Báo cáo khoa học: Universal positions in globular proteins From observation to simulation ppt

This study analysed these positions in 111 representatives of different protein folds, and then carried out dynamic Monte Carlo simulations of the first steps of the folding process, aimed

Universal positions in globular proteins

From observation to simulation

Nikolaos Papandreou1, Igor N Berezovsky2,3, Anne Lopes4, Elias Eliopoulos1and Jacques Chomilier4

1

Laboratory of Genetics, Agricultural University of Athens, Greece;2Department of Structural Biology, The Weizmann Institute of Science, Rehovot, Israel;3Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA;

4

Equipe Biologie Structurale, LMCP, Universite´s Paris 6 and Paris 7, Paris, France

The description of globular protein structures as an

ensem-ble of contiguous Ôclosed loopsÕ or Ôtightened end fragmentsÕ

reveals fold elements crucial for the formation of stable

structures and for navigating the very process of protein

folding These are the ends of the loops, which are spatially

close to each other but are situated apart in the polypeptide

chain by 25–30 residues They also correlate with the

loca-tions of highly conserved hydrophobic residues (referred

to as topohydrophobic), in a structural alignment of the

members of a protein family This study analysed these

positions in 111 representatives of different protein folds,

and then carried out dynamic Monte Carlo simulations of

the first steps of the folding process, aimed at predicting the origins of the assembling folds The simulations demon-strated that there is an obvious trend for certain sets of residues, named Ômostly interacting residuesÕ, to be buried at the early stages of the folding process Location of these residues at the loop ends and correlation with topohydro-phobic positions are demonstrated, thereby giving a route to simulations of the protein folding process

Keywords: folding nucleus; hydrophobic core; lattice simu-lation; protein folding

Despite the continuously increasing number of

experiment-ally determined protein structures, many new folds are still

to be discovered This was illustrated clearly in a recent

study [1], where a plot of the number of protein families vs

the number of resolved complete genomes resulted in a

quasi-linearly increasing function Elucidating the

evolu-tionary mechanisms leading to the emergence of a finite

number of protein folds [2,3] from the vast number of

protein sequences [4,5], as well as the mechanisms of the

formation of mature protein globules [6], remains a topic

both of great challenge and interest The latter mechanisms

are related to the physical basis of protein structure

formation and stability [7], and thus can point to possible

evolutionary routes [8]

This study is based on universal structural units of protein

folds, named Ôclosed loopsÕ [9] or Ôtightened-end fragmentsÕ

(TEFs) [10] These major elements are universally present in

all types of protein folds and have the following features in

common: (a) they usually start and end in the hydrophobic

core [11]; (b) they form loop-like structures of nearly

standard size (25–30 amino acid residues); (c) they serve as

universal units of protein domain structure [12]; (d) the

ends of these elements (or so-called locks [13]), mainly

correspond to clusters of hydrophobic amino acids in general (WIMVYLF), and highly conserved ones, the topohydrophobic (TH) positions [14,15], in particular Determination of the TH positions is based on the analysis

of multiple structural alignments of members of a protein family, limited to a pair sequence identity with a maximum

of 30% TH positions are of particular importance for the formation and stability of the protein core [16] From a dynamic point of view, the early formation of a nucleus composed of TH positions would favor the formation of closed loops and considerably speed up the folding process [17] The coupled concepts of TH and closed loops/TEFs therefore offer a simple and general scenario for the folding mechanism of globular proteins [11,15] and provide a set of critical positions in the protein core [10,11,13] The loop structure of globular proteins is a general concept, inde-pendent from secondary structure, as well as from the particular folding mechanism of each protein [9,10,13] This study addresses the question of predicting these critical positions from the sequence, a task of major importance to approach the structure of a protein of unknown folding To successfully build such a structure, numerous pieces of information have to be collected by combining various methods An initial calculation of critical positions could be a first step, providing a frame of structural restraints, as TEF limits and TH residues are located mainly inside the protein core

The notion of topohydrophobic positions suggests that the forces that bury these residues and lead to a stable core do not rely on the details of the amino acid side chain structure, but rather on an adequate succession of hydrophobic and polar amino acid residues along the polypeptide chain Thus simplified protein models, such as lattice ones, are adequate tools for calculations aimed at locating critical residues

Correspondence to N Papandreou, Laboratory of Genetics,

Agricul-tural University of Athens, Iera Odos 75, 11855 Athens, Greece.

