Autonomous Sequences in Myoglobin Emerging from X-ray Structure of Holomyoglobin.

The proposed continuous folding structure units are fundamental to analyze protein structure. Here, we could elucidate for the first time two types of hydrophobic core networks in apomyoglobin using continuous folding structure units. In myoglobin, two autonomous sequences emerged clearly. We could thus characterize the autonomous sequences using well-defined hydrophobic core networks within respective semifolds. A hydrophobic core is defined as a pair of topology-local hydrophobic amino acids in different folding structures. Hydrophobic core formation is indispensable to stabilize the different folding structures via an efficient hydrophobic interaction. Autonomous sequences in myoglobin encode tertiary structure information for semifolds. These sequences fold autonomously into small sets of continuous folding structure units to grow separate semifolds on each separate framework. The autonomous sequence can be defined as the local sequence assigned to the small set of continuous folding structure units. They create the discrete hydrophobic region in a semifold by assembly of their hydrophobic regions. Semifolds were characterized by discrete hydrophobic regions stabilized by respective type I hydrophobic core networks, which were present within each semifold. The discrete hydrophobic region of a semifold propagated itself with that of a different semifold by hydrophobic interactions in type II hydrophobic core network, which was present between different semifolds, as observed by the X-ray structures of semifolds. The most significant feature of semifolds in apomyoglobin was that they could be verified by the X-ray structure of holomyoglobin regardless of the instability of folds characteristic to autonomous sequence fragments. This work presents the first description of autonomous sequences.

Introduction

Protein-folding information is axiomatically encoded in the amino acid sequence of proteins.[1−6] It can be elucidated by analyzing the structure of well-established proteins as a structural analysis based on normalized structure information requires experimental evidence. Levinthal inferred that protein sequences are folded into native structures via specific folding pathways as there are too many possible conformations for determining native structures by random searching.[7,8] Originally, the tertiary structure of a protein can be derived by simple accumulation of the conformation of each amino acid, and the continuous secondary structures of the protein are the entire framework of a protein fold.[9] Thus, secondary structures were utilized as specific folding pathways for protein-folding analysis.[10−12] In general, 50–60% of amino acids in globular proteins are in α-helix and/or β-strand structures.[13,14] However, amino acid sequences have not been assigned secondary structure information, because many types of secondary structures are still undefined.

To cover all protein chains with defined-local structures, we introduced protein-folding structures instead of secondary structures because normalized secondary structure information could not be analyzed statistically.[5] Folding structure units were defined by using folding elements based on the observation of two-dimensional representations of the dihedral angles of each amino acid and the amino acid sequences of native protein structures.[9,15] Each folding structure unit was defined so that both the terminal di- and tripeptide sequences shared common sequences with the two adjacent folding structure units.[5] Thus, folding structures of protein folds are composed of continuous folding structure units with suitable overlapping regions. N-Terminal and C-terminal folding structures are always partial structures of folding structure units. Folding structure units are characterized by one-dimensional combinations of folding elements assigned to each amino acid in local sequences. Statistical analysis of folding structures instead of secondary structures led to a general solution for the formation of normalized folding structures in proteins based on the normalized folding structure information and probability theory.[5] Description of protein structure in terms of folding structure units with suitable overlapping regions enabled us to understand protein folding in well-established protein structures at a residue-specific level.

Overlapping regions determined the connection of folding structure units, which were assigned to the amino acid sequence. Continuous folding structure units covered the entire framework of a protein fold.[5] The entire framework of protein fold was formed by simple accumulation of folding elements to each amino acid in the protein sequence, based on the amino acid sequence by means of probability theory using the normalized folding structure information.[5] Thus, protein folding was considered to proceed by folding events mediated by hydrophobic interactions throughout the entire framework. Protein folding on the entire framework at the amino acid level distinctly differs from the specific pathway model and the energy landscape and folding funnel model.[4,6−8,10−12,16−23]

Recently, Dyson and Wright reviewed the myoglobin folding information, delineating the folding pathway at a residue-specific level.[6] The amino acid sequence of myoglobin can stabilize apomyoglobin as well as discrete folded native-like intermediates, referred to as “semifolds”. Apomyoglobin is the native structure of myoglobin. At pH 6, apomyoglobin folds into the same topology as holomyoglobin, except that the F helix is incompletely folded.[24] The semifold can be recognized by using continuous folding structure units assigned to the myoglobin sequence and is a minimum unit to analyze the tertiary structure information of an autonomous sequence. Autonomous sequences of globular proteins may certainly fold into semifolds. They separately fold into cooperative native local structures based on their tertiary structure information, even though fragment structures of protein chains are, in general, predominantly nonnative.[25,26] Given that autonomous sequences are identified in a protein chain, protein-folding information is clearly understood because it forms minimum tertiary structures as semifolds.

