Anergy in self-directed B lymphocytes from a statistical mechanics perspective

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 self-peptides. 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 (in particular, Varela theory is then contained into the two-signal model). 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

Meta-stable states in the hierarchical Dyson model drive parallel processing in the hierarchical Hopfield network

In this paper we introduce and investigate the statistical mechanics of hierarchical neural networks: First, we approach these systems \`a la Mattis, by thinking at the Dyson model as a single-pattern hierarchical neural network and we discuss the stability of different retrievable states as predicted by the related self-consistencies obtained from a mean-field bound and from a bound that bypasses the mean-field limitation. The latter is worked out by properly reabsorbing fluctuations of the magnetization related to higher levels of the hierarchy into effective fields for the lower levels. Remarkably, mixing Amit's ansatz technique (to select candidate retrievable states) with the interpolation procedure (to solve for the free energy of these states) we prove that (due to gauge symmetry) the Dyson model accomplishes both serial and parallel processing. One step forward, we extend this scenario toward multiple stored patterns by implementing the Hebb prescription for learning within the couplings. This results in an Hopfield-like networks constrained on a hierarchical topology, for which, restricting to the low storage regime (where the number of patterns grows at most logarithmical with the amount of neurons), we prove the existence of the thermodynamic limit for the free energy and we give an explicit expression of its mean field bound and of the related improved boun

Topological properties of hierarchical networks

Hierarchical networks are attracting a renewal interest for modelling the organization of a number of biological systems and for tackling the complexity of statistical mechanical models beyond mean-field limitations. Here we consider the Dyson hierarchical construction for ferromagnets, neural networks and spin-glasses, recently analyzed from a statistical-mechanics perspective, and we focus on the topological properties of the underlying structures. In particular, we find that such structures are weighted graphs that exhibit high degree of clustering and of modularity, with small spectral gap; the robustness of such features with respect to link removal is also studied. These outcomes are then discussed and related to the statistical mechanics scenario in full consistency. Lastly, we look at these weighted graphs as Markov chains and we show that in the limit of infinite size, the emergence of ergodicity breakdown for the stochastic process mirrors the emergence of meta-stabilities in the corresponding statistical mechanical analysis

Hierarchical neural networks perform both serial and parallel processing

In this work we study a Hebbian neural network, where neurons are arranged according to a hierarchical architecture such that their couplings scale with their reciprocal distance. As a full statistical mechanics solution is not yet available, after a streamlined introduction to the state of the art via that route, the problem is consistently approached through signal- to-noise technique and extensive numerical simulations. Focusing on the low-storage regime, where the amount of stored patterns grows at most logarithmical with the system size, we prove that these non-mean-field Hopfield-like networks display a richer phase diagram than their classical counterparts. In particular, these networks are able to perform serial processing (i.e. retrieve one pattern at a time through a complete rearrangement of the whole ensemble of neurons) as well as parallel processing (i.e. retrieve several patterns simultaneously, delegating the management of diff erent patterns to diverse communities that build network). The tune between the two regimes is given by the rate of the coupling decay and by the level of noise affecting the system. The price to pay for those remarkable capabilities lies in a network's capacity smaller than the mean field counterpart, thus yielding a new budget principle: the wider the multitasking capabilities, the lower the network load and viceversa. This may have important implications in our understanding of biological complexity

From Dyson to Hopfield: Processing on hierarchical networks

We consider statistical-mechanical models for spin systems built on hierarchical structures, which provide a simple example of non-mean-field framework. We show that the coupling decay with spin distance can give rise to peculiar features and phase diagrams much richer that their mean-field counterpart. In particular, we consider the Dyson model, mimicking ferromagnetism in lattices, and we prove the existence of a number of meta-stabilities, beyond the ordered state, which get stable in the thermodynamic limit. Such a feature is retained when the hierarchical structure is coupled with the Hebb rule for learning, hence mimicking the modular architecture of neurons, and gives rise to an associative network able to perform both as a serial processor as well as a parallel processor, depending crucially on the external stimuli and on the rate of interaction decay with distance; however, those emergent multitasking features reduce the network capacity with respect to the mean-field counterpart. The analysis is accomplished through statistical mechanics, graph theory, signal-to-noise technique and numerical simulations in full consistency. Our results shed light on the biological complexity shown by real networks, and suggest future directions for understanding more realistic models