Fax: +30 2105294322, Tel.: +30 2105294372,

E-mail: papandre@aua.gr

Abbreviations: MIR, mostly interacting residues; PDB, protein data

bank; SCOP, structural classification of proteins; TEF, tightened end

fragment; TH, topohydrophobic.

(Received 29 June 2004, revised 22 September 2004,

accepted 15 October 2004)

This study was carried out on a dataset of 111 globular

proteins with well-defined structures in the Protein Data

Bank (PDB), that were representative of various folds, and

for which the TEFs were available For a subset of 73

proteins of the above database, the TH positions have also

been determined

The initial stages of folding were simulated using a

simplified model, which consists of an alpha-carbon reduced

representation of the polypeptide chain on a 24-first

neighbour lattice A standard Monte Carlo algorithm

dynamically simulated the folding process and a statistical

mean force potential was used to describe the interactions

between noncontiguous residues A commonly accepted

lattice model has been used [18] and was focused on the first

stages of folding process, by measuring the tendency of

amino acids to be packed inside the hydrophobic core,

depending on the peculiarities of polypeptide chain

sequence

Starting from random conformations, the Monte Carlo

simulations revealed that a subset of hydrophobic residues

had a strong tendency to be buried These residues, named

Ômostly interacting residuesÕ (MIR), were found to

statisti-cally match TEF limits and TH positions

These results are in agreement with the hydrophobic

collapse mechanism, which can be further generalized onto

the nucleation–condensation mechanism, a hybrid of

hier-archical and hydrophobic collapse mechanism [23,24]

Materials and methods

The protein database consisted of 111 globular protein

chains, representing 78 different folds, according to the

structural classification of proteins (SCOP classification)

[22] In detail, there are 26 a class proteins, 23 b class, 26

a + b class, 18 a/b class and 18 of the small proteins class,

providing a balanced representation of the major known

folds The polypeptide chain lengths vary between 50 and

250 residues

Simulations have been carried out using a Ca

represen-tation of the polypeptide chains and the lattice geometry

(Fig 1) is as in [18]

On an underlying cubic lattice (Fig 1, dotted lines) with edges of unit length, contiguous alpha carbons are connec-ted by vectors of the form (± 2, ± 1, 0) (Fig 1, solid lines) The length of such a vector is ffiffiffi

5

p lattice units and is equivalent to 3.8 A˚, the typical distance between contiguous alpha carbons in proteins In this geometry, for residue i, there are 24 possible positions for residue i + 1 to occupy This kind of polypeptide chain projection allows for a more realistic representation of the polypeptide chain [18] Two spatial constraints are implemented First, the distance between noncontiguous alpha carbons cannot be less than 3.8 A˚ ( ffiffiffi

5

p lattice units), and second (contrary to cubic lattice, where only angles of 90 and 180 are possible), limit angles here are 66 and 143 (seven possible values), approximating the range of pseudo-angle s in natural proteins [19]

The different nature of amino acids is taken into account

in the force field used to attribute an energy value to each chain conformation The distance-independent 20· 20 residue pair energy matrix of Miyazawa and Jernigan was used [20] In detail, if two noncontiguous residues i and j are found within a distance smaller or equal to 5.88 A˚, a term Eij

is added to the total energy, depending on their nature The maximum interaction range of 5.88 A˚ corresponds to ffiffiffiffiffi

12 p lattice units and seems a reasonable estimate for the mean noncovalent interaction range between amino acid residues For each protein, 100 different initial conformations were randomly generated and used as starting points for 100 simulation runs, to avoid dependency from the initial state The only constraint placed on initial states is their noncompactness, in the sense that amino acid residues placed far away in the sequence were not allowed to be close

in space, to avoid clustering due to particular initial state conformation Quantitatively, this constraint introduces a minimum spatial distance, dmin, according to the separ-ation Delta¼ |i–j| between residues i and j: (1) Delta ¼ 6‚10, dmin ¼ 7 A˚; (2) Delta ¼ 11‚15, dmin ¼ 11 A˚; (3) Delta¼ 16‚20, dmin ¼ 19 A˚; (4) Delta more than 20, dmin¼ 27 A˚