The autonomous sequence corresponds to an autonomously folding peptide segment and creates the discrete hydrophobic region of a semifold by assembly of hydrophobic regions in continuous folding structure units. Thus, the small set of continuous folding structure units is a defining characteristic to the autonomous sequence. We believe that the semifold can be derived from the amino acid sequence by means of probability theory using the normalized folding structure information. We also propose the autonomous sequences of the well-established protein structure fold into semifolds, which can be verified by X-ray structure regardless of their instability. We consider that the identification of autonomous sequences is the most important for understanding protein-folding information.

Autonomous sequences in globular proteins have not been recognized because these fragment structures are, in general, nonnative.[26] However, we noticed the existence of autonomous sequences in the immunoglobulin-binding B1 domain of protein G (GB1). The C-terminal 16-residue sequence is autonomous because the peptide fragment G41–E56 can fold into a β-hairpin in GB1,[27,28] and the N-terminal 40-residue sequence is also autonomous because the unstable fold of the M1–D40 peptide fragment can be stabilized by addition of the G41–E56 peptide fragment, forming a native-like quaternary structure.[28] These results imply that the amino acid sequence of GB1 can be divided into an N-terminal 40-residue autonomous sequence (M1–D40) and a C-terminal 16-residue autonomous sequence (G41–E56) based on its X-ray structure,[29] which showed that the autonomous sequences formed native-like separate semifolds containing discrete hydrophobic regions. Thus, the entire framework of GB1 is divided into separate frameworks of semifolds. The X-ray structure of GB1 strongly supports that any globular protein should have one or more autonomous sequences folding into semifolds. However, no aggressive trial has been conducted to determine the autonomous sequences from protein sequence.

Here, to clarify and specify the autonomous sequences in any globular protein, we conduct the identification of two autonomous sequences in myoglobin and show that autonomous sequences in myoglobin can be characterized for the first time using a defining set of the proposed continuous folding structure units because myoglobin folding information is most precisely investigated. We first dissect the entire framework of apomyoglobin statistically by means of probability theory based on the normalized folding structure information, using the X-ray structure of holomyoglobin.[30] Second, we reveal that hydrophobic cores in apomyoglobin are dissected into two types of hydrophobic core networks (type I and II) using the continuous folding structure units. Third, we show that hydrophobic core networks decisively characterize the autonomous sequences in myoglobin. Finally, we emphasize that X-ray structures of semifolds formed by the autonomous sequences can be confirmed experimentally regardless of the instability of folds characteristic to the autonomous sequence fragments.

Results and Discussion

Dissection of the Entire Framework of Apomyoglobin

Myoglobin folding proceeds along the entire framework comprised of continuous folding structure units. Apomyoglobin is the native structure of myoglobin and can be dissected into continuous folding structure units by referring to a two-dimensional representation of the amino acid sequence in myoglobin and the dihedral angles of each amino acid of holomyoglobin. The two-dimensional representation (sequence vs dihedral angles) provided the relationship between the amino acid sequence and continuous folding structure units. As a result, the myoglobin sequence was annotated for corresponding folding structure units. The normalized folding structure information provided relative formation ability (RFA) values of local sequences for respective folding structure units based on probability theory.

