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Protein structures as complex systems: a simplification conundrum

Complex networks theory offers a unique chance to describe protein structures at the light of the intra-molecular interactions network. The perspective is appealing, supported by evidences of the topology weight on protein function and structures.
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  ADVANCES IN SYSTEMS BIOLOGY VOL.3 NO.1 2014  Protein structures as complex systems: a simplification conundrum Luisa Di Paola 1,*   and Alessandro Giuliani 2 (1) Faculty of Engineering, University Campus Bio-Medico of Rome, via Alvaro del Portillo, 21, 00128,  Roma, Italy; (2) Environment and Health Department, Istituto Superiore di Sanità, Viale Regina Elena 299, 00161,  Roma, Italy Abstract Complex networks theory offers a unique chance to describe protein structures at the light of the intra-molecular interactions network. The perspective is appealing, supported by evidences of the topology weight on protein function and structures.  Keywords — Computational Biochemistry, Complex Networks Theory, Protein folding. Cite this article as: Di Paola L and Giuliani A. Protein structures as complex systems: a simplification conundrum.  AdvSysBiol 2014. In press ealing with biology, we naturally observe elements and interactions as a deep network of unpredictable beauty and mystery. Life is endowed with complexity, the concept of complexity itself was generated upon the observation of  Nature, and almost as a defeat declaration, to understand or even predict the time evolution of natural systems. The great sense of improperness is largely due to the deterministic approach which represents the cultural basis of modern western thinking still prevailing in science. The contamination with ancient Eastern spiritual doctrines (such as Taoism, describing any life activity as interaction of opposites  ying and  yang 1 ) as well as the reconsidering of different western tradition of scientific and philosophical thoughts 2  set the philosophical bases for reconsidering the simplistic equation complexity = impossibility to approach by scientific methods. As a matter of fact, the uprising of systems thinking shifted the attention toward a much more interesting and surprisingly simple perspective 3  . Received on 27 June 2014. Corresponding Author Affiliation: Faculty of Engineering, University Campus Bio-Medico of Rome, via Alvaro del Portillo, 21, 00128, Roma, Italy; *Correspondence to Luisa Di Paola (e-mail: Simple systems are made of a few interacting elements, following the laws of Newtonian mechanics: their  behavior results are predictable, thanks to the possibility to write down quantitative relations between the parts in the form of differential equations. Complicated systems are made of many non-interacting elements (at least, interacting at very short range) whose behaviour is again predictable upon the application of statistical methods: this is the case of macroscopic properties of gases, which can be satisfactorily  predicted on the basis of the dynamics of the single gas molecules, following the Brownian dynamics. In this case, the system saves the same features of simple systems on a local scale and the properties of the whole system derive as the average of those of single elements. In other words, complicated systems are described as a whole whose properties are just the sum of the corresponding for the single elements. This holds only for negligible interactions between single elements. Complex systems, on the other hand, are made of many elements that interact with each other with a dynamically D 7  ADVANCES IN SYSTEMS BIOLOGY VOL.3 NO.1 2014  changing pattern of relations. The nature of this interaction affects the whole system, that cannot be reduced to the sum of the properties of its elements and its behaviour cannot be derived by a combination of single elements dynamics. In the last decades, the complex network theory emerged as a framework to uncover the behavior of systems whose variation laws were unknown or nonlinear, intermingled onto a deep network of interactions among a large number of elements. The application to biological systems reveals surprisingly simple patterns in living organisms, hitherto addressed to be unpredictable. When acquiring an initial purely descriptive attitude on the dynamics of natural (complex) systems, without imposing any preconceived theory on the observations, very regular collective patterns start to emerge. These patterns appear to be surprisingly similar across very different systems. In this respect, complex systems theory, i.e. , the theoretical framework focused on the heuristic classification of emerging  patterns in systems and their description through a mathematical toolkit, arouse as a universal scientific approach, which has been gathering evidences of its generality and applicability to many different natural and artificial systems, given they show the same type of complexity 3 . But where complexity starts? Is it possible to locate a  border between the realm of classical, differential equations driven, style of science and the necessarily less deep but more general, complex systems approach? In the case of natural systems we can easily identify this border in the grey zone between chemistry and biology, i.e. at the level of biopolymers 4  (proteins and nucleic acids). Biopolymers display molecular structures able to adapt to environment, so capable of interaction with other molecules. Proteins exert a large number of functions in organisms, from structural integrity to catalysis, lying in a  borderland, “where physics, chemistry and biology meet” 5 : their three-dimensional structure determines their function, and it is also the key for the adaptation to environment cues.  