Protein structures as complex systems: a simplification conundrum

ADVANCES IN SYSTEMS BIOLOGY VOL.3 NO.1 http://www.researchpub.org/journal/asb/asb.html

2014

Protein structures as complex systems: a simplification conundrum Luisa Di Paola1,* and Alessandro Giuliani2 (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 the philosophical bases for reconsidering the simplistic

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.

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 perspective3 . Simple systems are made of a few interacting

Keywords — Computational Biochemistry, Complex Networks Theory, Protein folding.

elements, following the laws of Newtonian mechanics: their behavior results are predictable, thanks to the possibility to

Cite this article as: Di Paola L and Giuliani A. Protein structures as complex systems: a simplification conundrum. AdvSysBiol 2014. In press

write down quantitative relations between the parts in the form of differential equations.

D

interactions as a deep network of unpredictable beauty and

non-interacting elements (at least, interacting at very short

mystery. Life is endowed with complexity, the concept of

range) whose behaviour is again predictable upon the

complexity itself was generated upon the observation of

application of statistical methods: this is the case of

Nature, and almost as a defeat declaration, to understand or

macroscopic properties of gases, which can be satisfactorily

even predict the time evolution of natural systems.

predicted on the basis of the dynamics of the single gas

Complicated

ealing with biology, we naturally observe elements and

systems

are

made

of

many

The great sense of improperness is largely due to the

molecules, following the Brownian dynamics. In this case, the

deterministic approach which represents the cultural basis of

system saves the same features of simple systems on a local

modern western thinking still prevailing in science. The

scale and the properties of the whole system derive as the

contamination with ancient Eastern spiritual doctrines (such as

average of those of single elements. In other words, complicated systems are described as a

Taoism, describing any life activity as interaction of opposites 1

ying and yang ) as well as the reconsidering of different

whole whose properties are just the sum of the corresponding

western tradition of scientific and philosophical thoughts2 set

for the single elements. This holds only for negligible interactions between single elements.

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: [email protected]).

Complex systems, on the other hand, are made of many elements that interact with each other with a dynamically 7

ADVANCES IN SYSTEMS BIOLOGY VOL.3 NO.1 http://www.researchpub.org/journal/asb/asb.html

2014

changing pattern of relations. The nature of this interaction

and determines the physical interactions of protein structure

affects the whole system, that cannot be reduced to the sum of

and environment.

the properties of its elements and its behaviour cannot be

In our opinion, the complexity of life starts here: albeit

derived by a combination of single elements dynamics.

the existence of a very reliable chemical full description of

In the last decades, the complex network theory

amino acids, there is no accepted theory linking the

emerged as a framework to uncover the behavior of systems

chemico-physical properties of residues and the properties of

whose variation laws were unknown or nonlinear, intermingled

the whole protein structure. Since 60’s, when Anfinsen

onto a deep network of interactions among a large number of

declared his dogma (“Each protein structure is determined only

elements. The application to biological systems reveals

by its amino-acid sequence), there is no confirmation of this

surprisingly simple patterns in living organisms, hitherto

dogma on a general group of proteins. This dogma does not

addressed to be unpredictable.

hold, for instance for proteins undergoing misfolding

When acquiring an initial purely descriptive attitude

processes, which activate in physiological environment upon

on the dynamics of natural (complex) systems, without

molecular

recognition

between

folded

and

misfolded

6,7

structures .

imposing any preconceived theory on the observations, very regular collective patterns start to emerge. These patterns

Recently, Nussinov and Tsai addressed a strong point

appear to be surprisingly similar across very different systems.

in protein science: simple representations of protein global

In this respect, complex systems theory, i.e., the theoretical

molecular properties (thus not factorized into the single

framework focused on the heuristic classification of emerging

residues chemical description) and function do foster the

patterns in systems and their description through a

comprehension of their behaviour8.

mathematical toolkit, arouse as a universal scientific approach,

We are used to think complex systems, as proteins are,

which has been gathering evidences of its generality and

require complex, very refined description: the more detailed the

applicability to many different natural and artificial systems,

information, the better the molecule knowledge. Chemists

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given they show the same type of complexity .

know since long time the capital importance of catching the

But where complexity starts? Is it possible to locate a

right resolution degree to fully understand the properties of

border between the realm of classical, differential equations

compounds. For instance, the Kekulè structural formula of

driven, style of science and the necessarily less deep but more

benzene has a generative character, for all macroscopic

general, complex systems approach?

properties of the compound, through functional groups based

In the case of natural systems we can easily identify

theories, notwithstanding this representation even neglects

this border in the grey zone between chemistry and biology, i.e.

atoms (H) present in the chemical formula.

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at the level of biopolymers (proteins and nucleic acids).

Out of this example, we must learn that using the right

Biopolymers display molecular structures able to adapt to

“mind lens”, focused on the right resolution for the molecular

environment, so capable of interaction with other molecules.

representation, we are able to reveal and predict emerging

Proteins exert a large number of functions in

properties of complex systems: citing Albert Einstein, we must

organisms, from structural integrity to catalysis, lying in a

only be careful to be “simpler as possible, but not simpler”,

borderland, “where physics, chemistry and biology meet”5:

carefully saving the essential, but not a bit less. For instance,

their three-dimensional structure determines their function, and

coming back to the benzene, if we decide to catch only the

it is also the key for the adaptation to environment cues.

information of the number of carbon (6) bond in a cyclic

Nonetheless, the chemical nature of residues is well established

molecule, we confuse cyclohexane and benzene, showing strikingly different macroscopic properties. On the other hand, 8

ADVANCES IN SYSTEMS BIOLOGY VOL.3 NO.1 http://www.researchpub.org/journal/asb/asb.html

2014

adding the information of electronic clouds of all atoms in the

in terms of richness of meaningful correlations between parts.

benzene molecule, not only does not increase our knowledge,

In Pascal’s terms2, in the most equilibrated blend of ‘esprit de

but contributes to confuse the essential, generative information

finesse’ (intuition) and ‘esprit de geometrie’ (mathematical

kept in the resonance aromatic ring.

rigor). Graph theory and, more in general, complex network analysis, offer a very powerful method to look for this blend.

In our opinion, protein contact networks represent a paradigm that fulfills these requirements9: representing only non-negligible intramolecular contacts between residues that are sensible to environment, in principle it is possible to catch

References

the essential features of the molecule – such as the Kekulé structural form is generative of its properties. As a matter of

[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).

fact, contact network formalism has allowed to sketch a consistent picture of protein folding10,11 and function12,13 on a purely topological ground. The coarse-grained

strong

reduction

representation

of of

information interactions

–

the

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

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