Figure shows the sequential combinations of folding elements assigned to each amino acid in local sequences of myoglobin. Each of the folding structure units was assigned to the myoglobin sequence based on the X-ray structure of holomyoglobin using our proposed strategy.[5] The continuous folding structure units of holomyoglobin were as follows: NH3 (V1–S3) (RFA of local sequence = 1.9), H20 (L2–V21) (29) (A helix), H19 (A19–P37) (14) (B helix), H10 (S35–D44) (45) (C helix), H9 (K42–K50) (1.0) (C′ helix), HH3 (L49–T51) (1.6), H10 (K50–E59) (10) (D helix), H24 (A57–G80) (6.1) (E helix), HH3 (K79–H81) (1.2), H20 (G80–I99) (3.0) (F helix), HH3 (K98–P100) (1.3), H22 (I99–P120) (35) (G helix), T7 (R118–G124) (2.8) (α-turn), H29 (F123–Y151) (380) (H helix), and HC4 (G150–G153) (5.3). The N-terminal and C-terminal folding structures are partial folding structure units. The RFA of any local sequence for a folding structure is the product of normalized formation probability (NFP) values of each amino acid in the local sequence for respective folding elements,[5] and describes the relative rate of formation of the folding structure at the beginning of the folding process.

Figure 1

Folding structure units in myoglobin.

Flexibility in the F helix led HH3 (K79–H81), H20 (G80–I99), and HH3 (K98–P100) to HH22 (K79–P100) and would allow insertion of the bulky heme.[24] NH3 (V1–S3), HH3 (L49–T51), HH22 (K79–P100), and HC4 (G150–G153) in apomyoglobin were N-terminal, interconnecting, and C-terminal folding structures, respectively, and were disordered.[5] Overlapping sequences such as A19–V21 for two different kinds of structure elements hii′ and a′ab in Figure determine the connection of folding structure units, which is a decisive feature for the composition of the entire framework of apomyoglobin.

The overlapping regions observed in apomyoglobin were derived from larger RFA values of local sequences for continuous folding structure units except for respective local sequences around H9 (K42–K50) and HH22 (K79–P100). The overlapping regions derived from larger RFA values strongly support that the entire framework of apomyoglobin is constructed at the beginning of the folding process. The entire framework of apomyoglobin was composed of continuous folding structure units, which were assigned to the myoglobin sequence. The normalized continuous folding structure units of apomyoglobin were formed statistically by simple accumulation of folding elements encoded in each amino acid along respective local sequences.

The exceptionally low RFA value (1.0) for H9 (K42–K50) strongly suggested that tertiary interactions of folding events were transferred from the D44 cap residue of H8 (F43–K50) to the F43 cap residue of C′ helix. The RFA value for H8 (F43–K50) was 6.8. Another RFA value (0.41) for HH22 (K79–P100) was also lower (3.0) than that for H20 (G80–I99). These RFAs suggested instability of the F helix. Thus, myoglobin folding proceeded along well-defined folding events throughout the entire framework. The entire framework of apomyoglobin comprised the normalized continuous folding structure units assigned to the myoglobin sequence based on those observed in holomyoglobin except for F helix (Figure ).

Well-Defined Hydrophobic Core Networks of Apomyoglobin

Hydrophobic core formation throughout the entire framework is undoubtedly the well-defined folding event of apomyoglobin. This is the most intuitive understanding of the folding event for apomyoglobin. The hydrophobic cores were defined as pairs of topology-local hydrophobic amino acids, which were present in entirely different folding structures and stabilized them via efficient hydrophobic interactions. They always originated from different folding structure units. It is the most important for the determination of hydrophobic cores to differentiate those from simple hydrophobic contacts in identical folding structures. The simple hydrophobic contacts were defined as pairs of sequence-local hydrophobic amino acids in identical folding structures in globular proteins. A folding structure unit is inherently unstable regardless of the existence of pairs of hydrophobic amino acids. Thus, continuous folding structure units in Figure play a pivotal role in the determination of hydrophobic cores in apomyoglobin. Hydrophobic amino acids for hydrophobic core formation were taken based on X-ray structures of proteins. They were as follows: A, C, F, I, L, M, P, V, W, and Y.[31−35]

