統計自由能偶合對應法的發展及應用(III)

行政院國家科學委員會專題研究計畫 成果報告

統計自由能偶合對應法的發展及應用(3/3)

中

華

民

國 92 年 8 月 17 日

91-2113-M-009-027

Calculation of Statistical Structural Entropy and its Applications to Protein Structures

Jenn-Kang Hwang

Department of Biological Science & Technology and Institute of Bioinformatics,

Abstract

We have developed a general method to compute the structure entropy of protein

sequences. Structure entropy gives a quantitative measure of structure conservation.

This relationship is similar to that between sequence entropy and sequence

conservation. Experimental studies in protein folding have suggested that residues

relevant to protein folding, or the so-called "hot spot" residues, are usually structurally

conserved, though not necessarily conserved in sequences. Hence, the ability to

compute structure entropy can help identify important residues related to protein

folding. In this work, we have applied our approach to several model proteins

frequently used in protein folding experiments. Our results suggest a close

relationship between the structure entropies of residues and their rates of amide proton

exchange, and we are able to identity regions of residues that are important in protein

INTRODUCTION

The conformation and structure of a protein are determined by its sequence.1 However,

both designed and naturally occurring sequences are shown to adopt different

conformations in different protein environments.2-5This observation suggests that the

structures of some local protein subsequences are context dependant. Certain parts

(the non-context-dependant parts) of the protein may be critical for protein folding

and structure determination; these parts are usually termed as “folding nucleus” or

“hot spot”.6, 7 Whether these folding nucleus are conserved in sequence is

controversy.8-10There are many cases where protein sequences with little sequence

identities have very similar folds. One of the conspicuous examples is the

triophosphate isomerase (TIM) fold,11 which in part supports the non-conservation of

folding nucleus. It is generally believed that the folding rates of proteins are closely

related to their topology, though the choice among topological features varies.12-14

Current analysis of protein topology requires experimentally determined or

dynamically sampled structures of proteins.14-16 A sequence based method that can

take into account the non-conservativeness and is able to evaluate whether local

protein fragments are structure determinants should prove valuable and useful.

For years the use of nuclear magnetic resonance (NMR) in hydrogen-deuterium

proteins and their folding intermediates.17, 18 Hydrogen-deuterium exchange

experiments for amide protons can detect residues that are protected in different

phases of protein folding processes. Therefore residues unfolded slowly can be

identified. These residues are seen as important residues in protein folding processes.

Their identification and consequent analysis are crucial to the study of protein folding

mechanisms. NMR study is indispensable and has become an important tool in

structural genomics.19 However, NMR equipments and experiments are expensive.

Also, pure protein samples and tedious operations are required for protein structure

determination and analysis using NMR. A purely sequence based method for the

analysis of protein conformation fluctuation and possibly folding mechanism is

attractive. Though sequence based methods could never replace experiments, they

may provide complementary information and hints for further experimental analysis.

Starting from the sequence of a protein, with consequent querying of the

subsequences’ occurrences in structure databases, a new assessment for conformation

fluctuation of proteins has resulted, i.e., the structure entropy of protein sequences.

With structure entropy, it is possible to identify structurally conserved regions in

protein sequences.

In this work, we have shown that the structure entropies of a protein are closely

of local protein sequences; these conservations are measured with structure entropies.

A computational approach to calculate the structural conservation of local protein

fragments is desirable. Such approach can provide insights to the stability and

adaptability of protein local conformations. We have used an information theory

based approach for the intrinsic structural entropy calculation. The method has been

applied to peptides and patterns to observe the generalized characteristics of the

conformation conservation. PROSITE patterns with non-conserved conformations

have been identified. Some specific systems are also investigated, including mutations

in Arc repressor and free energy of proton exchange in toxin proteins.Using an

information theoretical approach,20 we are able to calculate the structure propensity of

a peptide. The structure propensity was calculated using categorized protein backbone

conformations and was represented as a single value. This kind of practice is common

in constructing sequence conservation (diversity) index.21 It has also been applied to

side-chain22 and main-chain23 conformation analysis of proteins. The resulting score

could be termed as structure entropy, since it samples the local structure variations of

protein sequences. This score is able to show the conformation conservation of

PROSITE patterns. The score may also be used to construct the structure entropy

profiles of proteins. The structure entropy profile of a protein corresponds well with

protein folding with merely the presence of protein sequences.{Hamada, 1995

#25;Minor, 1996 #70;Cregut, 1999 #75}

METHODS

Representation of protein str ucture with secondar y str ucture elements

In order to apply information theory to local conformations of proteins, one must

categorize these conformations to a finite number. Protein structures in the Protein

Data Bank (PDB)24 are represented with the 3D coordinate of the atoms in each

protein. These structure information are exact, but in some cases impose too much

details; all-atom models of protein have too many degrees of freedom. It will be

preferable to represent the conformation of each residue in a protein using a single

symbol, much like the sequence of the protein. Therefore the routine sequence

analysis techniques could be applied to the simplified structure representation as well.