The single residue movements [18] are of two kinds; end flip movement for the N and C terminal residues and corner movements for the others The choice of the move set is more or less arbitrary, as the elementary one-residue moves are sufficient to bring the protein to a folded state In this case, the restriction to elementary moves only, apart from its simplicity, permits a sequential analysis of the chain tendency to form compact fragments around particular amino acid residues from the beginning of the simulation After each move, the calculated conformational energy was subjected to a standard Metropolis criterion, at constant temperature

Because the goal was to analyse the propensity of residues

to be buried from the start of folding, we ensured that the maximum number of Monte Carlo steps was sufficient to allow formation of compact chain fragments Due to the serial nature of the algorithm, this time limit is correlated to protein chain length L It was empirically determined that for small proteins of about 50 residues, the value tmaxis around 106Monte Carlo steps Thus, the following linear relation was adopted to generalize tmaxto proteins of any length L: tmax¼ INT (106L/50), where INT is integer part, because t is an integer by definition (Monte Carlo steps)

Fig 1 The lattice model The solid line represents the backbone from

Ca to Ca positions, while the dotted line is the underlying cubic lattice.

For each simulation, 104records of intermediate

confor-mations were taken at regular time intervals As the number

of simulations per protein is 100 (one for each initial state),

the end result is a set of 106records per protein

For every recorded conformation, and for each amino

acid residue the number of residues with which it is in

noncovalent interaction was calculated In spatial terms,

these noncovalent neighbours are the amino acid residues

lying within a distance of 5.88 A˚ or ffiffiffiffiffi

12

p lattice units For a given protein and for residue i, at the r-th record, the

number of noncovalent neighbours is nc(i,r) The time mean

of this quantity is

NCðiÞ ¼ 1

106

X10 6

r¼1 nc(i,r)

NC(i) values are rounded to the nearest integer This mean

number of noncovalent neighbours is a quantitative

meas-ure of the tendency of a residue to be buried from solvent

The higher the NC(i), the stronger this tendency

If NC is the mean value of NC(i) over the sequence for a

given protein, the residues for which NC(i) is significantly

higher than NC are of particular interest and are called

mostly interacting residues (MIRs) Their selection requires

fixing a cut-off value above the mean value NC It was

found that NC(i) varies between 1 and 8 and that NC¼ 4

for all studied proteins Figure 2 presents the distribution of

the different values of NC(i) over the amino acid residues of

all 111 proteins The most probable value is four, which

coincides with the mean sequence value, which is also four

for all proteins as stated above From this distribution, it

appears that 13% of residues have a number of noncovalent

neighbours equal to or higher than six, which was adopted

as the lowest NC(i) value for considering residue i as a MIR

In order to validate this model, once the positions of MIRs

were determined they were compared to TEF limits and to

topohydrophobic positions The comparison with TEFs was

performed on the complete database of 111 proteins The

comparison with TH positions was performed on a

73-protein subset of this database, where these positions were

determined For the remaining 38 proteins, the calculation of

TH positions was not possible, because to obtain this at least

four 3D structures of members of the same family are

required, with a pair identity not exceeding 30% [14,15] This

critirion was not fullfilled for these 38 cases

The PDB codes [21] of the database are given in Table 1

Results The Monte Carlo algorithm for folding simulation has been applied to the entire protein dataset and the histograms NC(i), containing the distribution of noncovalent neigh-bours along the amino acid sequence, have been obtained for each protein

In Fig 3 the positions of TEFs, TH and MIR for 10 proteins of the database representative of the various classes

as determined by SCOP [22] are illustrated

Among the 1920 calculated MIRs, 92% were hydropho-bic, following the definition of topohydrophobic residues (i.e they belonged to the set ÔVIMWYLFÕ) Also, the total numbers of MIRs and TH positions, in the 73-protein subset where they are compared, are relatively close (1299 MIRs vs 1011 TH) In the same subset, the total number of TEFs was 309; thus the number of TEF limits was 618, about half the number of MIRs

