Insights into the relation between noise and biological complexity

Understanding under which conditions the increase of systems complexity is evolutionary advantageous, and how this trend is related to the modulation of the intrinsic noise, are fascinating issues of utmost importance for synthetic and systems biology. To get insights into these matters, we analyzed chemical reaction networks with different topologies and degrees of complexity, interacting or not with the environment. We showed that the global level of fluctuations at the steady state, as measured by the sum of the Fano factors of the number of molecules of all species, is directly related to the topology of the network. For systems with zero deficiency, this sum is constant and equal to the rank of the network. For higher deficiencies, we observed an increase or decrease of the fluctuation levels according to the values of the reaction fluxes that link internal species, multiplied by the associated stoichiometry. We showed that the noise is reduced when the fluxes all flow towards the species of higher complexity, whereas it is amplified when the fluxes are directed towards lower complexity species.Comment: 5 pages, 3 figure

Stochastic noise reduction upon complexification: positively correlated birth-death type systems

Cell systems consist of a huge number of various molecules that display specific patterns of interactions, which have a determining influence on the cell's functioning. In general, such complexity is seen to increase with the complexity of the organism, with a concomitant increase of the accuracy and specificity of the cellular processes. The question thus arises how the complexification of systems - modeled here by simple interacting birth-death type processes - can lead to a reduction of the noise - described by the variance of the number of molecules. To gain understanding of this issue, we investigated the difference between a single system containing molecules that are produced and degraded, and the same system - with the same average number of molecules - connected to a buffer. We modeled these systems using Ito stochastic differential equations in discrete time, as they allow straightforward analytical developments. In general, when the molecules in the system and the buffer are positively correlated, the variance on the number of molecules in the system is found to decrease compared to the equivalent system without a buffer. Only buffers that are too noisy by themselves tend to increase the noise in the main system. We tested this result on two model cases, in which the system and the buffer contain proteins in their active and inactive state, or protein monomers and homodimers. We found that in the second test case, where the interconversion terms are non-linear in the number of molecules, the noise reduction is much more pronounced; it reaches up to 20% reduction of the Fano factor with the parameter values tested in numerical simulations on an unperturbed birth-death model. We extended our analysis to two arbitrary interconnected systems.Comment: 38 pages, 5 figures, to appear in J. Theor. Bio

Deciphering noise amplification and reduction in open chemical reaction networks

The impact of random fluctuations on the dynamical behavior a complex biological systems is a longstanding issue, whose understanding would shed light on the evolutionary pressure that nature imposes on the intrinsic noise levels and would allow rationally designing synthetic networks with controlled noise. Using the It\=o stochastic differential equation formalism, we performed both analytic and numerical analyses of several model systems containing different molecular species in contact with the environment and interacting with each other through mass-action kinetics. These systems represent for example biomolecular oligomerization processes, complex-breakage reactions, signaling cascades or metabolic networks. For chemical reaction networks with zero deficiency values, which admit a detailed- or complex-balanced steady state, all molecular species are uncorrelated. The number of molecules of each species follow a Poisson distribution and their Fano factors, which measure the intrinsic noise, are equal to one. Systems with deficiency one have an unbalanced non-equilibrium steady state and a non-zero S-flux, defined as the flux flowing between the complexes multiplied by an adequate stoichiometric coefficient. In this case, the noise on each species is reduced if the flux flows from the species of lowest to highest complexity, and is amplified is the flux goes in the opposite direction. These results are generalized to systems of deficiency two, which possess two independent non-vanishing S-fluxes, and we conjecture that a similar relation holds for higher deficiency systems

Optimality of the genetic code with respect to protein stability and amino acid frequencies

How robust is the natural genetic code with respect to mistranslation errors? It has long been known that the genetic code is very efficient in limiting the effect of point mutation. A misread codon will commonly code either for the same amino acid or for a similar one in terms of its biochemical properties, so the structure and function of the coded protein remain relatively unaltered. Previous studies have attempted to address this question more quantitatively, namely by statistically estimating the fraction of randomly generated codes that do better than the genetic code regarding its overall robustness. In this paper, we extend these results by investigating the role of amino acid frequencies in the optimality of the genetic code. When measuring the relative fitness of the natural code with respect to a random code, it is indeed natural to assume that a translation error affecting a frequent amino acid is less favorable than that of a rare one, at equal mutation cost. We find that taking the amino acid frequency into account accordingly decreases the fraction of random codes that beat the natural code, making the latter comparatively even more robust. This effect is particularly pronounced when more refined measures of the amino acid substitution cost are used than hydrophobicity. To show this, we devise a new cost function by evaluating with computer experiments the change in folding free energy caused by all possible single-site mutations in a set of known protein structures. With this cost function, we estimate that of the order of one random code out of 100 millions is more fit than the natural code when taking amino acid frequencies into account. The genetic code seems therefore structured so as to minimize the consequences of translation errors on the 3D structure and stability of proteins.Comment: 31 pages, 2 figures, postscript fil

