Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.
45

The Primary Structure-Folding Relationship

The primary amino acid sequence dictates the potential for secondary and tertiary structure formation, establishing the foundation for protein shape.
📜

The statement of the theorem

Let S=(a1,a2,…,aN)\mathbf{S} = (a_1, a_2, \dots, a_N) be the primary sequence, where ai∈{A,C,D,E,F,G,H,I,K,L,M,N,P,Q,R,S,T,V,W,Y}a_i \in \{A, C, D, E, F, G, H, I, K, L, M, N, P, Q, R, S, T, V, W, Y\}. Define the conformational energy function E(r)E(\mathbf{r}) as a function of the atomic coordinates r=(r1,…,rN)\mathbf{r} = (\mathbf{r}_1, \dots, \mathbf{r}_N). The folding process seeks the native state rN\mathbf{r}_N such that the free energy G(r)=E(r)−TS(r)G(\mathbf{r}) = E(\mathbf{r}) - T S(\mathbf{r}) is minimized: G(rN)=min⁡rG(r)subject to r being compatible with S.G(\mathbf{r}_N) = \min_{\mathbf{r}} G(\mathbf{r}) \quad \text{subject to } \mathbf{r} \text{ being compatible with } \mathbf{S}.