Abstract
Ben-Naim in three articles dismissed and “answered” the Levinthal’s paradox. He announces there are pitfalls caused by the “misinterpretation” of thermodynamic hypothesis. He claims no existence of Gibbs free energy formula where the variable is a protein’s conformation X . His Gibbs energy functional is G(T, P, N, P(R)), where the variable is probability distributions P (R) of the conformations. His “minimum distribution Peq” is wrong. By carefully establishing thermodynamic systems, we demonstrate how to apply quantum statistics to derive Gibbs free energy formula G(X). The formula of the folding force is given.
Highlights
In [1], Levinthal pointed out that assuming a protein folds by randomly searching its native structure it will need time longer than the age of the universe to achieve its native structure
By carefully establishing thermodynamic systems, we demonstrate how to apply quantum statistics to derive Gibbs free energy formula G X
He concluded that the natural protein folding must be cause-based, that is, the native structure has the minimum value of the Gibbs free energy
Summary
In [1], Levinthal pointed out that assuming a protein folds by randomly searching its native structure it will need time longer than the age of the universe to achieve its native structure. Ben-Naim invents a new “pitfall”: “This misinterpretation (of thermodynamic hypothesis) has inspired many scientists to search for a global minimum in the Gibbs energy as a function of the conformation of the protein, sometimes referred to as the Gibbs energy landscape. Ben-Naim’s conclusion is: “From the two true statements a) and b), people have concluded that the stable state of the protein must be in a global minimum in the GEL Even someone can get a correct minimum distribution for Ben-Naim, Ben-Naim’s shifting from statement (a) to statement (b) is still a misleading, or a real pitfall Because it shifts the study of protein structure to the study of probability distribution of conformations.
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