Open Access Article
Journal of Biomolecular Structure &
Dynamics, ISSN 0739-1102
Volume 28, Issue Number 2, (2010)
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A Stoichiometry Driven Universal Spatial
Organization of Backbones of Folded Proteins: Are
there Chargaff’s Rules for Protein Folding?
Aditya Mittal1#*
B. Jayaram1,2#*
Sandhya Shenoy2
Tejdeep Singh Bawa2
http://www.jbsdonline.com
1School
Abstract
Protein folding is at least a six decade old problem, since the times of Pauling and Anfinsen.
However, rules of protein folding remain elusive till date. In this work, rigorous analyses
of several thousand crystal structures of folded proteins reveal a surprisingly simple unifying principle of backbone organization in protein folding. We find that protein folding is
a direct consequence of a narrow band of stoichiometric occurrences of amino-acids in
primary sequences, regardless of the size and the fold of a protein. We observe that “preferential interactions” between amino-acids do not drive protein folding, contrary to all
prevalent views. We dedicate our discovery to the seminal contribution of Chargaff which
was one of the major keys to elucidation of the stoichiometry-driven spatially organized
double helical structure of DNA.
of Biological Sciences, Indian
Institute of Technology Delhi,
New Delhi, 110016, India
2Department
of Chemistry and
Supercomputing Facility for
Bioinformatics & Computational
Biology, Indian Institute of Technology
Delhi, New Delhi, 110016, India
#Equal
contribution.
Introduction
Protein folding is a grand challenge till date. From the time of elegant work of
Pauling (1) and Anfinsen (2, 3), and formulation of the Levinthal’s paradox (4, 5),
several views on protein folding have emerged in the last several decades (6-14).
With a remarkable increase in available computational hardware and tools in recent
times, attempts at determination of protein structure and function by modeling have
become somewhat routine (15-26). However, research in the field has primarily
focused on the possible variety of different interactions that can lead to specific
features in functional protein structures. This has led to a strong prevalence of
somewhat diverse views on how a protein folds (e.g., via electrostatics/hydrogen
bonding vs. hydrophobic interactions). Therefore, protein folding still remains the
biggest unsolved problem in modern biology.
Thus we asked the question: Is there a unifying theme or concept underlying the
magnificent diversity of folded protein structures.
The understanding of DNA structure came from a careful analysis of the backbone from X-ray diffraction data of a single molecular species-fibers of B-DNA
(27). Inspired by this, we decided to investigate the backbones of, not one or two,
but several thousands of folded proteins from their published crystal structures in
the protein data bank, PDB (28). Assuming protein folding resulted from specific
amino-acid interactions, the backbones of folded proteins would be organized
within the constraints of defined “neighborhoods” for CA atoms of each aminoacid. For example, if two amino-acids were to interact with each other (e.g., via
side-chains), their respective CA atoms would be expected to occur in fixed neighborhoods relative to each other, regardless of their actual position in the protein.
*Phone: 91-11-26591052
91-11-26591505
Fax: 091-11-26582037
E-mail: [email protected]
[email protected]
133
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Mittal et al.
Further, CA of an amino-acid occurring mostly in the “center” of folded proteins
would always be expected to be surrounded by a higher number of CA atoms of
other amino-acids. Figure 1 shows our approach for analyzing the protein backbones in terms of neighborhoods of every CA atom in several thousands of folded
proteins from their crystal structures.
Methods
Coordinates of all atoms in crystal structures of 4000 proteins were taken
from the Protein Data Bank. After specifically extracting the CA coordinates
for all the amino-acids (i.e., backbone of the folded protein) from a given PDB
file, neighborhood analysis was done as described in Figure 1. Of the total
crystal structures, 3718 were finally analyzed in detail (see legend to Figure 1).
For each protein, a 20 r20 matrix of number of “neighbors”, within a defined
neighborhood distance, resulted by considering each of the amino-acids
Figure 1: Analyzing backbones of 3718 folded proteins – CA backbone of the protein Mitochondrial
Serine Protease HtrA2 (PDB: 1LCY). (A) shows how the neighborhood of the CA shown in grey was
investigated. If the CA of any amino-acid was found to occur within a particular distance (represented
by blue circles in 2-D) in the 3-D crystal structure, it was scored as a neighbor. CA of the peptide-bonded
partners i.e., residues adjacent, to the amino-acid being investigated, along the primary sequence (shown
in red) were not scored as neighbors. (B) shows the neighborhood analysis for another CA in the same
protein. This analysis was done for all the CA atoms in the protein, with the neighborhood distances
(represented by radii of the blue circles) fixed at 0-9 Å, with increments of 1 Å, and 10-90 Å, with increments of 5 Å. Distances of 0-3 Å were chosen as an internal check (since zero neighbors were expected
at these distances). Beginning with neighborhood analysis of 4000 crystal structures, we finally analyzed 3718 total crystal structures (see supplementary Table S1) by including only those proteins with
50 or more residues and removing those structures that did not pass the internal check.
