2-Dimensional HP Foldings of Dermaseptin-J 2

Although the hydrophobic-polar (HP) model is a simple model to study protein folding, it is an approximation to the real-life case. Dermaseptin is a subfamily of frog skin active peptide family, which has various antimicrobial activities, and dermaseptin-J2 is a newly found peptide composed of 26 amino acids. In this study, the 2-dimensional HP model was used to analyze the foldings of dermaseptin-J2 and its nine mutants, which were converted to different HP sequences according to the normalized amino acid hydrophobicity index with respect to pH levels and the conversion of glycine as hydrophobic or polar, and each has 847,288,609,443 possible foldings. The results show that the foldings with minimal energy have different native states, which are chiral and can be numerically distinguished and ranked according to the normalized amino acid hydrophobicity index. The nine mutants of dermaseptin-J2 do not affect the minimal energy but affect their native states at pH 7. The results demonstrate that two pH levels and conversion of glycine as hydrophobic or polar affect the native state and minimal energy, suggesting these are two ways to modify dermaseptin-J2.


Introduction
Protein folding is important to understand its structurefunction relationship and folding process.The hydrophobic-polar (HP) model is a very simple model, which was based on the observation that hydrophobic interaction was the driving force for protein folding and the hydrophobicity of amino acids was the main force for developing a native conformation of small globular proteins [1].
The HP model suffers from critiques because its assumption was simple for protein folding, its description was far away from real-life case, its results were difficult to cooperate with the folding obtained from experiments, etc.Therefore, the HP model is not a model without limitations, however, any model is an approximation to the real-life case, and the difference between models relies on the degree of their approximations.If one takes a viewpoint from a single model, then all of the rest models will be problematic.
Actually, any model helps us to understand the world from a different angle.There are several reasons to study the HP model in great details: i) so far very few studies using HP model were applied to real-life case because the HP model needs extremely intensive computations, therefore the studies using HP model is a way to test our computing ability; ii) the extremely intensive computa-tions in HP model was classified as NP problem [2], being the first problem listed millennium prize, so the study on HP model is approaching to one of numerous unsolved examples of NP problem; iii) the study on HP model would help us develop optimal algorithms [3], which sheds light on solving intensively computational problems in biological branches such as phylogenetics, RNA pseudoknot [4]; iv) the HP model provides different insights into folding process; etc.
The HP model is workable for 2-dimensional (2D) and 3-dimensional (3D) folding.For both cases, each amino acid, either hydrophobic (H) or polar (P), walks along a line in 2D lattice or in 3D cube by taking a self-avoided step, then an H-H connection, which does not come from sequential step, has minus unity energy [5], and the folding with minimal energy would be a protein's native folding.
Current computing power can afford the studies on folding in a 2-demensional HP model for very short protein.Dermaseptin is a subfamily of frog skin active peptide family, which has various antimicrobial activities.Dermaseptin-J2 was a relatively newly found peptide of 26 amino acids [6].
The number of foldings increases dramatically with the increase in the length of protein sequence.For example, each amino acid would have three directions to go in self-avoided step in 2D lattice, so the number of three direction steps for n amino acids would be 3 (n-1) .In the case of 26-residue dermaseptin-J2, the possible foldings are 847,288,609,443 in 2D HP model.Practically, it is useful to know all the possible foldings of protein.The aim of this study is to use the 2D HP model to analyze all possible foldings of dermaseptin-J2 with hope to get insight into dermaseptin-J2 antibiotic activity.

Data
The amino acid sequence of dermaseptin-J2 was obtained from UniProt [7], and its accession number was P86636.The normalized amino acid hydrophobicity index was obtained from SigmaAldrich website [8].

HP Model
The HP model classifies amino acids as either hydrophobic or polar, but there is no indication regarding neutral amino acids.So we use the normalized amino acid hydrophobicity index [8] to assign amino acids in dermaseptin-J2 either as hydrophobic or as polar, however, this assignment is still not sufficient because this normalized amino acid hydrophobicity index is based on the fact that glycine as zero, thus we have to choose glycine either as hydrophobic or as polar.This leads to an amino-acid sequence of dermaseptin-J2 to have two HP sequences in terms of assigning glycine as hydrophobic or as polar.Again, the amino acid hydrophobicity is pH dependent [8], which leads us to consider the assignment of amino acids of dermaseptin-J2 at two pH levels.Taken two considerations together, one amino-acid sequence of dermaseptin-J2 has four HP sequences to be operated in HP model.