In actual fact, hydrophobic amino acids in different β-strand folding structure units of the C-terminal 16-residue autonomous sequence of GB1 form hydrophobic cores to stabilize a β-hairpin dramatically.[27,28] However, simple hydrophobic contacts in an identical β-strand folding structure cannot stabilize the β-strand folding structure entirely in any globular protein because of the reduction of conformational entropy.[35] Here, we defined a hydrophobic core of apomyoglobin using the distance between α-carbon coordinates of hydrophobic amino acids. We determined 8.5 Å (1 Å = 0.1 nm) as the limit distance to form a stable hydrophobic core under consideration of hydrophobic cores of GB1 fold and apomyoglobin. Hydrophobic cores in GB1 fold and apomyoglobin strongly support that the limit distance of 8.5 Å is adequate for GB1 and myoglobin sequences to fold into GB1 fold and apomyoglobin, respectively. For example, simple hydrophobic contacts below 8.5 Å of the distance between α-carbon coordinates in identical folding structures of GB1 could be observed in the X-ray structure of GB1[5,29] and were as follows: M1–Y3 (6.5), Y3–L5 (6.9), L5–L7 (6.3), A23–A24 (3.8), A23–A26 (5.2), A24–A26 (5.5), A26–V29 (5.3), A26–F30 (6.2), V29–F30 (3.9), V29–Y33 (6.1), F30–Y33 (5.0), F30–A34 (6.0), Y33–A34 (3.9), W43–Y45 (7.0), F52–V54 (6.9). The numbers in parentheses were the distances between α-carbon coordinates in Å.

Given that the distance between α-carbon coordinates of a hydrophobic core was below 8.5 Å, the hydrophobic cores in apomyoglobin were those shown in Figures and 3. These figures show the hydrophobic amino acids in myoglobin except for the region G80–I99, pairs of hydrophobic amino acids in hydrophobic cores, and the distances in Å between the α-carbon coordinates of the hydrophobic cores. The 63 hydrophobic cores in Figures and 3 were clearly observed in the X-ray structure of holomyoglobin.[30] Formation of nonlocal contacts reduces configurational entropy in protein chains to promote protein folding.[36] The hydrophobic zipper hypothesis was also proposed as cooperativity in hydrophobic core formation.[34] The hydrophobic core stabilized each folding structure remarkably via hydrophobic interactions. However, simple hydrophobic contacts in identical folding structures did not stabilize the folding structures. The instability of simple hydrophobic contacts promotes protein folding with adequate rapidity.[37]

Figure 2

Type I hydrophobic core networks in myoglobin.

Figure 3

Type II hydrophobic core network in myoglobin.

The autonomous sequence in GB1 chain is a sequence corresponding to an autonomously folding peptide segment, and the semifold is a folding intermediate encoded by the autonomous sequence to create a discrete hydrophobic region. Myoglobin sequence as well as GB1 sequence revealed two discrete hydrophobic regions of semifolds, which were assigned to two separate frameworks.[29,30] Each of the two separate frameworks of apomyoglobin was composed of a set of α-helix folding structure units. The corresponding two autonomous sequences of myoglobin could be characterized as autonomously folded peptide segments that assigned those small sets of α-helix folding structure units to the myoglobin sequence (Figure ).

The 63 hydrophobic cores on the entire framework produced two types of hydrophobic core networks. The hydrophobic cores in apomyoglobin were classified into type I hydrophobic core networks within respective semifolds (blue and purple lines in Figure ) and type II hydrophobic core network between different semifolds (red lines in Figure ) based on the X-ray structure of holomyoglobin using continuous folding structure units in Figure . Autonomous sequences encoded the tertiary structure information for semifolds and folded autonomously into semifolds that created discrete hydrophobic regions.

The type I and type II hydrophobic core networks of apomyoglobin were formed based on the tertiary structure information of autonomous sequences and that of myoglobin sequence, respectively.