To assess the overall quality of agreement between predicted critical positions (MIR) and structure-defined ones (TH and TEF limits), a statistical analysis is required This has been carried out over the whole database, i.e over all 111 proteins for the comparison between MIR and TEF limits and for the subset of 73 proteins for the comparison between MIR and TH The results are presented in two histograms in Figs 4 and 5 The histogram of Fig 4 gives the comparison between MIR and TH positions and is constructed as follows Each TH position is placed at the origin of the abscissa Then, the neighbouring MIRs that are closer to this central TH than to any other TH are located Their number is plotted as a function of their sequence distance with respect

to the central TH This is reproduced for all THs along all the

73 proteins of the data set Thus Fig 4 shows a histogram of the separation between TH and the closest MIR The plotted distances range from )20 to +20, and MIRs lying at

distances greater than ± 20 residues from the closest TH are added to the histogram at the ± 20 positions The second histogram (Fig 5) follows the same rules and concerns the comparison of MIR to TEF limits It is constructed using the whole database of 111 proteins From observation of Figs 4 and 5 it is evident that comparison of MIR with TH and TEF limits clearly presents a peak at the origin This is an indication that the residues predicted to be MIRs actually do correspond to TH positions They also statistically correlate with TEF limits, which are mostly hydrophobic [13] as it was already shown that most TH positions are located in or in vicinity of TEF ends [10] The agreement between MIR and

TH is very clear and 63% of MIR were found within ± 5 positions from a TH residue The TEF histogram presents two main secondary maxima at positions ± 3 and 57% of MIR was found within ± 5 positions from a TEF limit This good agreement between prediction and analysis [13] is of great interest in the prediction of elements of the protein core from the sequence

Discussion The existence of critical positions in protein structures, punctuated by TH positions and/or TEF limits, is of great importance for protein folding and stability Consecutive formation of the globule core [10,11,17] composed essen-tially of these residues [13] leads to tremendous

optimi-Fig 2 Distribution of the mean number of noncovalent neighbours over

all 111 sequences of the dataset.

Table 1 A list of the PDB codes, names and SCOP classes of the proteins studied The TEFs are known for all these proteins Proteins with known

TH positions are in bold The uppercase letters at the end of the code correspond to the chain.

PDB

PDB

PDB

1aep Apolipophorin-III a 2sns Staphylococcal

nuclease

1–4-b-glucanase

phosphoribosyltransferase

a/b

subunit Iib

a/b

acetyltransferase

a/b

1poc Phospholipase A2 a 2stv STNV coat protein b 3chy Signal transduction protein a/b

1lbd Retinoid-X receptor a a 1qabA Transthyretin b 1dhr Dihydropteridin reductase a/b

2ilk Interleukin-10 a 1cbs Cellular

retinoic-acid-binding protein

b 1asu Retroviral integrase,

catalytic domain

a/b

ligand binding core

a/b 2sas Calcium-binding

protein

a 1ptf Histidine-containing

phosphocarrier

1hbg Glycera globin a 153 L Lysozyme, Goose a + b 1akz Uracil-DNA glycosylase a/b

2mhbA Hemoglobin (horse) a 1acf Profilin a + b 1 ns5A Hypothetical protein YbeA a/b 1dkeA Hemoglobin (human) a 1ctf Ribosomal protein

L7/12

a + b 1jkeB D-Tyr tRNAtyr deacylase a/b

1lki Leukemia inhibitory

factor

a 1apyA Glycosylasparaginase a + b 1dtdB Carboxypeptidase inhibitor small 3cytO Mitochondrial

cytochrome c

invariantchain fragment

small 3c2c Cytochrome c2 a 1dtp Diphtheria toxin a + b 2bbkL Methylamine dehydrogenase small

1enh DNA-binding protein a 2pii Signal transduction

protein

Peptostreptococcus

a + b 1i8nA Anti-platelet protein small 1pht Phosphatidylinositol

3-kinase

b 1fxd Ferredoxin II,

Desulfovibrio gigas

1pwt a-Spectrin, SH3 domain b 1c0bA Ribonuclease A a + b 1ehs Heat-stable enterotoxin B small 1semA Signal transduction protein b 1shaA c-src Tyrosine kinase a + b 1tgj TGF-b3 small 1cauB Seed storage protein

7 s vicillin

b 1ag2 Prion protein domain a + b 4rxn Rubredoxin,

Clostridium pasteurianum

small

Pyrococcus furiosus

small

factor)