We have picked the secondary structure of a protein for such purpose. Other

representations are also applicable.25, 26 The secondary structure assignments of the

proteins in PDB are available in DSSP database.27 The local conformations of

residues in a protein are categorized into 8 classes according to their hydrogen

bonding patterns. The 8 secondary structure types areβ-bridges (designated as B),

extended β-sheet (E), 310-helix (G), α-helix (H), π-helix (I), bend (S), turn (T), and

one-dimensional sequences composed of their secondary structure assignments. These

conformations in one-dimensional representations are used in the calculation of

structure entropy.

Str ucture entropy

For a protein sequence x with arbitrary length l, we conduct query on the occurrences

of x in structure database. The occurrences of x and their one-dimensional

representations are recorded, as shown in Fig. 1. Fig. 1 illustrated two sequences,

ELKEL and ELVGK. Both have multiple occurrences in different proteins. For each

position in the protein sequence, there is a frequency distribution of the 8 secondary

structure types. For example, the frequency to find helix (H) in the 3rd position of

ELKEL is 1.0, and 0 for any other secondary structure types. The entropy at this

position in sequence x could be calculated using:

∑

where pos is the position in sequence x, i is the secondary structure types, and pi is the

frequency of i at position pos in sequence x. A conserved position will have a low

entropy value, whereas a position with diverse conformations will have a high entropy

value. The structure entropy of sequence x is estimated with:

∑

0

S S Sx = x −

∆ , (3) where S0 is the reference entropy. The reference entropy was calculated using

Equation (1), neglecting sequence and position. The frequency distribution used to

calculate S0 is based on the distribution of each secondary structure types in the entire

structure database.

Constr uction of str ucture entropy profiles

For a given protein sequence, a sliding window of arbitrary length has been used to

split the sequence into shorter fragments. These fragments are queried against the

structure database, and the structure entropies are calculated accordingly. The

structure entropies are assigned to the central residues in these fragments. It is not

relevant whether the given protein presented in the structure database or not. These

entropies form the sequence-based structure entropy profile of a protein sequence.

Identification of slow exchange and low entropy residues

The exchange rates of residues may be presented in various forms. For example, it

could be represented as free energy,28 as protection factor,29 as rate (1/t, where t is

time),30 or as time.31 Because of these variations, a consistent comparison between

exchange rate and structure entropy is difficult. We have divided the residues in a

protein into slow/non-slow exchange residues with certain criteria, which mainly

proton exchange ones for various proteins are summarized in Table 1.

In order to assign a structure entropy cutoff value suitable for most proteins,

correlations between slow exchange residues and residues identified by different

cutoff values are calculated iteratively. For most proteins, the threshold value

∆S=-1.08 will yield maximal correlations between slow exchange and low entropy residues. However, in the case of Chymotrypsin inhibitor 2, this cutoff value needs to

be relaxed to –0.88 for inclusion of more residues. The structure entropy cutoff values

and residues identified by these values for various proteins are also listed in Table 1.

RESULTS

Str ucture entropy of PROSITE patter ns

PROSITE is a database of functionally conserved sequence patterns.33 Most patterns

in PROSITE are structurally conserved.34 However, we have found some PROSITE

patterns with exceptionally high structure entropy, indicating non-conserved

conformations. We have listed some typical examples of PROSITE pattern with high

and low structure entropy in Table 2. Among the four low entropy patterns are malate

dehydrogenase active site signature (PS00068), cutinase active sites signatures

(PS00155), plant thionins signature (PS00271), and ferritin iron-binding regions

signatures (PS00540). The high entropy patterns are EGF-like domains (PS00022),

transfer proteins signature (PS00215), and the Trp-Asp (WD-40) repeats signature

(PS00678). The superimposed trace structures of these motifs are shown in Fig. 23.

We can see that the backbones of the low entropy patterns are structurallywell

-overlapped (Fig. 23A), while those of the high entropy patterns contains quite varied

conformations (Fig. 23B). The computed structure entropies give a quantitative

measure of conformational conservation of sequence patterns.

Str ucture entropy and proton exchange events

We have examined the structure entropy profiles for four proteins, and compare the

results with their proton exchange events. These proteins are chymotrypsin inhibitor 2

(CI2), cytochrome c (cyt c), protein G B1 domain (GB1), and cardiotoxin analogous

type III (CTX III). These proteins have all been extensively studied on their folding

mechanisms.