Similarly, the 25 hydrophobic cores of GB1 fold are observed in the X-ray structure of GB1.[29] The 25 hydrophobic cores on the entire framework of GB1 fold produce two types of hydrophobic core networks. Type I hydrophobic cores in GB1 fold were as follows: M1–A20 (5.5), M1–V21 (6.1), Y3–A20 (7.3), Y3–A23 (7.8), Y3–A26 (6.8), L5–F30 (7.2), A7–A34 (8.4), L7–V39 (8.5), L12–V39 (7.5), A20–V21 (3.7), A20–A23 (7.3), A20–A26 (5.5), V21–A23 (7.3), V21–A26 (7.8), A34–V39 (5.1) W43–F52 (7.0), W43–V54 (4.5), Y45–F52 (4.4). The numbers in parentheses were the distances between α-carbon coordinates (Å). Type II hydrophobic cores in GB1 fold were as follows: Y3–F52 (7.6), L5–F52 (4.7), L5–V54 (7.6), L7–V54 (5.4), F30–F52 (8.4), A34–V54 (8.3), V39–V54 (8.1). The numbers in parentheses were the distances between α-carbon coordinates (Å). GB1 sequence was divided into two autonomous sequences, M1–E42 and G41–E56, based on the X-ray structure of GB1 using continuous folding structure units. These sequences fold autonomously into separate semifolds independently. Type I hydrophobic core networks are present within respective semifolds, and type II hydrophobic core networks are present between different semifolds. Hydrophobic interactions in type I and type II hydrophobic core networks based on the limit distance (8.5 Å) are the most intuitive understanding of the folding event for GB1 fold.

Folding of autonomous sequences commenced on multiple defined folding pathways synchronously by hydrophobic interactions in type I networks. In fact, type I hydrophobic core networks of a 16-residue autonomous sequence fragment of GB1 stabilized a β-hairpin dramatically via hydrophobic cores between different folding structures,[27,28] whereas type II hydrophobic core networks assembled semifolds to yield GB1 fold based on the tertiary structure information of GB1. Similarly, type I hydrophobic core networks of apomyoglobin stabilized respective semifolds independently, whereas type II hydrophobic core networks of apomyoglobin conducted cooperative stabilization of both the semifolds dramatically by another level of organization in semifolds, that is, assembly. Those of different levels of organization in semifolds, folding and assembly, are fundamental concepts in protein structure construction. This organization in semifolds supports the jigsaw puzzle model and foldon-based defined pathway model.[16,23]

Two Autonomous Sequences in Myoglobin Characterized by Type I Hydrophobic Core Networks

Each autonomous sequence in myoglobin was defined by a small set of continuous folding structure units forming a semifold, in which α-helix folding structure units of apomyoglobin were connected by hydrophobic cores within respective semifolds. Figure shows the full view of type I hydrophobic core networks of apomyoglobin and two autonomous sequences. Type I hydrophobic core networks within respective semifolds were the decisive feature for characterizing the autonomous sequences. The small set of continuous folding structure units in Figure were assigned to the corresponding autonomous sequence. Two autonomous sequences in myoglobin fold into the corresponding two semifolds. Similarly, two sets of continuous folding structure units in GB1 assembled into the corresponding two semifolds. Apomyoglobin and GB1 fold are composed of one domain, and these domains are comprised of two respective semifolds.

The N-terminal and C-terminal α-helix folding structure units of each autonomous sequence have no hydrophobic core with the adjacent autonomous sequences. In case of apomyoglobin, E helix was not connected with G helix via a hydrophobic core. As a result, the myoglobin sequence was divided into two autonomous sequences, 1 and 2, using hydrophobic cores and continuous α-helix folding structure units, shown in Figure .

Autonomous sequence 1 and 2 folded autonomously into respective separate semifold 1′ and 2′ based on the tertiary structure information for semifolds. Blue lines in Figure represent a hydrophobic core network I-1 [L2–W7 (6.3), W7–L76 (8.4), V10–L76 (8.0), L11–L76 (7.4), W14–L76 (8.5), V17–V21 (5.8), A19–V21 (6.3), V21–L69 (6.8), V21–V66 (5.9), A22–L69 (8.4), A22–V66 (5.2), L29–L61 (8.1), I30–M55 (6.7), L32–P37 (7.7), L32–L40 (8.2), F33–P37 (5.0), F33–L40(5.3), L40–F46 (6.8), F46–M55 (8.3), F46–L61 (7.0), L49–M55 (6.0), M55–L61 (7.1), A57–L61 (8.1)]. The numbers in parentheses are distances between α-carbon coordinates of hydrophobic cores (Å). The hydrophobic core network was formed within autonomous sequence 1 of 80 amino acid residues V1–G80 to stabilize the discrete hydrophobic region in semifold 1′.