Nonetheless, the chemical nature of residues is well established and determines the physical interactions of protein structure and environment. In our opinion, the complexity of life starts here: albeit the existence of a very reliable chemical full description of amino acids, there is no accepted theory linking the chemico-physical properties of residues and the properties of the whole protein structure. Since 60’s, when Anfinsen declared his dogma (“Each protein structure is determined only  by its amino-acid sequence), there is no confirmation of this dogma on a general group of proteins. This dogma does not hold, for instance for proteins undergoing misfolding  processes, which activate in physiological environment upon molecular recognition between folded and misfolded structures 6,7 . Recently, Nussinov and Tsai addressed a strong point in protein science: simple representations of protein global molecular properties (thus not factorized into the single residues chemical description) and function do foster the comprehension of their behaviour  8 . We are used to think complex systems, as proteins are, require complex, very refined description: the more detailed the information, the better the molecule knowledge. Chemists know since long time the capital importance of catching the right resolution degree to fully understand the properties of compounds. For instance, the Kekulè structural formula of  benzene has a generative character, for all macroscopic  properties of the compound, through functional groups based theories, notwithstanding this representation even neglects atoms (H) present in the chemical formula. Out of this example, we must learn that using the right “mind lens”, focused on the right resolution for the molecular representation, we are able to reveal and predict emerging  properties of complex systems: citing Albert Einstein, we must only be careful to be “simpler as possible, but not simpler”, carefully saving the essential, but not a bit less. For instance, coming back to the benzene, if we decide to catch only the information of the number of carbon (6) bond in a cyclic molecule, we confuse cyclohexane and benzene, showing strikingly different macroscopic properties. On the other hand, 8  ADVANCES IN SYSTEMS BIOLOGY VOL.3 NO.1 2014  9 adding the information of electronic clouds of all atoms in the  benzene molecule, not only does not increase our knowledge,  but contributes to confuse the essential, generative information kept in the resonance aromatic ring. In our opinion, protein contact networks represent a  paradigm that fulfills these requirements 9 : representing only non-negligible intramolecular contacts between residues that are sensible to environment, in principle it is possible to catch the essential features of the molecule – such as the Kekulé structural form is generative of its properties. As a matter of fact, contact network formalism has allowed to sketch a consistent picture of protein folding 10,11  and function 12,13  on a  purely topological ground. The strong reduction of information – the coarse-grained representation of interactions between alpha-carbons gets rid of all information for the remaining atoms – not only allows to derive as much information as the all-atoms representation, but “clearing the way”, it elucidates emerging properties otherwise hidden by a larger (all-atoms) number of information. All in all we can safely state the key to success in complex system elucidation does not reside in the race to the ‘most detailed’ or ‘most extreme’ representation power (think of the Big Science race toward high energies gigantic accelerators) but in the catching of the most informative layer in terms of richness of meaningful correlations between parts. In Pascal’s terms 2 , in the most equilibrated blend of ‘ esprit de  finesse ’ (intuition) and ‘ esprit de geometrie ’ (mathematical rigor). Graph theory and, more in general, complex network analysis, offer a very powerful method to look for this blend. References [1]   Barnett, R. J. Taoism and biological science. 21, 297-318 (1986). [2]   Pascal, B. Pensées. (Hackett Publishing, 1662). [3]   Mazzocchi, F. Exceeding the limits of reductionism and determinism using complexity theory. EMBO Rep. 9, 10-14 (2008). [4]   Frauenfelder, H. & Wolynes, P. G. Biomolecules: Where the Physics of Complexity and Simplicity Meet. Phys. Today 47, 58 (1994). [5]   Shakhnovich, E. Protein Folding Thermodynamics and Dynamics?: Where Physics , Chemistry , and Biology Meet Fundamental Model of Protein Folding. Chem. Rev. 106, 1559-1588 (2006). [6]   Prusiner, S. Prions. PNAS 95, 13363-13383 (1998). [7]   Dobson, C. M. Protein folding and misfolding. Nature 426, 884-90 (2003). [8]    Nussinov, R. & Tsai, C.-J. Free energy diagrams for protein function. Chem. Biol. 21, 311-8 (2014). [9]   Di Paola, L., De Ruvo, M., Paci, P., Santoni, D. & Giuliani, A. Proteins Contact Networks: an emerging paradigm in chemistry. Chem Rev (2012). [10]   Shank, E. A., Cecconi, C., Dill, J. W., Marqusee, S. & Bustamante, C. The folding cooperativity of a protein is controlled by its chain topology.  Nature 465, 637-640 (2010). [11]   Baker, D. A surprising simplicity to protein folding. Nature 405, 39-42 (2000). [12]   Amitai, G. et al. Network analysis of protein structures identifies functional residues. J. Mol. Biol. 344, 1135-46 (2004). [13]   Del Sol, A., Fujihashi, H., Amoros, D. & Nussinov, R. Residues crucial for maintaining short paths in network communication mediate signaling in proteins. Mol. Syst. Biol. 2, 2006.0019 (2006).
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