Chymotr ypsin inhibitor 2

Chymotrypsin inhibitor 2 (CI2) is a small protein and has been studied extensively in

terms of protein folding.35 The proton exchange experiments of CI228, 36 have revealed

several slow exchange residues (those with free energy of exchange ∆G_exapp larger than 7.0 kcal/mol-1). These residues located on hydrophobic region formed by the

C-terminal of α-helix and central strand of the β-sheet (Fig. 3A, left). The low

right), though not all slow exchange residues are found by structure entropy. It is

notable that a number of residues on the reactive site loop region (the long loop in the

right of the figure) are labeled as having low structure entropy values. These residues

are I37, M40, E41, R43, and I44. However, the exchange rates for these residues are

not available, and a comparison is not feasible for these residues.

Cytochrome c

Cytochrome c is an important component of the energy-harvesting complex on

mitochondria, and its folding kinetics is also of great interest.37 The proton exchange

experiments showed that protected protons are mainly located on the terminal

(N-terminal and C-terminal) helices (Fig. 3B, left).29, 38 Slow exchange residues are

those with protection factor P larger than 107, where P= kc/kex, kc is the intrinsic

exchange rate, and kex is the measured hydrogen-deuterium exchange rate.29 There is a

contact region between the two terminal helices (lower part of Fig. 3B). The proton

exchange experiment and structure entropy analysis both identified the two terminal

helices. Another helix (60’s helix; from it’s sequence numbering) is also identified by

both proton exchange experiment and structure entropy analysis. A number of

residues are labeled as low structure entropy ones but not slow exchange residues.

Half of these residues (D2, L35, and P44) do not have available proton exchange rates.

each other on residue L32.

Protein G B1 domain

Protein G is a multidomain cell wall protein with several immunoglobulin G (IgG)

binding domains. The B1 domain of Protein G is one of these IgG binding domains.

Protein G B1 domain (GB1) is a small protein with well-defined structures and has

been studied extensively. The proton exchange experiments on GB1 have revealed

several residues with slow exchange rates, these residues are categorized with rates

smaller than 0.005 (h-1).30 These residues formed a compact hydrophobic core (Fig.

3C, left). Structure entropy analysis identified a number of slow exchange residues

(F30, T44, and F52) in this hydrophobic core, but not all (Fig. 3C, right). Two

residues outside the hydrophobic core, T2 and D22, were identified by structure

entropy analysis. D22 acts as a helix cap and may be essential for helix formation,39

whereas the exact role of T2 in the folding pathway is unclear.

Car diotoxin analogous type III

Cardiotoxin analogous type III (CTX III) is a small, allβ-sheet protein. CTX III contains two β-sheets, one is double stranded (formed by β1 and β2) and the other is triple stranded (formed by β3, β4, and β5). There are four disulfide bonds in CTX III. Proton exchange study of CTX III has revealed that the slow exchange protons are

those with time constant of refolding shorter than 15 ms. Structure entropy analysis

identified most of these residues and more (most of these do not have proton

exchange rates available, see Table 1) in the same region (Fig. 3D, right). Two

residues were identified by structure entropy analysis exclusively, K2 and N55. It is

interesting to note, that by loosen the time constant criterion to 25 ms, K2 and N55

will be included as slow exchange residues.

DISCUSSION

We have linked structure entropy analysis to proton exchange experiments. Previous

study by Hisler and Freire (1996) has suggested that calculations based on protein

structure may provide hints to protein folding pathway.40 Our approach does not

require the structure of the target protein. Though the correspondences we found

between proton exchange experiment and structure entropy analysis are mostly

qualitative, we believe our approach is more general and require much less resources

than structure based approach.

The further improvement of structure analysis and its correspondences on proton

exchange experiments relies on several issues. First, the available experimental data

were collected under various conditions, and their interpretation requires careful

calibrations. Second, the use of secondary structure to represent local conformation

better correspondences. Third, structure entropy measures local conformation

conservation, thus it may or may not be able to capture tertiary interactions among

subsequences of proteins. It is likely that structure entropy could never fully describe

protein folding pathways in detail; but it may provide helpful structural information

with merely the availability of protein sequences.