1anu Cohesin-2 domain b 1hucB (Pro)cathepsin B a + b 1hpi HIPIP, Ectothiorhodospira

vacuolata

small 1f3g Glucose-specific factor III b 2act Actinidin a + b 1hip HIPIP, Allochromatium

vinosum

small 1sno Staphylococcal nuclease b 2 ci2 Chymotrypsin

inhibitor CI-2

a + b 1knt Collagen type VI small

zation of the folding process, by reducing the

conform-ational space to be explored Thus, the prediction of these

ÔhotÕ residues becomes an important step in approaching

the native three-dimensional structure A first approach to this goal was undertaken in this study The guiding hypothesis was that, in order to achieve fast folding,

Fig 3 Examples of comparison of MIR, TH and TEF for 10 sequences of various folds In each example, the PDB code (with the chain) is given, followed by the name, the SCOP class and the fold of the protein in parentheses The following lines represent the sequence and the TEFs The residues belonging to a TEF are indicated ÔIÕ In case of TEF overlap, two lines are used for this representation (for example in protein 1shaA) The next line shows TH positions, where the corresponding residues are indicated ÔTÕ The final line shows MIR residues, indicated by ÔMÕ For 3chy and 5p21, due to the sequence length, the results appear in two consecutive blocks.

critical residues should have a tendency to contact each

other and thus form the origins of the hydrophobic core

The results confirmed this hypothesis Using a simple

alpha-carbon lattice model, formation of the nucleation

sites at initial steps of the folding process was

demon-strated

These results suggest that folding initiation can be based

on the early formation of a set of nucleation sites around

selected hydrophobic residues [10,11,13] This is essentially

the basis of the hydrophobic collapse mechanism [23], which

supposes formation of hydrophobic tertiary interactions

that initiate secondary structure It can be extended onto a

unified nucleation–condensation mechanism, which is a

combination of hierarchical and hydrophobic collapse

mechanisms [23,24] In the latter case, hydrophobic tertiary

interactions are consolidated at the same time as elements of

secondary structure (with possible variations of the kinetics

of the mechanism caused by the different intrinsic stabilities

of the secondary structural elements) These models have

been developed from experiments and simulations of

folding and unfolding of several small proteins [23,24] and

particularly from the analysis of the residual structure of

denatured states, which are thought to correlate to the

nucleation sites The comparison of MIR predictions with

this type of data is being considered for future studies

The secondary peaks in the histogram representing the

correlation between MIR and TEF (Fig 5) come from

the proteins belonging mainly to the a class For these

folds, the TEF limits are often located inside a helices and

are mainly hydrophobic Sometimes, the predicted MIR are not exactly these limits but are the nearest hydropho-bic residues, which in a helix are located three positions away because of the a-helix periodicity This observation

is in full agreement with the definition of the van der Waals locks, as extended (three to five residues long) segments of polypeptide chains interacting with each other, and thus forming Ôloop-n-lockÕ structures in globu-lar proteins [13]

The main conclusion of this study is that burying MIR positions can serve as the creation of anchors for sequential formation of closed loops These results remarkably corro-borate experimental evidence on the initial stages of the folding process NMR analysis of folding intermediates of protein bovine pancreatic trypsine inhibitor [25] revealed loop formation in early, non-native states, stabilized by nonlocal interactions Also, an NMR study on the folding of lysozyme [26] showed the early formation of hydrophobic clusters, which are linked together by long-range inter-actions These interactions were shown not to occur in the native structure, but they are apparently important for keeping the loop structure and thereby speeding up the folding procedure The appearance of these essential features

in this folding simulation permits an initial estimation of the anchor regions for loop formation This approach therefore provides a set of structural constraints from first principles for an unknown structure This information could be incorporated at the early steps of a prediction method for building protein structures from the sequence by producing anchor residues known to belong to the structural core In a second stage they can be introduced as a set of constraint distances in a more detailed modeling process Acknowledgements

This project has been funded by a Concerted Action from the European Union, QLG2-CT-2002–01298, and by the Greek-French bilateral PLATO program (grant no 04146WM) I N B was also supported

by the Post-Doctoral Fellowship of the Feinberg Graduate School, Weizmann Institute of Science.

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