Organization and evolution of synthetic idiotypic networks

Agliari, Elena; Asti, Lorenzo; Barra, Adriano; Ferrucci, Luca

doi:10.1103/physreve.85.051909

Cited by 15 publications

(34 citation statements)

References 54 publications

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“…We refer to the excellent books [29,30] for comprehensive reviews of the immune system, and to a selection of papers [2,3,4,23,24,31] for theoretical modeling inspired by biological reality. Our prime interest is in B-cells and in T-cells; in particular, among T-cells, in the subgroups of so-called 'helpers' and 'suppressors'.…”

Section: The Underlying Biologymentioning

confidence: 99%

Immune networks: multitasking capabilities near saturation

Agliari

Annibale

Barra

et al. 2013

J. Phys. A: Math. Theor.

120

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Abstract. Pattern-diluted associative networks were introduced recently as models for the immune system, with nodes representing T-lymphocytes and stored patterns representing signalling protocols between T-and B-lymphocytes. It was shown earlier that in the regime of extreme pattern dilution, a system with N T Tlymphocytes can manage a number N B = O(N δ T ) of B-lymphocytes simultaneously, with δ < 1. Here we study this model in the extensive load regime N B = αN T , with also a high degree of pattern dilution, in agreement with immunological findings. We use graph theory and statistical mechanical analysis based on replica methods to show that in the finite-connectivity regime, where each T-lymphocyte interacts with a finite number of B-lymphocytes as N T → ∞, the T-lymphocytes can coordinate effective immune responses to an extensive number of distinct antigen invasions in parallel. As α increases, the system eventually undergoes a second order transition to a phase with clonal cross-talk interference, where the system's performance degrades gracefully. Mathematically, the model is equivalent to a spin system on a finitely connected graph with many short loops, so one would expect the available analytical methods, which all assume locally tree-like graphs, to fail. Yet it turns out to be solvable. Our results are supported by numerical simulations.

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Section: The Underlying Biologymentioning

confidence: 99%

Immune networks: multitasking capabilities near saturation

Agliari

Annibale

Barra

et al. 2013

J. Phys. A: Math. Theor.

120

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“…This is a crucial point because, once implemented the Hebbian prescription to account for multiple pattern storage, it allows proving that the system not only executes extensive serial processingà la Hopfield, but its communities perform autonomously, hence making parallel retrieval feasible too. We stress that this feature is essentially due to the notion of metric the system is endowed with, differently from the parallel retrieval performed by the mean-field multitasking networks which require blank pattern entries [10,11].…”

mentioning

confidence: 99%

“…performing serial processing) [8,9] neither multitasking ones (i.e. performing parallel processing) [10,11]. In fact, these models are intrinsically mean-field, thus lacking a proper definition of metric distance among neurons.…”

mentioning

confidence: 99%

Retrieval Capabilities of Hierarchical Networks: From Dyson to Hopfield

Agliari¹,

Barra²,

Galluzzi³

et al. 2015

Phys. Rev. Lett.

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We consider statistical-mechanics 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.PACS numbers: 07.05. Mh, In the last decade, extensive research on complexity in networks has evidenced (among many results [1, 2]) the widespread of modular structures and the importance of quasi-independent communities in many research areas such as neuroscience [3,4], biochemistry [5] and genetics [6], just to cite a few. In particular, the modular, hierarchical architecture of cortical neural networks has nowadays been analyzed in depths [7], yet the beauty revealed by this investigation is not captured by the statistical mechanics of neural networks, nor standard ones (i.e. performing serial processing) [8,9] neither multitasking ones (i.e. performing parallel processing) [10,11]. In fact, these models are intrinsically mean-field, thus lacking a proper definition of metric distance among neurons.Hierarchical structures have been proposed in the past as (relatively) simple models for ferromagnetic transitions beyond the mean-field scenario -the Dyson hierarchical model (DHM) [12]-and are currently experiencing a renewal interest for understanding glass transitions in finite dimension [13,14]. Therefore, times are finally ripe for approaching neural networks embedded in a nonmean-field architecture, and this letter summarizes our findings on associative neural networks where the Hebbian kernel is coupled with the Dyson topology.First, we start studying the DHM mixing the AmitGutfreund-Sompolinsky ansatz approach [9] (to select candidable retrievable states) with the interpolation technique (to check their thermodynamic stability) and we show that, as soon as ergodicity is broken, beyond the ferromagnetic/pure state (largely discussed in the past, see e.g., [15,16]), a number of metastable states suddenly appear and become stable in the ...

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“…to measure the complementarity between two bit-strings Ψ µ , Ψ ν , and introduce a phenomenological coupling (whose details will be deepened in Sec. IV, see also [3,48])…”

Section: Preliminary Remarks On the Structure Of The B-networkmentioning

confidence: 88%

“…Finally, it is worth considering how W is distributed as this provides information about the occurrence of inertial nodes in the system. Exploiting the fact that couplings J µν are log-normally distributed [48], one can approximate the distribution P (W ) as…”

Section: Preliminary Remarks On the Structure Of The B-networkmentioning

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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Organization and evolution of synthetic idiotypic networks

Cited by 15 publications

References 54 publications

Immune networks: multitasking capabilities near saturation

Immune networks: multitasking capabilities near saturation

Retrieval Capabilities of Hierarchical Networks: From Dyson to Hopfield

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

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