Results and Discussion
Currently we have no ability to compute every folding in proteins longer than 30 amino acids.In this study, the Lenovo ThinkPat laptop with due CPU of 2 GHz computed 200,000 to 250,000 foldings per second, for a 26amino-acid dermaseptin-J2, the computing time was between 39 and 49 days.
With the normalized amino acid hydrophobicity index [8], we can find how neutral amino acids affect the HP sequences (Table 1), where nine mutants have no effects on HP sequences, so their HP foldings are identical implying harmless mutations.
Of 847,288,609,443 possible foldings for each HP se-  1, it was important to know how many native states the dermaseptin-J2 had (Table 2), where dermaseptin-J2 has more than one native state, for example, 12 native states are found at pH 2 with glycine assigned as polar, and each native state has the same amount of minimal energy, -13.The fact that there is more than one native state suggests the flexibility of folding mechanisms in dermaseptin-J2.
Figure 1 shows only 8 native states of dermaseptin-J2 at pH 7 with glycine assigned as polar, in order to have a full picture on the folding process in 2D lattice.In any folding, it begins from position 1 to position 26, which can be viewed as a pathway to form a folding.An interesting point is that the native state is chirally symmetric between the left-hand side and the right-hand side, namely, the pathways to construct the same folding are chiral because they cannot be superimposed in mirror image.The chiral symmetry in Figure 1 suggests that all foldings of proteins have possibly chiral symmetry in 2D HP lattice.Therefore a protein can find its native state  On the other hand, we notice that the native states and the minimal energy in Table 2 are different with respect to pH levels and the conversion of glycine as hydrophobic or polar.Figure 2 shows the amino acid sequence of dermaseptin-J2 and four foldings at pH 2 and ph 7 with glycine assigned as hydrophobic as well as polar.But these four foldings have the same pathway.Here, we need to see the non-sequential H-H connections due to two pH levels and two assignments of glycine.At pH 2 with glycine assigned as hydrophobic (left-hand configuration in middle panel in Figure 2), there are 13 nonsequential H-H connections: 3H -6H, 3H -24H, 6H -25H, 7H -10H, 7H -26H, 10H -13H, 13H -26H, 14H -17H, 16H -19H, 17H -26H, 18H -21H, 18H -25H, and 21H -24H, whose minimal energy is -13 and larger than that of the native states in Table 2.At pH 2 with glycine assigned as polar (right-hand configuration in middle panel in Figure 2), there are 13 non-sequential H-H connections, whose minimal energy is -13 and equal to that of the native states in Table 2.At pH 7 with glycine assigned as hydrophobic (left-hand configuration in lower panel in Figure 2), there are 12 non-sequential H-H connections, whose minimal energy is -12 and larger than that of the native states in Table 2.At pH 7 with glycine assigned as polar (right-hand configuration in lower panel in Figure 2), there are also 12 non-sequential H-H connections, whose minimal energy is -12 and equal to that of the native states in Table 2. Glycines in dermaseptin-J2 marked by arrows are located at edge of HP folding, so they generally do not construct H-H connections with internal Hs, we would expect more dramatic difference if glycines are located in internal part of protein.
Now let us look at Table 2 again, where a native state has different numbers of folding, such as 40 folding confirmations at pH 2 with glycine assigned as hydrophobic.An intriguing question raised here is whether we can numerically distinguish and rank those folding confirmations?This question comes from such a consideration that a non-sequential H-H connection only gives a unit of G = H at pH 2 Amino acid sequence G = P at pH 2 G = P at pH 7 G = H at pH 7 minimal energy, however, an H-H connection is composed of amino acids with different hydrophobicity, and therefore it would be important to further quantify non-sequential H-H connections with normalized amino acid hydrophobicity index [9].Figure 3 shows the use of the normalized amino acid hydrophobicity index to numerically distinguish and rank 40 folding of native state with the same minimal energy -16, we thus classify those 40 foldings of native state with the same minimal energy -16 into three groups with different foldings.
Furthermore, Table 3 lists the native state of folding with the minimal energy when the glycine is assigned as hydrophobic or polar at pH 2 or pH 7, including dermaseptin-J2 and its nine mutations.Clearly, those mutants do not have the effects on the folding with minimal energy but have effects on their native states to different degrees.An important observation is the fewer the Hs in an HP sequence, the more the foldings with minimal energy.For an antibiotic, if the number of foldings could be related to the range of antibacterial spectrum, then the state with minimal energy could be related to the speci-ficity.On the other hand, the lower specificity would imply less potency against targets.
Experiments revealed that some dermaseptin has an inherent propensity to an extended conformation in aqueous solution and self-assembles into amyloid fibrils in a reversible pH-controlled fashion [10].Implication of this study is one should increase the number of H in order to decrease the minimal energy in a native state.Practically, we can use a hydrophobic amino acid to replace a neutral or hydrophilic amino acid to get a native state with lower minimal energy if this native state concerns chemical reactions.
Finally, the results suggest the possible ways to modify dermaseptin-J2 that we can either modify dermaseptin-J2 via replacing polar amino acids with hydrophobic amino acids or modify dermaseptin-J2 via replacing amino acids according to the normalized amino acid hydrophobicity index.This is meaningful because the antibacterial activity of dermaseptin depends markedly on a threshold number of hydrophobic residues to be present on both extremities of the helix [11].The dermaseptin super-family encompasses a wide variety of structural motifs, and combined approaches have been used to elucidate their antimicrobial effects based on biophysical and cellular biology methods [12].This study helps to understand dermaseptin folding in terms of HP model.

Figure 2 .
Figure 2. Dermaseptin-J2 sequence and four HP foldings at pH 2 and pH 7 with glycines assigned as hydrophobic as well as polar.

Figure 3 .
Figure 3. Native states under G=H at pH 2 with normalized amino acid hydrophobicity index.All has a minimal energy -16, which is the sum of dotted lines and different sum of hydrophobicity index of H-H connections.Left-hand site: HP sequence; Right-hand site: Dermaseptin-J2 sequence.

Table 2 . Number of native states of foldings with minimal energy of dermaseptin-J2 according to different HP con- versions.
Figure 1. 8 native states of folding under HP conversion of G=H at pH 7. Dotted lines are non-sequential H-H connection, which is considered as a unit of negative energy -1, and their sum is the minimal energy -15.