Hydrophobic regions of A, B, C, C′, D, and E helices were stabilized by hydrophobic cores in the network I-1. The hydrophobic cores in the network I-1 were pairs of topology-local hydrophobic amino acids in different folding structure units. The terminal hydrophobic amino acids of folding structures, such as L2, A19, V21, P37, and A57 in Figure , formed hydrophobic cores as the cap (L2) or internal (A19, V21, P37, and A57) residues of adjacent folding structures. Helix bends A/B, B/C, and D/E created hydrophobic cores in the network I-1. The C′ helix was a distorted 310-helix, and the hexapeptide sequence L49–E54 formed a π-turn, which was an overlapping secondary structure. The distance between the N-terminal and C-terminal α-carbon coordinates of the π-turn was 5.8 Å.

Hydrophobic core network I-2 [P100–Y151 (8.0), I101–I142 (8.0), I101–A143 (6.7), I101–Y146 (8.4), I112–M131 (7.4), L115–P120 (7.7), L115–F123 (6.9), F123–A125 (6.7), F123–A127 (5.2), Y146–Y151 (4.9), L149–Y151 (5.8)] (purple lines in Figure ) was formed within autonomous sequence 2 of 55 amino acid residues I99–G153, and the hydrophobic regions of G and H helices were stabilized by hydrophobic cores in the network I-2. The numbers in parentheses are distances between α-carbon coordinates of hydrophobic cores (Å). Semifold 2′ was a folding intermediate. Practically, it was an unstable α-hairpin forming the hydrophobic cores between hydrophobic amino acids in the N-terminal sequence of G helix and those in the C-terminal sequence of H helix.[26] The C-terminal amino acid Y151 of H29 (F123–Y151) formed hydrophobic cores as the cap residue of HC4 (G150–G153). The hexapeptide sequence Y146–Y151 formed the π-turn of Schellman motif.[38]

The hydrophobic region of a semifold is always observed in the X-ray structure of holomyoglobin regardless of the stability of the semifold characteristic to the autonomous sequence fragment. The stability of semifolds strongly depends on hydrophobic cores in respective semifolds. Autonomous sequences encoding tertiary structure information for semifolds are pivotal probes of protein-folding information.

Discrete Hydrophobic Regions of Separate Semifolds Characterized by Respective Autonomous Sequences

A semifold of apomyoglobin creates the discrete hydrophobic region by assembly of hydrophobic regions in the corresponding continuous folding structure units. Thus, the autonomous sequence was also defined by the tertiary structure information for the semifold using hydrophobic regions in continuous folding structure units. To characterize the hydrophobic region of the semifold decisively, precise definitions of hydrophobic and hydrophilic regions in apomyoglobin were required. We characterized the hydrophobic region of apomyoglobin using hydrophobic regions of amphiphilic helices and hydrophobic cores. Necessarily, discrete hydrophobic regions of separate semifolds of apomyoglobin were characterized by using respective autonomous sequences decisively.

Each amino acid in an α-helix can be numbered according to a heptad repeat sequence (1234567). Seven successive amino acids proceed two turns of the α-helix.[39] To define the hydrophobic and hydrophilic regions of amphiphilic α-helices, hydrophobic amino acids in the hydrophobic region were numbered to maximize the number of hydrophobic amino acids in positions 1, 2, 4, 5, and 7. When amino acids at positions 2 and 7 were hydrophobic, the hydrophobic region was defined as positions 1, 2, 4, 5, and 7, whereas the hydrophilic region was defined as positions 3 and 6. The positions 1, 4, and 5 as well as 3 and 6 are always hydrophobic and hydrophilic regions, respectively, regardless of the amino acids.

Most hydrophobic amino acids of the A, B, C, C′, D, E, G, and H helices of apomyoglobin grew respective hydrophobic regions, and residual ones distributed in hydrophilic regions. The residual ones were as follows: L9 (6) and V13 (3) in A helix, V66 (6) in E helix, I112 (6) in G helix, A130 (3), L137 (3), and Y146 (6) in H helix. The numbers in parentheses are the position numbers of wheel description of each helix. The C′ helix was a distorted 310-helix, and F43, F46, and L49 were hydrophobic amino acids in the hydrophobic region.