individually. Thus, the total number of 20 r20 matrices was equal to the total
number of the defined neighborhood distances. Data of all the 20 20 matrices
was analyzed in MATLAB (Mathworks Inc., USA). The PDB ids of proteins
classified as “unstructured” were taken from the database at www.ebi.ac.uk/
interpro (29).
Results and Discussion
To investigate the presence of preferential neighborhoods expected to arise out
of the four well established non-covalent interactions (hydrogen bonds, electrostatic, hydrophobic and van der Waals), we plotted the number of times a specific
amino-acid appears as a neighbor of a given amino-acid. For example, Figure 2A
shows 20 data sets, each representing the number of times each of the 20 aminoacids appears as a neighbor for leucine within a defined neighborhood distance,
in 3718 folded protein crystal structures. A clear sigmoidal trend is observed
regardless of the identity of the neighbor. Similar sigmoidal trends were observed
for neighborhoods of all the 20 amino-acids, as shown (as examples) for glycine,
tryptophan and asparagine in Figures 2B-2D respectively. These sigmoidal trends,
surprisingly independent of the nature of amino-acids (e.g., polar vs. non-polar or
big vs. small), could essentially imply existence of several spatial distributions,
each uniquely defining neighborhoods of each amino-acid based on its presumed
preferences. Alternatively it could also imply a single underlying spatial distribution of neighborhoods for all amino-acids, regardless of their conventional classification. If the former were true then one would require different equations to fit the
different sigmoids. If the latter were true then one would need only one equation
that would fit all of the sigmoids for all the amino-acid neighborhoods.
The first extraordinary result found by us was that a generalized, single, sigmoidal
equation fits all the sigmoids (see legend of Figure 2). This reflected existence
of an underlying (single) spatial distribution of neighborhoods of amino-acids,
contrary to all prevailing views of the role of amino-acids in folded proteins. Visual
inspection of the sigmoids appeared to show “clustering” or “groups” of specific
amino-acids within the neighborhoods of a given amino-acid based on their asymptotic values. These asymptotes of sigmoids, reflecting the maximum possible total
number of contacts between two amino-acids, were clearly different and pointed to
our obvious next step.
If an amino-acid occurs the highest number of times in a primary sequence, it
would be expected to be found as a neighbor of all 20 amino-acids (including itself)
highest number of times, assuming no preferential interactions between amino-acids.
Thus, the total number of contacts for the amino-acid occurring most number of times
in a protein, reflected by the sum of all asymptotes of the 20 sigmoids for that aminoacid, would be expected to be the highest. Therefore, the total number of contacts
for each amino-acid would be expected to be directly correlated to the frequency
of occurrence of each amino-acid. However, if this were the case, it would imply
that neighborhoods of amino-acids in folded proteins are simply governed by their
individual frequencies of occurrences (stoichiometries) rather than any preferential
interactions with other partners. Alternatively, in case amino-acids prefer certain
neighborhoods due to preferential interactions (e.g., hydrophobic, hydrogen bonding,
electrostatics), one would not be able to predict a direct relationship between the total
number of contacts of a given amino-acid with its frequency of occurrence in folded
proteins. For example, if an amino-acid occurs the highest number of times, but does
not prefer to interact with many partners, the total number of contacts for this aminoacid would be expected to be much lower than an amino-acid occurring lesser number
of times but interacting preferentially with several other amino-acids.
To test which of the above two hypotheses was true, we plotted the sum of the
20 asymptotes for each amino-acid against the average percentage occurrence of
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Universal Spatial
Organization of Backbones
of Folded Proteins
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Mittal et al.
that particular amino-acid in our 3718 folded proteins. To our surprise, the total
number of contacts made by an amino-acid were correlated excellently with the
average occurrence of that amino-acid (stoichiometry) in folded proteins as shown
by Figure 2E. This strongly supported our first hypothesis and directly implied an
“absence” of any preferential interactions between amino-acids.
