A ligand is bound to a protein with a spring-like square-law energy e(x), where x is the distance between the ligand and protein as shown in the figure. e(x) = }cx² Protein Ligand (a) For constant (T,V,N), write an expression for the probability distribution p(x) of the ligand separation from the protein. (b) Sketch a plot of p(x) vs x. (c) Write an expression for the average location of the ligand, (x). (d) Write an expression for the second moment of the location of the ligand, (x²). (e) Calculate the average energy, (e) of the system.

A ligand is bound to a protein with a spring-like square-law energy e(x), where x is the distance between the ligand and protein as shown in the figure. e(x) = }cx² Protein Ligand (a) For constant (T,V,N), write an expression for the probability distribution p(x) of the ligand separation from the protein. (b) Sketch a plot of p(x) vs x. (c) Write an expression for the average location of the ligand, (x). (d) Write an expression for the second moment of the location of the ligand, (x²). (e) Calculate the average energy, (e) of the system.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

15. Modeling ligand binding.
A ligand is bound to a protein with a spring-like square-law energy e(x), where x is the
distance between the ligand and protein as shown in the figure.
e(2) = }ca²
Protein
Ligand
(a) For constant (T,V,N), write an expression for the probability distribution p(x) of the
ligand separation from the protein.
(b) Sketch a plot of p(x) vs x.
Write an expression for the average location of the ligand, (x).
(d) Write an expression for the second moment of the location of the ligand, (x2).
(e) Calculate the average energy, (e) of the system.

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