Random energy model

Solving the master equation for the minimally frustrated random energy model showed that the kinetics depend on the connectivity [23]. Eor the globally connected model it was found that the resulting kinetics vary as a function of the energy gap between the folded and unfolded states and the roughness of the energy landscape. The model... 

B. Derrida, Random-energy model limit of a family of disordered models. Phys. Rev. Lett. 45, 79-82 (1980). 

There has been a wealth of activity based on the idea that glassy dynamics is due to some underlying thermodynamic transition [1-25], If a glass former shows a jump in some an appropriate order parameter without the evolution of latent heat, then such a system is said to exhibit a random first-order transition [94,95]. Models of this kind, which include the p-spin glasses [110], and the random energy model [111], do not have symmetry between states but do have quenched random long-range interactions and exhibit the so-called Kauzmann entropy crisis. 

Random energy model The random energy model (REM) results from using a fitness distribution p(f) to assign fitnesses randomly to points in the landscape [ 14,59,60,70,71,81, 91,92], p(f) is the probability that a point in the sequence space has fitness fand is exactly analogous to affinity distribution p(Ka). Such landscapes have zero correlation (are very rugged), have many local fitness peaks, and result in very short adaptive walks. Very few of the local peaks are accessible by adaptive walks from any particular point. 

In the limit K = N — 1, the TVA-lanclscape becomes the random energy model (Derrida, 1980 Derrida, 1981). The fitness function is written as... 

Because the landscape of real proteins is unknown, most of the results we describe in Section III rely on assumptions discussed in Section II. The results are presented for a range of different theoretical landscapes—for example, the random energy model and the uncoupled case—with the assumptions that the real protein landscape lies between these bounds and can be described statistically. Determining the most effective combination of parameters, adjusting them according to the landscape fea-... 

In a similar study, protein evolution has been analyzed using the random energy model (Macken and Perelson, 1989). Macken and Perel-son calculate the probability of a random walk taking k steps to a local optimum as... 

B. Derrida, Random-energy Model An Exactly Solvable Model of Disordered Systems,... 

It is fortunate that a model that relates figure of merit to amino acid sequence for a specific protein is not needed. Tlie requirement is simply a model that produces figure-of-merit landscapes in sequence space that are analogous to those that would be measured in the laboratory on an ensemble of proteins. This type of model is easier to construct, and a random energy model can be used to accomplish the task. 

The generalized NK model is just such a random energy model. The NK model was first introduced to model combinatorial chemistry experiments on peptides (Kauffman and Levin, 1987 Kauffman, 1993 Kauffman and MacReady, 1995). It was subsequently generalized to account for secondary structure in real proteins (Perelson and Macken, 1995). The model was further generalized to account for interactions between the secondary structures and for the presence of a binding pocket (Bogarad and Deem, 1999). 

Bryngelson, J.D. and Wolynes, P.G. (1989) Intermediates and barrier crossing in a random energy-model (with applications to protein folding). J. Phys. Chem. 93 6902-6915. 

We should mention here that independent Gauss distributed energies were first considered by Bernard Derrida (in the FVench Center for Nuclear Research in Saclay near Paris) in a completely diflerent context, and this is known in the literatme as Random Energy Model (REM). 

Randomness is introduced by allowing the interaction energy to be random on each and every bond. The first model, model A, has independent random energy on all the 2b bonds. The randomness in the second model, model B, is taken only along the longitudinal direction so that equivalent bonds on all directed paths have identical random energy. Model B is a hierarchical lattice version of the continuum RANI model. 

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