Subject: CCL: Levinthal's paradox

From: JATI KASTANJA <[email-masked]>
Date: Fri, 30 Jul 1999 17:53:16 +0000

Dear CCLers,
does anyone know something about the Levinthal paradox? 
It deals with the fact that proteins do fold into unique states in 
seconds. Considering the number of all possible conformations it 
seems to be quite impossible to do the fold in such a short time.
Until now I am unsuccessful in finding out the journal where Cyrus 
Levinthal first published something about this paradox. 
I would be very glad to get any advice. Thanks in advance.

Regards, Jati 

**********************************************************************************
 Jati Kastanja                              Phone:+49/241/4469138                 
 German Woolresearch Center                 Fax:+49/241/4469100                 
 at the University of Technology Aachen     email:[email-masked] 
 Veltmanplatz 8, 52062 Aachen, Germany                                                                                         
                                         
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From: Peter Shenkin <[email-masked]>
Date: Fri, 30 Jul 1999 16:35:45 -0400 (EDT)

> does anyone know something about the Levinthal paradox? 
...
> Until now I am unsuccessful in finding out the journal where Cyrus ...

Hi,

If you do find the Journal, you will find that it contains only
a passing reference to what has become known as the Levinthal
paradox.  The idea really derives from a comment Cyrus once made at a
meeting.

The idea is this.  Take a 100-residue protein.  Let's suppose each
residue can have only, say, 3 conformational states.  Then there
are 3^100, or about 10^48, possible states.  Now suppose the protein
can explore a new state with every moleculear vibration.  Suppose 
each vibration takes about a femtosecond.  Then exploring all 
the states would take about 10^48 fs, or 10^33 s.  There are about 10^8 s
in a year, so exploring all the states would take about 10^25 years.
But this is longer than the age of the universe.  

Now, in order for a protein to fold into its global
thermodynamic energy minimum, the folding process has to
be ergodic.  That is, it has to explore all its states
within the time-span of the process.  But protein folding takes
typically seconds to minutes.  So a protein can't be folding 
into its thermodynamic energetic minimum, since it can't
possibly find it in so short a time.

Therefore, protein folding must be a kinetically controlled process.
I.e., proteins fold to the most accessible minimum, rather than the 
most stable minimum.  In this, protein folding must resemble the
kinetically controlled reactions of organic (and bio-) chemistry.

The reason it's considered a "paradox" is that most people
don't believe it (at least for globular proteins as small
as 100 residues). Cyrus didn't believe it either, in fact.
But it is fun to think about, and it's great for impressing
people at cocktail parties.  (You have to go to the right cocktail 
parties, though. :-) )

-P.

--
********* Peter S. Shenkin; Schrodinger, Inc.; (201)433-2014 x111 *********
*********** [email-masked]; http://www.schrodinger.com ***********

---

From: "Jim Kress" <[email-masked]>
Date: Fri, 30 Jul 1999 17:45:13 -0400

In highly nonlinear systems sudden transitions in states (from one to
another) are a well known behavior.  Could it be that the 'paradox' is just
the result of a simple state change in a protein driven by the highly
nonlinear forces that control its configuration?

Jim

Check out my web site  http://www.kressworks.com/
It'll blow your mind (politically), stimulate your senses (artistically)
and provide scientific insights that boggle the mind!

----- Original Message -----
From: Peter Shenkin <[email-masked]>
To: <[email-masked]>
Sent: Friday, July 30, 1999 4:35 PM
Subject: CCL:Levinthal's paradox

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