Now, asymptotic distances essentially define neighborhoods of the amino-acids
only in terms of possible long range interactions. Thus, in case of a complete
absence of any long range preferential interactions between amino-acids, their
total number of contacts would directly reflect their frequencies of occurrences,
as observed above. Therefore we carried out a closer inspection of the sigmoids to
investigate the presence of short and medium range interactions. We utilized the
fact that the sigmoids are characterized by two other parameters, namely “n” and
“k” (see legend of Figure 2), which signify neighborhoods in much closer proximities of the reference amino-acid. “n” reflects the distance at which the lift-off of the
Figure 2: CA neighborhood
analysis from crystal structures of
3718 proteins reveals a single,
amino-acid independent spatial distribution – (A) Number of CA
atoms of each amino-acid in a given
neighborhood distance for a leucine
CA, from crystal structures of 3718
proteins. If CA of an amino-acid is
found within the fixed neighborhood distance from any leucine CA,
it is scored as a contact with leucine
CA. By doing so, 20 “sigmoidal”
data-sets are observed ( ). Each
point on a sigmoid corresponds to
number of leucine-X CA pairs, with
X corresponding to one of the 20
amino-acids. The “sigmoidal”
behavior is parameterized by Y YMax(1-ekX)n, shown by smooth
lines. (B), (C), (D) Neighborhood
contacts of CA pairs for glycine-X,
tryptophan-X and asparagine-X
respectively. (E) Sum of all 20 YMax
values for any amino-acid, indicating the total possible contacts for
CA of a given amino-acid, correlates excellently (r2 0.99) with
percentage occurrence of that particular amino-acid in 3718 proteins.
(F) Average values of “n” ( ) and
“k” ( ) are independent of the percentage occurrence of aminoacids.
sigmoid occurs (i.e., less than 5-12 Å for all sigmoids) and “k” reflects the intermediate neighborhoods (i.e., between 20-30 Å at the inflection point in all sigmoids).
Thus, if there were any preferential neighborhoods, they would be reflected particularly in “n” (representing “close” interactions) and possibly in “k” (medium range
interactions). Figure 2F shows (i) both n and k have very similar values regardless
of the amino-acid, and, (ii) both n and k are independent of the frequency of occurrence for any amino-acid.
137
Universal Spatial
Organization of Backbones
of Folded Proteins
To re-iterate the significance of the above findings, especially Figure 2F in terms
of short range interactions, we “zoomed” into the sub-10 Å region of the sigmoids
shown in Figure 2. Figure 3 demonstrates that (a) the absence of preferential interactions between amino-acids, and, (b) dependence of amino-acid neighborhoods primarily on their respective percentage occurrences, in folded proteins is clearly true at
sub-10 Å distances as well. Having observed this for the four examples of individual amino-acids in Figure 3, we next explored the universal spatial distribution
Figure 3: The single, aminoacid independent, spatial distribution is observed even for
“zoomed in” neighborhoods
within 10 Å – (A) Number of CA
atoms of each amino-acid within
10 Å for a leucine CA, from
crystal structures of 3718 proteins. The single, amino-acid
independent, spatial distribution
(parameterized in Figure 2) is
shown by smooth lines. Inset
shows that all the sigmoids collapse to almost a single sigmoid
even at distances of 10 Å and
lower, when each of the sigmoids
is normalized w.r.t. the number
of times a given amino-acid
appears as a neighbor of leucine
at 10 Å. (B), (C), (D) show the
same results as in (A) for glycine, tryptophan and asparagine
neigborhoods respectively. (E)
Sum of all 20 neighborhood values at 10 Å for leucine, glycine,
tryptophan and asparagine correlates excellently (r2 0.99)
with percentage occurrence of
each of the four amino-acids in
3718 proteins. (F) Average values of “n” ( ) and “k” ( ) are
independent of the percentage
occurrence of leucine, glycine,
tryptophan and asparagine.
138
Mittal et al.
in greater detail to be able to test our findings on the remaining sixteen amino-acids.
Figure 4A shows sigmoids varying only in their “n” values, with fixed values of
YMax ( 1.462 r 106) and k ( 6.87 r 10–2). Clearly, the lift-off points of sigmoids,
shown by arrows, are strongly dependent on “n” ( 1, 2, 3, 5, 7, 10). Therefore,
if the neighborhood sigmoids of the amino-acids (e.g., those shown in Figures
2A-2D) were different due to preferential short range contacts (i.e., 10 Å) with
specific neighbors, one would expect very different “n” values from individual sigmoids. Clearly, this is not the case as seen previously in Figure 2F, i.e., the “n”
values for all the neighborhood sigmoids are very similar (4.35 – 4.87). On similar
lines, Figure 4B shows sigmoids varying only in their “k” values ( 6.87 x 10–2, 1.5
r 6.87 r 10–2, 2 r 6.87 r 10–2, 3 r 6.87 r 10–2, 5 r 6.87 r 10–2), with fixed values
of YMax ( 1.462 r 106) and n ( 5). Firstly, the lift-off points of simoids, shown
by arrows, are very similar (in contrast to Figure 4A). Secondly, if the neighborhood sigmoids of amino-acids were different due to any preferential medium range
interactions with specific neighbors, one would expect very different “k” values
for all the sigmoids. Clearly, this is also not the case, i.e., the “k” values for all the
neighborhood sigmoids are very similar (6.43 r 10–2 – 7.36 r 10–2), as seen previously in Figure 2F.
