Friday, April 04, 2008

Levinthal's Paradox

Back in 1969, Cyrus Levinthal was thinking about protein folding (Levinthal, 1969). He wondered how long it would take for a protein to fold correctly if it had to sample all possible conformations in three-dimensional space.

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Protein Structure
Imagine that there was only a single bond between each amino acid in a protein of 101 amino acid residues. Imagine that there were only three possible configurations around each of those bonds. This means that the protein could adopt 3100, or 5 × 1047 different conformations.

If the protein is able to sample 1013 different bond configurations per second then it would take 1027 years to sample all possible conformations of the protein (Zwanzig et al. 1992). This is quite a long time. Far longer, in fact, than the age of the universe.

Small proteins usually fold spontaneously within seconds and even the largest proteins fold within minutes. The difference between the theoretical calculation and the observed result is known as Levinthal's Paradox.

It isn't really a paradox. Levinthal knew full well that proteins did not fold by sampling all possible conformations. He knew that protein folding involved local cooperative interactions such as formation of α helices and that the formation of such secondary structure elements proceeded in parallel and not sequentially as his thought experiment proposed.

We now know that protein folding is largely driven by hydrophobic collapse as the regions of secondary structure come together to exclude water. This process is a global process involving simultaneous rearrangements of hundreds of bonds at the same time. That's why proteins fold so rapidly. Cyrus Levinthal knew this.

The point of Levinthal's paradox is to demonstrate that when a mathematical calculation shows that some routine process is impossible, then it's the calculation that's wrong, or the assumptions behind the calculation. This point is lost on most Intelligent Design Creationists. They are tremendously fond of complex calculations proving that some biological process is impossible. To them, this is not proof that their calculations are flawed—it's proof that a miracle occurred.


Levinthal, C. (1969) How to Fold Graciously. Mossbauer Spectroscopy in Biological Systems: Proceedings of a meeting held at Allerton House, Monticello, Illinois. J.T.P. DeBrunner and E. Munck eds., University of Illinois Press Pages 22-24 [complete text]

Zwanzig, R., Szabo, A. and Bagchi, B. (1992) Levinthal's paradox. PNAS 89:20-22. [PNAS]

13 comments:

  1. A slightly more subtle point is that there is no such thing as the "correct" folding pattern. To say that a protein folds "correctly" is to place a human value judgement on what the protein is doing. A non-anthropomorphic way of describing this phenomenon would be to discuss the "reproducibility" of the protein's folding pattern, rather than its "correctness".

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  2. I haven't had much time to comment of late, but I am doing my best to following the protein folding issue.

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  3. Intelligent Folding: Where there's folding, there must have been a Folder. How can you deny this obvious truth?

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  4. LM

    I left a comment on your post "THEME: protein folding" from March 18th, about a link that doesn't work. The HTML for the link to the student movie has a supernumerary > + break tag that causes the link to fail.

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  5. This is a great example; I must remember it.

    I heard Cyrus Levinthal lecture in 1966, and found him very impressive. If I hadn't had my immediate future already settled I might easily have applied to him. I think he probably made the point you're referring to in his lecture, but after so much time I can't be certain.

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  6. I spend my time doing research on the net concerning the benefits of using proteins, I was told that you can increase your muscle mass very easy by ingesting proteins.

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  7. Thanks ! Im so glad somebody finally came out and admitted the fact that "Levinthal's Paradox" is, by the definition of the word, NOT a paradox.

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  8. Indeed. Must say you very well dealt with the subject. I am a student currently Studying the protein folding in our structural Biology class. Have also been trying to learn some stat-mech and X-Ray crystallography by self to make calculations and understand data in research papers.

    Recently, some of my friends in university who for the first time have came across this so call pseudo-paradox have developed the thinking that this is a miracle. And knowing I am an atheist have tried to convince me that without God life would not have evolved since protien folding is impossible by self. So they say existence of chaperons are compulsory and such complex design can only be designed.

    Well now let me come to my point.

    I answered them with Energy Bias and Hydrophobic collapse theory. Also explained them how even side chains can form H-Bonds with backbone that would explain missing H-Bonds b/w some hydrophillic side chains. And all that energy bias would exponetially decrease the time required for folding to 10^-1 and so.

    Well But when I had the same argument with my professor. She told me that Proteins can't fold without cheporones. I mean I know cheporones will create more limitations to possible state and and maximize probability of E(j) state.

    Well gr8. But I have a doubt in mind. I always thought proteins can fold after danaturation in lab solutions back to native state if we give them right environment.

    But my professor claims that we have to add cheporones even to lab solution or some enzymes and all.

    But I think Chaperones role emerged to reduce energy cost while protein is being synthesized by coating the hydrophobic groups which can otherwise create mess with nearby ribosome attaching simillar Hydrophobic AAs. And it can also fold proteins.

    But however I am not very convinced with my professor in need of cheparones in lab buffers after protein denaturation. Atleast some if not many proteins in my view should be able to achieve their respective native state given the environment is like required for that state.

    can anyone help to resolve my doubt regarding refolding after denaturation? does it or does it not require us to add cheparones?

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    Replies
    1. From Anfinsen's original experiment with RNAseA, we know that a protein CAN and DOES fold without any other factors present (spontaneously) in one minute or less (after removing denaturant and reducing agent). Some more complicated proteins (more domains, larger, etc.) do require chaperones and protein folding in the context of the dense cell is quite different than this purified protein at low concentration that Anfinsen and other biochemists use for in vitro folding studies.

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    2. There are two obvious but major flaws with everyone's synopsis of the Levinthal Paradox:

      1. In order for the "protein folding" process to be considered a "routine" process, a certain set of criteria must be fulfilled. Without these requirements already established or in place, such "routine" processes become non-existent or no longer deemable as routine. This is what the experiment actually showed, absent of such criteria, but in a more probabilistic outcome. Time, alone, cannot change this outcome without the necessary set of requirements. A simple example may be trying to water your garden when the water to the hose is shut off. Certain rules must be followed before the watering may commence.
      2. "The point of Levinthal's paradox is to demonstrate that when a mathematical calculation shows that some routine process is impossible, then it's the calculation that's wrong, or the assumptions behind the calculation" (?)

      That's a false assertion. by definition something that's routine means it's known to happen, at least in some particular way. So in essence your statement claims something which has already been done on a regular basis is deemed impossible to occur? I would think any 3rd grader would know the calculations must be wrong, since it already happens! But are we to believe that these comments actually reflect the intent behind the paradox or assess its interpretations properly? Moreover, do you really believe this experiment disproves the observed, proven and universal Natural Law of Probabilities? If so, then someone forgot to remove it from the books? Your conclusion lack a logical perspective and understanding for both the laws of science and this experiment.

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  9. Hey,
    Excellent initiative! This is good posting information..

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  10. Two flaws with everyone's synopsis of the Levinthal Paradox:
    1. The "protein folding" may only considered as a routine process after a certain set of criteria have been fulfilled. After which, the folding process may occur and then becomes routine. However what the experiments showed is that those requirements to achieve such abilities through natural processes is indeed "IMPOSSIBLE"! Why do you all overlook such a basic Fact?
    2. "The point of Levinthal's paradox is to demonstrate that when a mathematical calculation shows that some routine process is impossible, then it's the calculation that's wrong, or the assumptions behind the calculation"(?)
    Do you really believe that this experiment disproves the observed, proven and universal Natural Law of Probabilities? Guess someone forgot to tell them to remove the law from the books? That alone defies all logic and reason!

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