Star products on extended massive non-rotating BTZ black holes

$AdS_3$ space-time admits a foliation by two-dimensional twisted conjugacy classes, stable under the identification subgroup yielding the non-rotating massive BTZ black hole. Each leaf constitutes a classical solution of the space-time Dirac-Born-Infeld action, describing an open D-string in $AdS_3$ or a D-string winding around the black hole. We first describe two nonequivalent maximal extensions of the non-rotating massive BTZ space-time and observe that in one of them, each D-string worldsheet admits an action of a two-parameter subgroup (\ca \cn) of \SL. We then construct non-formal, \ca \cn-invariant, star products that deform the classical algebra of functions on the D-string worldsheets and on their embedding space-times. We end by giving the first elements towards the definition of a Connes spectral triple on non-commutative $AdS$ space-times.Comment: 25 pages, 1 figur

Noncommutative Locally Anti-de Sitter Black Holes

We give a review of our joint work on strict deformation of BHTZ 2+1 black holes \cite{BRS02,BDHRS03}. However some results presented here are not published elsewhere, and an effort is made for enlightening the instrinsical aspect of the constructions. This shows in particular that the three dimensional case treated here could be generalized to an anti-de Sitter space of arbitrary dimension provided one disposes of a universal deformation formula for the actions of a parabolic subgroup of its isometry group.Comment: 10 pages, based on a talk given by P.B., to appear in the proceedings of the workshop `Noncommutative Geometry and Physics 2004' (Feb. 2004, Keio University, Japan) (World Scientific

The first peptides: the evolutionary transition between prebiotic amino acids and early proteins

The issues we attempt to tackle here are what the first peptides did look like when they emerged on the primitive earth, and what simple catalytic activities they fulfilled. We conjecture that the early functional peptides were short (3 to 8 amino acids long), were made of those amino acids, Gly, Ala, Val and Asp, that are abundantly produced in many prebiotic synthesis experiments and observed in meteorites, and that the neutralization of Asp's negative charge is achieved by metal ions. We further assume that some traces of these prebiotic peptides still exist, in the form of active sites in present-day proteins. Searching these proteins for prebiotic peptide candidates led us to identify three main classes of motifs, bound mainly to Mg^{2+} ions: D(F/Y)DGD corresponding to the active site in RNA polymerases, DGD(G/A)D present in some kinds of mutases, and DAKVGDGD in dihydroxyacetone kinase. All three motifs contain a DGD submotif, which is suggested to be the common ancestor of all active peptides. Moreover, all three manipulate phosphate groups, which was probably a very important biological function in the very first stages of life. The statistical significance of our results is supported by the frequency of these motifs in today's proteins, which is three times higher than expected by chance, with a P-value of 3 10^{-2}. The implications of our findings in the context of the appearance of life and the possibility of an experimental validation are discussed.Comment: 22 pages, 2 figures, J. Theor. Biol. (2009) in pres

SODa: An Mn/Fe superoxide dismutase prediction and design server

Background: Superoxide dismutases (SODs) are ubiquitous metalloenzymes that play an important role in the defense of aerobic organisms against oxidative stress, by converting reactive oxygen species into nontoxic molecules. We focus here on the SOD family that uses Fe or Mn as cofactor. Results: The SODa webtool http://babylone.ulb.ac.be/soda predicts if a target sequence corresponds to an Fe/Mn SOD. If so, it predicts the metal ion specificity (Fe, Mn or cambialistic) and the oligomerization mode (dimer or tetramer) of the target. In addition, SODa proposes a list of residue substitutions likely to improve the predicted preferences for the metal cofactor and oligomerization mode. The method is based on residue fingerprints, consisting of residues conserved in SOD sequences or typical of SOD subgroups, and of interaction fingerprints, containing residue pairs that are in contact in SOD structures. Conclusion: SODa is shown to outperform and to be more discriminative than traditional techniques based on pairwise sequence alignments. Moreover, the fact that it proposes selected mutations makes it a valuable tool for rational protein design. © 2008 Kwasigroch et al; licensee BioMed Central Ltd.Journal ArticleResearch Support, Non-U.S. Gov'tinfo:eu-repo/semantics/publishe