Thus, data from crystal structures of 3718 folded proteins demonstrates
absence of any long, medium or even short range preferential interactions
between amino-acids. The data also shows that protein folding is simply governed
by frequencies of occurrences (stoichiometries) of individual amino-acids. To
re-examine, we plotted the data of Figure 2E for each amino-acid. Figure 4C shows
that regardless of the amino-acid, the percentage occurrence overlaps with
the total number of contacts. In fact, this holds true regardless of the size of the
protein, as shown in Figure 4D.
Here, it is important to note that extremely meticulous inspection of Figures 3B
and 3D might suggest minor deviations of the fits to the data, completely absent/
invisible in Figures 2B and 2D. Thus, we also re-plotted the data of Figure 2F for
each amino-acid. Figure 5A shows that n and k are independent of the amino-acid.
A clear independence of “n” from the nature of the amino-acid shows the absence
of any preferential interactions even at the closest possible distance ranges. This is
so because the minor deviations of fits to the data at a very few individual points in
Figures 3B and 3D are clearly a part of only noise in the data. Still, it can be argued
from Figure 5A that some residues like C and H may have minor differences in “n”
values compared to other amino-acids. These differences, if they exist indeed are
(a) very different in nature from the prevalent views of role of amino-acid interactions in protein folding, and (b) are open to further investigation.
In summary, crystal structures of 3718 folded proteins show that protein folding is
primarily dictated by the frequencies of occurrence of amino-acids in the primary
sequence, i.e., its stoichiometry, regardless of the length/size. One essential prediction from our results is that stoichiometry of “unstructured” proteins (as listed in
the PDB, see methods for source reference, see supplementary Table S2 for PDB
ids) would deviate from the frequencies of occurrence of amino-acids in folded
proteins. Figure 5B shows this to be the case indeed.
Conclusions
The foundations of all diverse and prevalent views on protein folding currently
lay in “classifications” of constituent amino-acids (e.g., polar, non-polar). We
have found that the crystal structures of 3718 folded proteins do not support this
conventional view.
We have shown that protein folding is directly correlated to the stoichiometry of
amino-acids in the primary sequence (i.e., frequency of occurrence). Table I shows
the percentage occurrence of each amino-acid in 3718 folded proteins. These percentage occurrences are essentially the “Chargaff’s Rules”, dedicated to the seminal contribution of Chargaff for DNA structure (30), applicable to the primary
sequence compositions that result in folded proteins. This means that to achieve
a folded protein, the stoichiometric ratios of individual amino-acids have to be
139
Universal Spatial
Organization of Backbones
of Folded Proteins
Figure 4: CA neighborhoods are
a direct consequence of frequency
of occurrence of amino-acids, rather
than any preferential interactions,
in folded proteins – (A) For fixed
values of “YMax” and “k” (see legend to Figure 2), sigmoids that are
different only in “n” values show a
clear separation at their “lift-off”
points as indicated by arrows
(shown for n 2, 3, 5, 7 and 10
respectively). (B) For fixed values
of “YMax” and “n”, sigmoids that are
different only in “k” values do not
show much separation at “lift-off”
points as indicated by arrows, but
are substantially separated at the
half-maximum point. (C) Data in
Figure 2E is re-plotted for each
amino-acid. Total number of contacts (u, left Y-axis) overlaps with
the percentage occurrence (u, right
Y-axis) of each amino-acid in
folded proteins. (D) Subsets of data
from (C) for different sizes of proteins. Total number of contacts
made by individual amino-acids in
folded proteins of sizes 101-150
( ), 151-200 ( ), 201-250 ( ), 251300 () and 301-350 ( ) are plotted.
All subsets show exactly the same
trend and vary in only the actual
numbers. Thus, any of the subsets are
scalable to observe exactly the same
result as shown in (C).
140
Mittal et al.
Table I
The average percentage occurrence of each aminoacid for folded proteins gives the “Chargaff’s rules”
for protein folding and the standard deviations give
the “margin of life”.
