What is Protein Design?

Transcription

1 Protein Design

2 What is Protein Design? Given a fixed backbone, find the optimal sequence. Given a fixed backbone and native sequence, redesign a subset of positions (e.g. in the active site). What does optimal mean? So far we have: =(...,r i,...) E( ) = X i6=j E i,j + X i E i = arg min E( ) Pr[ ] / e E( ) = arg max Pr[ ] G = X p( )E( )+T X p( )ln(p( )) = ln Z

3 What is Protein Design? We can view protein design as just a generalization of sidechain placement. But the free-energy perspective may be more realistic. How do we computationally minimize free energy during protein redesign? We can apply all the same approaches as for side chain placement, or, search for the optimal sequence.

4 Free Energy Computation x f 3 Marginalization Find the marginal value of variable. For example: on a particular f 2 y g z = X u,v,x,y f 1 (u, v) f 2 (v, x) f 3 (x, y) f 4 (y, z) f 5 (z) v f 4 We are interested in the partition function, which is just the sum of all values of, and is nearly the same as computing any marginal. f 1 u z f 5 In a tree-structured factor graph, the running time is linear in the size and domain of the model. In a general graph, it is exponential in the tree width! Do any of our pruning strategies make sense for marginalization?

5 More Practical Protein Design Why are we redesigning a protein in the first place? If we are redesigning an active site (of an enzyme, for example), then our goal is to find a new sequence that binds another molecule better than the native ligand. To better model this situation, we can use the rate at which a ligand binds/unbinds to the protein:! It turns out K a K a = k on k o = [PL] [P ][L] is actually related to the partition function!

6 Goal of Enzyme Redesign Phenylalanine Leucine

7 Exact Search with Pruning Lilien et. al compute an estimate for choice of mutations. K a, for every For each mutation choice, the partition functions are approximated by pruning. FIG. 4. Intramutation pruning. Here q is the running approximation to the partition function, and p is an upper bound on the partition function of the pruned conformations. The function B( ) computes a lower energy bound for the given conformation. The function ComputeMinEnergy( ) returns the energy of the energy-minimized conformation as computed using steepest-descent minimization and our implementation of the amber energy function (as described in Step 2 of Section 2.2). At the end, q represents an ϵ-approximation to the true partition function q such that q (1 ϵ)q.

8 Even More Pruning FIG. 8. Intermutation pruning used in computing the bound partition function q PL. The values q and p and the functions B( ) and ComputeMinEnergy( ) are as described in Fig. 4. For all mutations with q PL K o γ q P, the computed q will represent an ϵ-approximation to the true partition function q such that q (1 ϵ)q. In addition to pruning individual conformations using a lower bound, we can use previously computed partition function estimates to help prune successive mutation sequences.

9 Does it Work? Table 2. Dissociation Constants a and Standard Errors (in Parentheses) Measured by Fluorospectrophotometry for Amino Acid Binding to GrsA-PheA and the Novel Mutants 301G/330W and 301G/330F Dissociation constant (µm) K D Substrate WT 301G/330W 301G/330F L-Phe 26 (2.6) 94 (17.2) 53 (4.9) L-Leu 50 (11.6) 45 (9.5) 30 (2.4) a A lower dissociation constant is associated with tighter binding. FIG. 7. Change in fluorescence vs. Leu concentration for 301G/330F. (Inset) Reciprocal plot of the fluorescence quenching data and the linear regression (correlation coefficient of 0.977) showing a dissociation constant of 30 µm. Dissociation constants and standard errors were computed using SPSS Rel (SPSS Inc., Chicago, IL).