Acides amines : 20 pas plus pas moins

[jp the z]

Dans le numero d'Octobre de La Recherche :

Un physicien (T. Tlusty) a donne une explication au fait que les genes ne codent que pour 20 acides amines.
D'apres lui cest le meilleur compromis entre le nombre d acides amines que l on peut coder et le risque d'erreur a la lecture de l information genetique lors de leur synthese.
pour demontrer cela , il a imagine chaque codon comme noeud d un graphe, les codons etant relies entre eux s ils different d'une seule base (adenine , thymine, cytosine, guanine). Il ya en tout 45 noeuds (64 -16-3), on ne compte pas 3 sequence qui codent pour stop et l auteur admets que lorsque T et C sont en troisieme position elles sont equivalente.
Ensuite Tlusty montre que la minimisation du rapport surface/volume d une region du graphe codant pour un acide amine est ce qui donne la meilleure protection contre les erreurs de codage (d'apres ce que j'ai compris c'est la partie la plus difficile. Elle n est pas detaillee dans l'article de La Recherche).
Il y aurait selon lui seulement 20 regions du graphe pour lesquelles la synthese d acide amines n entrainerait pas trop d erreurs de codage

Ref: T.Tlusty, PNAS, 105, 8 238, 2008
et T. Tlusty, J. Theor. Biology, 249, 331, 2008

on trouvera aussi de bonnes infos de base sur wikipedia

L'entrefilet paru dans La Recherche est assez sybillin et ne donne pas selon moi une veritable explication au fait que nos gens ne fabriquent que 20 sortes d'acides amines. Il montre juste que seuls 20 sont viables, sans expliquer pourquoi notre corps s'abstient de fabriquer ceux a haut risque d erreur de codage. Peut-etre plus d explication dans les articles originaux auxquels je n ai pas acces.
C'est peut etre parceque la question des codons synonymes est ignoree par Tlusty. Il semble faire l hypothese implicite d un codon pour un acide amine et un seul.

Mais le plus interessant dans l histoire (sous reserve de verification du resultat), c est de voir comment un raisonnement purement mathematico-physique (theorie des graphes et statistiques entre autres) peut permettre d'expliquer des phenomenes non triviaux dans une discipline dont on ne connait rien ou presque.
C'est bien foutu l'univers quand meme.

[Bull]

Très intéressant JP !

Je ne pourrais absolument pas donner mon avis sur cet article (celui de PNAS est l'article majeur), n'étant... absolument pas qualifié.

Pour info, l'abstract et le Materiel et methode (qui est du "chinois" pour moi)

Proc Natl Acad Sci U S A. 2008 Jun 17;105(24):8238-43.


Casting polymer nets to optimize noisy molecular codes.

Tlusty T.
Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel. tsvi.tlusty@weizmann.ac.il

Life relies on the efficient performance of molecular codes, which relate symbols and meanings via error-prone molecular recognition. We describe how optimizing a code to withstand the impact of molecular recognition noise may be understood from the statistics of a two-dimensional network made of polymers. The noisy code is defined by partitioning the space of symbols into regions according to their meanings. The "polymers" are the boundaries between these regions, and their statistics define the cost and the quality of the noisy code. When the parameters that control the cost-quality balance are varied, the polymer network undergoes a transition, where the number of encoded meanings rises discontinuously. Effects of population dynamics on the evolution of molecular codes are discussed.

Cost of a Code-Table.The cost of a code-table is traditionally measured by the mutual information I between the symbols and the meanings that they encode, I = S ME + S SY − S MS, where S ME and S SY are the entropies of the meaning space and symbol space, respectively, and S MS is the joint entropy of these two spaces. The entropy of meanings S ME is determined by their given distribution P α, S ME = −Σα P α ln P α, and similarly, S SY = −ΣiPi ln Pi = ln(n s). These are constant terms in the cost I that we can neglect, and consider only the joint entropy S MS, which can be optimized by tuning the average partition pattern eij. S MS is simply the entropy of all of the possible coloring patterns as determined by all possible networks and the number of possible ways to color every such pattern. It follows that the cost is therefore minus the coloring entropy I = −S MS = −S C.

Graph Embedding and the Dual Graph.The embedded graph divides the surface into faces or cells, hexagons in our example (Fig. 1). Then, one finds the dual graph by the following correspondence (10): Every vertex in the symbol graph corresponds to a cell in the dual (a triangle in this example) whereas every cell in the symbol graph (a hexagon) corresponds to a vertex of the dual. The correspondence between the edges in the symbol graph and its dual is one-to-one; every edge corresponds to the edge that crosses it in the dual. The resulting dual graph is a triangular lattice. The hexagonal lattice is a regular graph in which all of the vertices have the same coordination number. However, the embedding procedure described here applies to any connected graph whether it is regular or not.

Mean-Field Approximation.The spin probability distribution decouples into a product of independent single-spin distributions, ρ = ∏ijρij(Sij). We use a variational inequality, which sets an upper limit on the spin free energy, F S ≤ F M = 〈ρH S〉 + T〈ρ ln ρ〉, where ρ satisfies probability conservation, 〈ρ〉 = 1. We augment F M with a Lagrange multiplier to account for probability conservation, L = F M + η〈ρ〉, and take the derivative δL/δρij = 0. The resulting distributions are ρij(Sij) = exp(gijSij)/〈exp(gijSij)〉, where the effective fields are gij = ∂H S/∂Sij = ∂(hi + h j)/∂Sij = aibij[∏k(i)≠j(1 + biksik) + ∏k(j)≠i(1 + bjksjk) − 2] with sij = 〈ρSij〉 = 〈Sijρij(Sij)〉. From the n = 0 property, it follows that 〈exp(gijSij)〉 = Σk gijk〈Sk〉/k! = 1 + gij 2/2 and 〈Sijexp(gijSij)〉 = gij. This leads to the self-consistency relations, sij = 〈Sijρij(Sij)〉 = 〈Sij exp(gijSij)〉/〈exp(gijSij)〉 = gij(1 + gij 2/2)−1 (Eq. 7). In a similar fashion, we obtain the mean-field approximation for the free energy, F S ≈ F M = −Σihi + Σi−j gijsij − Σi−j ln(1 + gij 2/2), and it is easy to verify that Eq. 7 defines the extremum ∂F S/∂sij = 0. Eq. 7 is analogous to the self-consistency relation of an Ising magnet, s = sinh(gs)/cosh(gs); the different form is due to the truncation of the power-series expansion of the hyperbolic functions thanks to the n = 0 property. Solving Eq. 7 for gij as a function of sij, we find that the solution can be described graphically as the points where the function eij = gijsij/2 crosses the ellipse 2sij 2 + (2eij − 1)2 = 1 (Fig. 3 A).

Use of Euler's Characteristic.When we apply Eq. 3, an underlying assumption is that the embedding is cellular (10); i.e., every meaning island is homeomorphic to an open disk. This is not necessarily true when the number of islands is less than the number of holes in the surface, that is the genus, γ = 1 − χ/2. In this case, some islands are expected to wrap between two holes and therefore are not homeomorphic to a disk. However, in the “thermodynamic limit” of many islands per hole, n f ≫ |χ|, the embedding is mostly cellular and is well approximated by Eq. 3.