A solvable model of the genesis of amino-acid sequences via coupled dynamics of folding and slow-genetic variation

Rabello, Silvio; Coolen, A. C. C.; Perez-Vicente, C. J.; Fraternali, Franca

doi:10.1088/1751-8113/41/28/285004

Cited by 9 publications

(11 citation statements)

References 45 publications

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“…One of the strongest starting point when dealing with random coupling is their independence: for example Blake pointed out [28] that exons in haemoglobin correspond both to structural and functional units of protein, implicitly suggesting a not null level of correlation among the "randomness" we have to deal with when trying a statistical mechanics approach. Not too different is the viewpoint of Coolen and coworkers [38] [70].…”

Section: Introduction To Social and Biological Networkmentioning

confidence: 98%

Equilibrium statistical mechanics on correlated random graphs

Barra¹,

Agliari²

2011

J. Stat. Mech.

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Biological and social networks have recently attracted enormous attention between physicists. Among several, two main aspects may be stressed: A non trivial topology of the graph describing the mutual interactions between agents exists and/or, typically, such interactions are essentially (weighted) imitative. Despite such aspects are widely accepted and empirically confirmed, the schemes currently exploited in order to generate the expected topology are based on a-priori assumptions and in most cases still implement constant intensities for links. Here we propose a simple shift [−1, +1] → [0, +1] in the definition of patterns in an Hopfield model to convert frustration into dilution: By varying the bias of the pattern distribution, the network topology -which is generated by the reciprocal affinities among agents (the Hebbian kernel)-crosses various well known regimes (fully connected, linearly diverging connectivity, extreme dilution scenario, no network), coupled with small world properties, which, in this context, are emergent and no longer imposed a-priori. The model is investigated at first focusing on these topological properties of the emergent network, then its thermodynamics is analytically solved (at a replica symmetric level) by extending the double stochastic stability technique, and presented together with its fluctuation theory for a picture of criticality: both a statistical mechanics and a topological phase diagrams are obtained. Overall the picture depicted from statistical mechanics is quite intuitive: at least at equilibrium, dilution (of whatever kind) simply decreases the strength of the coupling felt by the spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main difference with respect to previous investigations and a naive picture is that within our approach replicas do not appear: instead of (multi)-overlaps as order parameters, we introduce a class of magnetizations on all the possible sub-graphs belonging to the main one investigated: As a consequence, for these objects a closure for a self-consistent relation is achieved. 1As we will see, small values of a give rise to highly correlated, diluted networks, while, as a gets larger the network gets more and more connected and correlation among links vanishes.Even though the theory is defined at each finite V and L, as standard in statistical mechanics, we are interested in the large V behavior (such that, under central limit theorem permissions, deviations from averaged values become negligible and the theory predictive). To this task we find meaningful to let even L diverge linearly with the system size (to bridge conceptually to high storage neural networks), such that lim V →∞ L/V = α defines α as another control parameter. Finally, since we are interested in the regime of large V and large L we will often confuse V with V − 1 and L with L − 1. 4

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Section: Introduction To Social and Biological Networkmentioning

confidence: 98%

Equilibrium statistical mechanics on correlated random graphs

Barra¹,

Agliari²

2011

J. Stat. Mech.

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“…• Fact: Antibodies (as any other protein) are not random objects (for instance, randomly generated proteins may not even be able to fold into a stable structure [38]) [39]. Hence, once expressed trough e.g.…”

Section: Methodsmentioning

confidence: 99%

“…As stated in the introduction, despite a certain degree of stochasticity seems to be present even in biological systems, proteins are clearly non-completely random objects [38]: Indeed, the estimated size of the set of self-proteins is much smaller than the one expected from randomly generated sets [39]. Within an information theory context, this means that the entropy of such repertoire is not maximal, that is, within the set S some self-proteins are more likely than others (see Appendix Three).…”

Section: High Connectivity Leads To Anergymentioning

confidence: 99%

Anergy in self-directed B lymphocytes: A statistical mechanics perspective

Agliari

Barra

Ferraro

et al. 2015

Journal of Theoretical Biology

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The ability of the adaptive immune system to discriminate between self and non-self mainly stems from the ontogenic clonal-deletion of lymphocytes expressing strong binding affinity with selfpeptides. However, some self-directed lymphocytes may evade selection and still be harmless due to a mechanism called clonal anergy.As for B lymphocytes, two major explanations for anergy developed over three decades: according to "Varela theory", it stems from a proper orchestration of the whole B-repertoire, in such a way that self-reactive clones, due to intensive interactions and feed-back from other clones, display more inertia to mount a response. On the other hand, according to the 'two-signal model", which has prevailed nowadays, self-reacting cells are not stimulated by helper lymphocytes and the absence of such signaling yields anergy.The first result we present, achieved through disordered statistical mechanics, shows that helper cells do not prompt the activation and proliferation of a certain sub-group of B cells, which turn out to be just those broadly interacting, hence it merges the two approaches as a whole (strictly speaking Varela theory is then included into the two-signal model, not vice-versa).As a second result, we outline a minimal topological architecture for the B-world, where highly connected clones are self-directed as a natural consequence of an ontogenetic learning; this provides a mathematical framework to Varela perspective. As a consequence of these two achievements, clonal deletion and clonal anergy can be seen as two inter-playing aspects of the same phenomenon too.

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“…Let us finally note that the expression (12) in terms of the R-transform, which can be written as a series expansion starting from (11), establishes a relation between the cumulants of the random variable A ii , the diagonal matrix element, or the cumulant of the off-diagonal matrix element A i j and the free cumulant C k of the matrix ensemble under consideration.…”

Section: Applicationsmentioning

confidence: 99%

“…In more detail, Hidden Mattis phases, a particular instance of this, have indeed been discussed long ago (see section 2) in [7,8] and the idea of self-planting due to time evolving disorder has been pointed out more recently in the perceptron model [9]. Slowly varying interactions with applications to physics and biology have also been considered in [10,11]. There is also a closely related computation of Dean and Majumdar [12,13], which involves the large deviations of the lowest eigenvalue of a Gaussian matrix: here we are interested on those towards lower values, the one towards higher values is not relevant here.…”

Section: Introductionmentioning

confidence: 99%

Annealed averages in spin and matrix models

Foini¹,

Kurchan

2022

SciPost Phys.

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A disordered system is denominated `annealed' when the interactions themselves may evolve and adjust their values to lower the free energy. The opposite (`quenched') situation when disorder is fixed, is the one relevant for physical spin-glasses, and has received vastly more attention. Other problems however are more natural in the annealed situation: in this work we discuss examples where annealed averages are interesting, in the context of matrix models. We first discuss how in practice, when system and disorder adapt together, annealed systems develop `planted' solutions spontaneously, as the ones found in the study of inference problems. In the second part, we study the probability distribution of elements of a matrix derived from a rotationally invariant (not necessarily Gaussian) ensemble, a problem that maps into the annealed average of a spin glass model.

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A solvable model of the genesis of amino-acid sequences via coupled dynamics of folding and slow-genetic variation

Cited by 9 publications

References 45 publications

Equilibrium statistical mechanics on correlated random graphs

Equilibrium statistical mechanics on correlated random graphs

Anergy in self-directed B lymphocytes: A statistical mechanics perspective

Annealed averages in spin and matrix models

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