Amino Acid
A
V
I
L
Y
F
W
P
M
C
T
S
Q
N
D
E
H
R
K
G
Folded Proteins –
Margin of Life
(mean o std,
n 3718)
7.8 o 3.4
7.1 o 2.4
5.8 o 2.4
9.0 o 2.9
3.4 o 1.7
3.9 o 1.8
1.3 o 1.0
4.4 o 2.0
2.2 o 1.3
1.8 o 1.5
5.5 o 2.4
6.0 o 2.5
3.8 o 2.0
4.3 o 2.2
5.8 o 2.0
7.0 o 2.7
2.3 o 1.4
5.0 o 2.3
6.3 o 2.8
7.2 o 2.8
Figure 5: CA neighborhoods do not show any preferential interactions at either short (^10 Å) or
medium distance (^25 Å) ranges in folded proteins – (A) Data in Figure 2F is re-plotted for each
amino-acid. The sigmoidal parameters, “n” (u, right Y-axis) and “k” (u, left Y-axis), show similar
values for all amino-acids. (B) Average percentage of occurrence of amino-acids in 212 “unstructured” proteins is plotted against average percentage occurrence of the corresponding amino-acids in
the 3718 folded proteins investigated in this work. The correlation is weak (r2 0.83) compared to
that observed in Figure 2E.
defined as per Table I. It is clear that the low standard deviations of the percentage
occurrences of amino-acids in folded proteins represent (what we would like to call
as) the “margin of life”.
Our results raise the “grand-challenge” question again, with a plausible solution:
how does the Anfinsonian view allow specific primary sequence dependent fold
(hence functionality) to a protein? To answer this question, we need to appreciate
that all proteins occur in predominantly aqueous environments. Water is known to
have unique properties that thermodynamically (i.e., given infinite time) exclude
any solute, independent of its solubility, given a high enough concentration of
the solute. A protein molecule is a large solute, equivalent to a group of highly
concentrated small solutes, within the hydration layer of the protein (independent
of whether the protein exists as an open chain or in some globular form). Thus,
aqueous environment would force the surface-to-volume minimization of the solute within the hydration layer. This would constrain a protein to pack/fold in an
“exclusion by water” manner to minimize the overall surface-to-volume ratio, governed by shapes of individual amino-acids. This must be done while satisfying the
structural constraints of the primary sequence composition and constitution (i.e.,
the order in which a given stoichiometry of amino-acids appear). Thus, we propose
that most important parameters for protein folding (and protein engineering) are
(i) exclusion by water and (ii) shape characteristics of individual amino-acids along
the sequence that would minimize the surface-to-volume ratio. One can visualize
protein folding like fitting “Lego Blocks” tied with a thread and packed into the
lowest surface-to-volume ratio.
Supplementary Material
Supplementary Table S1 lists PDB ids of all 3718 folded proteins, with length (no.
of amino-acids) of each protein, crystal structures of which have been analyzed in
this work. Supplementary Table S2 lists PDB ids of 212 unstructured proteins (23),
with length (no. of amino-acids) of each protein, sequence compositions of which
have been analyzed for Figure 5B. The supplementary material can be downloaded
free of charge from:
http://web.iitd.ac.in/~aditya/MJ_Chargaff_Supp_TableS1.pdf or
http://www.scfbio-iitd.res.in/publication/MJ_Chargaff_Supp_TableS1.pdf
http://web.iitd.ac.in/~aditya/MJ_Chargaff_Supp_TableS2.pdf or
http://www.scfbio-iitd.res.in/publication/MJ_Chargaff_Supp_TableS2.pdf
Acknowledgements
BJ acknowledges the funding support from the Department of Biotechnology, and
Department of Information Technology, Govt. of India. BJ and AM are grateful
to Prof. D. L. Beveridge for his critical reading of the manuscript. SS is grateful
to the Department of Science and Technology (WOS scheme), Govt. of India.
AM and BJ are particularly grateful to Prof. S. Prasad, Director, IIT Delhi, and,
Prof. B. N. Jain, ex-Dy. Director (Faculty), IIT Delhi for providing the right platform for carrying out this work. We are grateful to our four anonymous reviewers
for their constructively critical assessment and positive response to our work.
We especially acknowledge “referee 1” in pushing us to prepare a much better
manuscript. And finally, we are very grateful to the Chief Editor of J. Biomol.
Struct. Dyn. for having faith in our ability to be able to address the queries of the
reviewers in a timely manner.
Author Contributions
AM and BJ designed the study, analyzed the data and wrote the manuscript. SS and
TSB collected the data.
Competing Financial Interests
There are no competing financial interests.
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Date Received: April 13, 2010
Communicated by the Editor Ramaswamy H. Sarma