However, all the hydrophobic amino acids in hydrophilic regions formed hydrophobic cores to stabilize the hydrophobic regions of semifolds within respective autonomous sequences. L9 and V13 residues in A helix formed hydrophobic cores with (F123, A127, A130, and M131) and (L115, F123, and A127), respectively, in type II network (Figure ); V66 (E helix) and I12 (G helix) residues with (V21 and A22) and M131, respectively, in type I networks (Figure ); A130 and L137 residues in H helix with L2 and V1, respectively, in type II network (Figure ); and Y146 residue in H helix with Y151 in type I network (Figure ). Thus, parts of hydrophobic amino acids in hydrophilic regions of amphiphilic α-helices were classified into those of hydrophobic regions in respective semifolds by hydrophobic core formation with a different semifold. As a result, all hydrophobic amino acids in the helices were those in the hydrophobic regions of each semifold. The hydrophobic amino acids of respective discrete hydrophobic regions in semifolds 1′ and 2′ were as follows. Semifold 1′: V1, L2, W7, L9, V10, L11, V13, W14, A15, V17, A19, V21, A22, I28, L29, I30, L32, F33, P37, L40, F43, F46, L49, A53, M55, A57, L61, V66, V68, L69, A71, L72, A74, I75, and L76; semifold 2′: P100, I101, Y103, L104, F106, I107, A110, I111, I112, V114, L115, P120, F123, A125, A12p7, A130, M131, A134, L135, L137, F138, I142, A143, A144, Y146, L149, and Y151.

Put in a concrete form (e.g., L9, V13, A130, and L137) above, all the hydrophobic amino acids in each semifold were stabilized by hydrophobic interactions in type I and type II hydrophobic core networks (Figures and 3) within each autonomous sequence. V1 and L2, P120 and F123, and Y151 were hydrophobic amino acids in the N-terminal folding structure, α-turn, and C-terminal folding structure, respectively. The discrete hydrophobic regions of separate semifolds were characterized decisively by respective autonomous sequences. Finally, all the hydrophobic amino acids in myoglobin except for the sequence H81–I99 were those in the hydrophobic region of apomyoglobin.

Type II Hydrophobic Core Network Assembles Semifolds To Yield Apomyoglobin

The tertiary structure information in autonomous sequences was characterized by preferential formation of discrete hydrophobic regions of respective semifolds within each autonomous sequence. They were independently stabilized by hydrophobic interactions in type I hydrophobic core networks. On the contrary, type II hydrophobic core network was formed between the discrete hydrophobic regions of different semifolds. Thus, it assembled semifolds to yield apomyoglobin based on the tertiary structure information of myoglobin.

The type II hydrophobic core network of apomyoglobin was as follows. Hydrophobic core network II-1′, 2′ (V1–L137, L2–A130, L2–A134, W7–A130, W7–M131, W7–A134, L9–F123, L9–A127, L9–A130, L9–M131, V10–A127, V10–A130, V10–M131, V10–A134, V13–L115, V13–F123, V13–A127, V17–L115, I28–I107, I28–A110, I28–I111, I28–V114, L29–I107, L29–A110, L32–F106, L32–I107, L32–A110, I75–F138 and L76–A134) (red lines in Figure ) was formed between semifolds 1′ and 2′. The hydrophobic region of apomyoglobin propagated between those of semifolds 1′ and 2′ via hydrophobic interactions in type II hydrophobic core network, to dramatically stabilize both the semifolds. The semifolds assembled to yield apomyoglobin.

Myoglobin forms the most thermodynamically stable structure based on its amino acid sequence. This is Anfinsen’s tenet of protein folding.[1,2] Thus, the assembly of semifolds by hydrophobic interactions in type II hydrophobic core network strongly supports that autonomous sequences of myoglobin take up the most thermodynamically stable state (semifolds) as folding intermediates at the beginning of the folding process, based on the amino acid sequence. For example, the autonomous sequence V1–G80 formed semifold 1′ autonomously at the beginning of the folding process of the autonomous sequence, and semifold 1′ was fixed at the end of the assembly process of semifolds.