The major concern about information theory based scoring is that it cannot account

for the distances among the symbols.41 Both sequence and structure entropy suffer

from this caveat. However, there are fundamental differences between sequence

entropy and structure entropy. We have constructed both sequence and structure

entropy profiles for CTX III (Fig. 4). In previous sections we have shown that

structure entropy have close relationships with proton exchange events. Fig. 4A

illustrated the sequence entropy profile of CTX III. It could be seen that the sequence

of cardiotoxin is very conserved, but makes no distinction among the secondary

structure elements. All these secondary structure elements are equally conserved in

sequence entropy profile. On the other hand, structure entropy suggests that strands

β3 and β5 are more stable than others (Fig. 4B), which agrees well with the proton exchange results (Fig. 3D and Table 1).31 This result confirms that sequence

conservations are not necessary corresponding to slow exchange residues or folding

not necessary more conserved in sequence identities.8

Structure entropy analysis is among many attempts to uncover the sequence-structure

relationships. It is efficient, and may be proved valuable in genomics scale protein

structure analysis. Current results have revealed some of the connections between

protein sequences and structure conservation. Its applications to protein structure and

folding analysis are promising and may be of great help for researchers in the named

fields. A web page has been build to facility the usage of structure entropy. This web

page was named “StEQ: Structure Entropy Query” and can be accessed at

http://atp.life.nctu.edu.tw/~entropy/.

Key Words

Structure entropy; Proton exchange; Protein secondary structure; Protein folding;

Protein sequence/structure relationships

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TABLES

Table 1

List of residues with slow exchange rates and those with low structure entropy values

in several proteins.

Slow Exchange Criteria1 Residues with Slow

Exchange Rates2

Structure

Entropy Cutoff

Residues with Low Structure

Entropy Values Chymotrypsin inhibitor 2 (CI2) app ex G

∆ > 7.0 kcal/mol-1 K11, V19, I20, L21, I30, L32, V47, R48, L49, F50,

V51

∆S < -0.88 K23, T33, E4, V19, I293, I373, M403, E413, R433, I443,

R48, L49 Cytochrome c (cyt c) P > 107 F10, L32, L68, L94, I95, A96, Y97, L98, K99 ∆S < -1.08 D23, Q12, H18, T19, L32, L353, P443, E66, Y67, K79, M80, L94, Y97, L98, K99 Protein G B1 domain (GB1)

rate < 0.005 h-1 L5, I6, E27, F30, T44,

T51, F52, T53, V54

∆S < -1.08 T2, D22, F30, T44, F52

Cardiotoxin

analogue type

III (CTX III)

time constant < 15 ms K23, I39, V49, Y51, V52,

C53, D57, R58 ∆S < -1.08 K2, C21, Y22, K23, M243, F253, I39, D403, P433, Y51, V52, C53, C543, N55 1 app ex G

kc is the intrinsic exchange rate, and kex is the measured hydrogen-deuterium exchange

rate.

2

Experimental results are obtained from Itzhaki et al.,28 Jeng et al.,29 Orban et al.,30

and Sivaraman et al.,31 and reorganized for CI2, cyt c, GB1, and CTX III,

respectively.

3

The exchange rate of these residues are not determined or not probed in

Table 2

Summaries of some selected PROSITE patterns with low and high structure entropies.

Accession Number1 Entry Name1 ∆S RMSD2 (Å )

Sequence motifs of low Entropy

PS00068 MDH -1.68 0.35

PS00155 CUTINASE_1 -1.65 0.10

PS00271 THIONIN -1.64 0.23

PS00540 FERRITIN_1 -1.66 0.19

Sequence motifs of high Entropy

PS00022 EGF_1 -0.79 2.19

PS00030 RNP_1 -0.67 2.18

PS00215 MITOCH_CARRIER -0.58 3.64

PS00678 WD_REPEATS -0.84 3.59

1

The accession number and the entry name are taken directly from PROSITE

database.

2

FIGURE CAPTIONS

Figure 1 Protein sequences have different conformation preferences. Both sequences

(ELKEL and ELVGK) occur multiple times in different proteins. The PDB ids for

these proteins are provided. ELKEL is in helix (H) conformation in most cases,

whereas ELVGK adapts different conformations in different protein environments.

Figure 2 Superimposed structures of PROSITE patterns with low and high structure

entropies. The structures are shown in trace representation. A: the low entropy

patterns, where the backbone of the occurrences of the patterns fit well. B: the high

entropy patterns, for each high entropy pattern there are two or more distinctive

conformations.

Figure 3 Correspondences between slow proton exchange residues and structure

entropy in several proteins. Slow exchange regions in proteins are marked in red, so

are the residues with low structure entropy. A: Chymotrypsin Inhibitor 2 (CI2). B:

Cytochrome c (cyt c). C: Protein G B1 domain (GB1). D: Cardiotoxin analogous type

III (CTX III). The PDB ids used to plot the structures are 2CI2 (CI2), 1HRC (cyt c),

1PGA (GB1), and 2CRT (CTX III), respectively.

Figure 4 Comparison of A: sequence entropy (∆Sseq) and B: structure entropy (∆Sstr)

profiles of CTX III. The secondary structures (β1~β5) of CTX III are labeled on B.

quantities. It is clear that sequence entropy cannot distinguish among these strands

(sequences of all the strands are highly conserved), while structure entropies are