Protein ground state candidates in a simple model: An enumeration study

Abstract

The concept of the reduced set of contact maps is introduced. Using this concept we find the ground state candidates for a hydrophobic-polar lattice model on a two-dimensional square lattice. Using these results we exactly enumerate the native states of all proteins for a wide range of energy parameters. In this way, we show that there are some sequences which have an absolute native state. Moreover, we study the scale dependence of the number of members of the reduced set, the number of ground state candidates, and the number of perfectly stable sequences by comparing the results for sequences with lengths of 6 up to 20.

Use of machine learning algorithms to classify binary protein sequences as highly-designable or poorly-designable

“…These results are shown in Figure 2a for the hexagon, and Figure 2b for the triangle, where the logarithm of the number of conformations log N conf having N s sequences folding to them is plotted against N s . These two graphs express qualitatively the same ideas reported in earlier studies [ 17 , 24 , 28 , 29 , 33 , 38 ]. There are many conformations with relatively few (or no) sequences folding to them and a rather smaller number of conformations that have many sequences folding to these structures.…”

“…Figure 3 shows the most designable conformations for each shape. The most designable conformation for the hexagonal shape shows features of symmetry that have been found in previous studies [ 17 , 24 , 28 , 29 , 33 , 38 ]. Both of the conformations contain many peptide bonds between the protein surface and the core, a feature that has been suggested to play an important role in the flexibility of proteins [ 38 ].…”

Statistical theory of phenotype abundance distributions: A test through exact enumeration of genotype spaces

“…The first column lists the maps studied and some of its quantitative properties: total number of phenotypes, number of non-empty (NE) phenotypes (this quantity resulting from folds with non-negative energy and the large number of degenerated genotypes that are discarded, see Appendix A), number of sequences assigned to a unique phenotype (UaS), average abundance of phenotypes Sav, total number of neutral components (NCs), and fraction of non-functional sequences (f ∅ ). Non-compact HP20 (n-c HP20) is included to compare with n-c HP20 with minimal contact maps (n-c HP20 S) as phenotypes (a distribution of phenotype abundances for n-c HP20 can be found in [33]). 1 Data obtained with two energy parameters, U (H, H) = −2.3 and U (H, P ) = U (P, H) = −1.…”

Shape-dependent designability studies of lattice proteins

“…1B is 14,579 (obtained by summing over the individual numbers of conformations for each shape). Because we study proteins with 24 residues and we are using the binary hydrophobic-polar (HP) alphabet, this amount to having 2 24 (˜3.2×10 7 ) different possible sequences (for chains having two distinguishable ends: C-terminal and N-terminal), each of which is threaded onto all available conformations. There are many possible energy functions even for the binary alphabet, and here we use the simplest one where each H-H non-bonded contact is given an energy score of -1.0 while all other contacts (H-P and P-P) are scored as 0.…”

“…In past studies of protein designability, amino acid sequences were threaded onto all possible compact conformations of a given shape and for each threading the total energy of the fold was computed based on a specified energy function (19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35). If there is a conformation that has a total energy lower than all other conformations, we assume that the sequence will fold to that specific conformation.…”