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
3
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.
4
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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