Geometric and structural constraints greatly restrict the selection of folds adapted by protein backbones, and yet, folded proteins show an astounding diversity in functionality. For structure to have any bearing on function, it is thus imperative that, apart from the protein backbone, other tunable degrees of freedom be accountable. Here, we focus on side-chain interactions, which non-covalently link amino acids in folded proteins to form a network structure. At a coarse-grained level, we show that the network conforms remarkably well to realizations of random graphs and displays associated percolation behavior. Thus, within the rigid framework of the protein backbone that restricts the structure space, the side-chain interactions exhibit an element of randomness, which account for the functional flexibility and diversity shown by proteins. However, at a finer level, the network exhibits deviations from these random graphs which, as we demonstrate for a few specific examples, reflect the intrinsic uniqueness in the structure and stability, and perhaps specificity in the functioning of biological proteins.
Deep Dive into Random Network Behaviour of Protein Structures.
Geometric and structural constraints greatly restrict the selection of folds adapted by protein backbones, and yet, folded proteins show an astounding diversity in functionality. For structure to have any bearing on function, it is thus imperative that, apart from the protein backbone, other tunable degrees of freedom be accountable. Here, we focus on side-chain interactions, which non-covalently link amino acids in folded proteins to form a network structure. At a coarse-grained level, we show that the network conforms remarkably well to realizations of random graphs and displays associated percolation behavior. Thus, within the rigid framework of the protein backbone that restricts the structure space, the side-chain interactions exhibit an element of randomness, which account for the functional flexibility and diversity shown by proteins. However, at a finer level, the network exhibits deviations from these random graphs which, as we demonstrate for a few specific examples, reflect
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Random Network Behaviour of Protein Structures
Brinda K.V.1, Saraswathi Vishveshwara2 and Smitha Vishveshwara3
1 Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, TX
78712, USA.
2 Molecular Biophysics Unit, Indian Institute of Science, Bangalore, 560012, India.
31110 W. Green Street, Dept. of Physics, University of Illinois at Urbana-Champaign,
Urbana IL 61801, USA.
Corresponding author: Smitha Vishveshwara, E-mail: smivish@illinois.edu
Supplementary Material can be found in the journal version in Molecular BioSystems.
Abstract:
Geometric and structural constraints greatly restrict the selection of folds adapted by
protein backbones, and yet, folded proteins show an astounding diversity in functionality.
For structure to have any bearing on function, it is thus imperative that, apart from the
protein backbone, other tunable degrees of freedom be accountable. Here, we focus on
side-chain interactions, which non-covalently link amino acids in folded proteins to form a
network structure. At a coarse-grained level, we show that the network conforms
remarkably well to realizations of random graphs and displays associated percolation
behavior. Thus, within the rigid framework of the protein backbone that restricts the
structure space, the side-chain interactions exhibit an element of randomness, which
account for the functional flexibility and diversity shown by proteins. However, at a finer
level, the network exhibits deviations from these random graphs which, as we demonstrate
for a few specific examples, reflect the intrinsic uniqueness in the structure and stability,
and perhaps specificity in the functioning of biological proteins.
Key words: protein structure network, non-covalent connections, probabilistic distribution, percolation
transition, giant cluster
Introduction:
A protein is a hetero-polymer composed of a sequence of amino acids, which, among
billions of possibilities for putative configurations, stunningly assumes a unique
structure, whose precise functions govern life‟s processes (1). It is well known that
proteins respect severe constraints imposed by folding entropy (2) resulting in a limited
menu of protein folds (3). The backbone of the polypeptide chain endows the protein a
skeletal structure composed of optimally packed (4), immutable folds (5, 6), which are
resilient to local variations and mutations (7, 8). Moreover, the underlying structure of
amino acid linkages formed via non-covalent side-chain interactions is also known to be
crucial for the stability and uniqueness of protein structure. While the backbone
accounts for robustness of structure, its regular packing alone explains neither the
diversity of sequences for a given fold, nor functional specificity and diversity of
proteins. However, the role of side-chain linkages in this regard has received much less
attention. In the present work, by analyzing a large dataset of protein structures, we find
that the three-dimensional network (9-12) formed by these amino acid side chain links
exhibits features of randomness (13). Although randomness has been established in
2
amino acid sequences (7, 8, 14), it has only sparsely been investigated in the context of
interactions in spatial structure in proteins (15,16,17). For example, Bryngelson and
Wolynes have introduced earlier a random energy model for understanding the nature of
the folding energy landscape of proteins (18,19). This phenomenological model has
established the concepts of ruggedness and smoothness in the folding energy landscape
and has also provided a way for understanding the kinetics of protein folding. The
present study, which is based on experimentally determined protein structures, shows
that the non-covalent interactions in their native state structures have elements of
randomness as seen by the percolation behaviour of the amino acid networks in protein
native structures. And the results underscore the presence of order, reflected in the
presence of a rigid backbone, coexisting with disorder, reflected in the random
percolation-like behaviour of the side-chains, in protein structures. We suggest that the
interplay between order and disorder yields stability, on the one hand, and sensitivity
towards changes such as in cellular environment and ligand binding, on the other, to
protein structures. Further, this random behavior, or more precisely, a probabilistic
distribution for the formation of links within the protein structure, provides an extensive
parameter space to host variations while conforming to structural, chemical and
biological constraints. Hence, we believe that the side chain linkages, within the
framework of the backbone architecture, offer the degrees of freedom required to host a
tremendous range of specific structures which may be crucial in accounting for the
marvelous diversity observed in Nature‟s functioning proteins. Furthermore, the
devi
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