Hydrophobic interactions in type II hydrophobic core network differentiate the stability of semifolds in apomyoglobin from the instability of folds characteristic to autonomous sequence fragments because of the absence of type II network. This differentiation leads to the general observation that fragment structures of protein chains are predominantly nonnative.[25,26] Semifolds were always observed in the X-ray structure of holomyoglobin. Thus, the most significant feature of semifolds in apomyoglobin was that they could be verified by the X-ray structure of holomyoglobin regardless of the instability of folds characteristic to autonomous sequence fragments.

Conclusions

Myoglobin folding proceeded along normalized folding structure formation together with hydrophobic core formation throughout the myoglobin sequence, which was composed of continuous folding structure units of apomyoglobin. It is the most important for the determination of hydrophobic cores to differentiate those from simple hydrophobic contacts in identical folding structure units using continuous folding structure units in Figure . The hydrophobic cores in apomyoglobin were classified into type I hydrophobic core networks within respective semifolds and type II hydrophobic core networks between different semifolds using continuous folding structure units. Each autonomous sequence in myoglobin was defined by a small set of continuous folding structure units forming a semifold. Each of the separate semifolds was stabilized by hydrophobic interactions in type I hydrophobic core networks. Autonomous sequence 1 and 2 in myoglobin were characterized by respective type I hydrophobic core networks to fold autonomously into separate semifolds 1′ and 2′ on each separate framework. The entire framework assigned to the myoglobin sequence was divided into two separate frameworks, and the defined characteristic of the autonomous sequences was small sets of continuous α-helix folding structure units connected by hydrophobic cores. The autonomous sequence was also defined by the tertiary structure information for a semifold. The tertiary structure information was characterized by preferential formation of the discrete hydrophobic region of the semifold by assembly of hydrophobic regions in continuous folding structure units. Necessarily, the discrete hydrophobic regions of each separate semifold were characterized decisively by using respective autonomous sequences. The discrete hydrophobic region of a semifold propagated itself by hydrophobic interactions in type II hydrophobic core network between different semifolds. Hydrophobic interactions in type II hydrophobic core network differentiate the instability of folds characteristic to autonomous sequence fragments from the stability of semifolds in apomyoglobin. This differentiation leads to the general observation that fragment structures of protein chains are predominantly nonnative.[25,26] The most significant feature of semifolds in apomyoglobin was that they could be verified by the X-ray structure of holomyoglobin regardless of the instability of folds characteristic to autonomous sequence fragments.

Methods

Dissection of the X-ray Structure of Holomyoglobin into Continuous Folding Structure Units

The X-ray structure of holomyoglobin was dissected into continuous folding structure units using a two-dimensional structural representation as described precisely in ref (5). Folding structure units were determined based on the continuity of backbone dihedral angles (ϕ and φ) in α-regions (−130 ≤ ϕ ≤ −30, −80 ≤ φ ≤ +30). Dihedral angles of the cap residues of α-helix and turn folding structure units are outside the α-region. Interconnecting folding structure units were located between the α-region sequences. Continuous folding structure units in Figure play a pivotal role in determination of hydrophobic cores.

Calculation of RFA Values

RFA values of local sequences for respective folding structure units were calculated using the table of NFP in ref (5), as mentioned in the text. For example, RFA value of C helix (S35–D44) in myoglobin was calculated as follows: RFA (C helix) = (NFP of S35 for a′) × (NFP of H36 for a) × (NFP of P37 for b) × (NFP of E38 for c) × (NFP of T39 for d) × (NFP of L40 for f) × (NFP of E41 for g) × (NFP of K42 for h) × (NFP of F43 for i) × (NFP of D44 for i′) = 45.

Selection of Hydrophobic Cores

Hydrophobic cores were selected from a table of distances of the α-carbon coordinates of hydrophobic contacts. The table is available in the Supporting Information. They were determined using the α-carbon coordinates of holomyoglobin and GB1 (Protein Data Bank accession: 1MBC and 1PGB). α-Carbon coordinates were obtained from DSSP files for 1MBC and 1PGB. It is the most important for selection of hydrophobic cores to differentiate those from simple hydrophobic contacts in identical folding structure units using continuous folding structure units in Figure . For example, W7–L9 (5.3), W7–V10 (4.8), and W7–L11 (6.0) are simple hydrophobic contacts in α-helix folding structure unit. They do not form hydrophobic core. They were excluded from hydrophobic core selection according to the definition of simple hydrophobic contacts.