transition temperature Tc. As we see, the point M moves on the curve with the changes in the slope (1/T).
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pcbi.1004212.g003: The entropy S(E) as a function of energy for the random energy model.The curve is entropy S(E) = ln[n(E)], where n(E) is the density of states with energy E from the spectrum, Ec is the corresponding energy of the trapping transition temperature Tc. As we see, the point M moves on the curve with the changes in the slope (1/T).

Mentions: It should be noted that in the aforementioned analytical random energy model [33, 38, 39], from the thermodynamic Maxwell relation of δS(E)/δE = 1/T(Fig 3) where S(E) is the entropy of the system. Since entropy is related to the distribution of the states in energy or density of states (S = ln[n(E)]), we can see the relationship between the energy (left side of the equation) and temperature (right side of the equation). Physically it is clear that the slope of distribution is inversely proportion to temperature (Fig 3). In other words when the temperature is high (the slope of the distribution 1/T is low), then the energy is at the center of the distribution and when the temperature is low (slope of the distribution 1/T is high), then the energy is at the tail of the distribution (Fig 3). This can be seen clearly in Fig 3. Since free energy is related to energy, high energy leads to high free energy. Therefore, when temperature is high, then the free energy is at the center of the distribution and when the temperature is low, then the free energy is at the tail of the distribution (Fig 3). This is also true for the affinity, equilibrium constant, ISR and kinetic rate distributions where all of these variables are directly related to the free energy. Therefore, these give the correspondences of the analytical results for distribution of the variables in different temperature ranges with the simulation results for distribution of the variables in different variable ranges. On the other hand, since partition function Z has an asymptotic form and a power law distribution at the tail, the associated free energy is therefore exponentially distributed at the tail (x→∞)(See details in S1 Text). In other words, for the distribution of free energy, we can obtain two distinct regions (such as low and high free energy) of the corresponding physical variable.


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

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

The entropy S(E) as a function of energy for the random energy model.The curve is entropy S(E) = ln[n(E)], where n(E) is the density of states with energy E from the spectrum, Ec is the corresponding energy of the trapping transition temperature Tc. As we see, the point M moves on the curve with the changes in the slope (1/T).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi.1004212.g003: The entropy S(E) as a function of energy for the random energy model.The curve is entropy S(E) = ln[n(E)], where n(E) is the density of states with energy E from the spectrum, Ec is the corresponding energy of the trapping transition temperature Tc. As we see, the point M moves on the curve with the changes in the slope (1/T).
Mentions: It should be noted that in the aforementioned analytical random energy model [33, 38, 39], from the thermodynamic Maxwell relation of δS(E)/δE = 1/T(Fig 3) where S(E) is the entropy of the system. Since entropy is related to the distribution of the states in energy or density of states (S = ln[n(E)]), we can see the relationship between the energy (left side of the equation) and temperature (right side of the equation). Physically it is clear that the slope of distribution is inversely proportion to temperature (Fig 3). In other words when the temperature is high (the slope of the distribution 1/T is low), then the energy is at the center of the distribution and when the temperature is low (slope of the distribution 1/T is high), then the energy is at the tail of the distribution (Fig 3). This can be seen clearly in Fig 3. Since free energy is related to energy, high energy leads to high free energy. Therefore, when temperature is high, then the free energy is at the center of the distribution and when the temperature is low, then the free energy is at the tail of the distribution (Fig 3). This is also true for the affinity, equilibrium constant, ISR and kinetic rate distributions where all of these variables are directly related to the free energy. Therefore, these give the correspondences of the analytical results for distribution of the variables in different temperature ranges with the simulation results for distribution of the variables in different variable ranges. On the other hand, since partition function Z has an asymptotic form and a power law distribution at the tail, the associated free energy is therefore exponentially distributed at the tail (x→∞)(See details in S1 Text). In other words, for the distribution of free energy, we can obtain two distinct regions (such as low and high free energy) of the corresponding physical variable.

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.