Vacuolar Localization via the N-terminal Domain of Sch9 is Required for TORC1-dependent Phosphorylation and Downstream Signal Transduction

The budding yeast Sch9 kinase (functional orthologue of the mammalian S6 kinase) is a major effector of the Target of Rapamycin Complex 1 (TORC1) complex in the regulation of cell growth in response to nutrient availability and stress. Sch9 is partially localized at the vacuolar surface, where it is phosphorylated by TORC1. The recruitment of Sch9 on the vacuole is mediated by direct interaction between phospholipids of the vacuolar membrane and the region of Sch9 encompassing amino acid residues 1-390, which contains a C2 domain. Since many C2 domains mediate phospholipid binding, it had been suggested that the C2 domain of Sch9 mediates its vacuolar recruitment. However, the in vivo requirement of the C2 domain for Sch9 localization had not been demonstrated, and the phenotypic consequences of Sch9 delocalization remained unknown. Here, by examining cellular localization, phosphorylation state and growth phenotypes of Sch9 truncation mutants, we show that deletion of the N-terminal domain of Sch9 (aa 1-182), but not the C2 domain (aa 183-399), impairs vacuolar localization and TORC1-dependent phosphorylation of Sch9, while causing growth defects similar to those observed in sch9Δ cells. These defects can be reversed either via artificial tethering of the protein to the vacuole, or by introducing phosphomimetic mutations at the TORC1 target sites, suggesting that Sch9 localization on the vacuole is needed for the TORC1-dependent activation of the kinase. Our study uncovers a key role for the N-terminal domain of Sch9 and provides new mechanistic insight into the regulation of a major TORC1 signaling branch

Multi-species mean-field spin-glasses. Rigorous results

We study a multi-species spin glass system where the density of each species is kept fixed at increasing volumes. The model reduces to the Sherrington-Kirkpatrick one for the single species case. The existence of the thermodynamic limit is proved for all densities values under a convexity condition on the interaction. The thermodynamic properties of the model are investigated and the annealed, the replica symmetric and the replica symmetry breaking bounds are proved using Guerra's scheme. The annealed approximation is proved to be exact under a high temperature condition. We show that the replica symmetric solution has negative entropy at low temperatures. We study the properties of a suitably defined replica symmetry breaking solution and we optimise it within a ziggurat ansatz. The generalized order parameter is described by a Parisi-like partial differential equation.Comment: 17 pages, to appear in Annales Henri Poincar\`

Effect of biofilm removal from the occlusal tooth surfaces on fluorescence measurements. A clinical study

Aim: Early diagnosis and monitoring of caries lesions are the most important issues of primary and secondary prevention policies.The intraoral VistaCamiX(DurrDental, Bietigheim‐Bissingen,Germany) uses the fluorescence phenomenon for a non‐invasive, quantitative caries diagnosis. In order to make a precise evaluation the tooth surface must be completely cleaned and without biofilm. The current study aimed to evaluate the effects of biofilm removal, using air‐polishing device (Combi,MectronSpA) with glycine, on fluorescence VistaCam iX camera quantitative measurements of caries. Methods: Patients with complete permanent dentition without any kind of restorative treatments in the lateral and posterior section of upper and lower dental arches were enrolled. The occlusal surfaces of molars and premolars were photographed using the fluorescence terminal Proof of the intraoral camera VistaCam iX before and after air polishing glycine procedures, registering the highest value gained for each occlusal surface. Results:133cuspidate permanent teeth of patients aged between 13 and 25 were analyzed. Descriptive analysis showed an average of 0.82 (SD=0.65; Min=0.00; Max=1.80; Median=1.20) and of 0.93 (SD=0.60; Min=0.00; Max=1.70; Median=1.20) for values before and after treatment, respectively.The scores assigned by VistaCam iX Proof fluorescence based camera to the occlusal surfaces, after the air‐polishing treatment, are averagely higher than those before treatment, especially in the diagnosis of initial tooth decay. Conclusion: Biofilm removal with glycine air‐polishing improves the VistaCam camera accuracy in recognizing healthy tissue from the decayed one, due to the fact that air-polishing treatment increases the decayed tissue reaction to the fluorescence