Anergy in self-directed B lymphocytes: A statistical mechanics perspective
Open accessAbstract
Self-directed lymphocytes may evade clonal deletion at ontogenesis but still remain harmless due to a mechanism called clonal anergy. For B-lymphocytes, two major explanations for anergy developed over the last decades: according to Varela theory, anergy stems from a proper orchestration of the whole B-repertoire, such that self-reactive clones, due to intensive feed-back from other clones, display strong inertia when mounting a response. Conversely, according to the model of cognate response, self-reacting cells are not stimulated by helper lymphocytes and the absence of such signaling yields anergy. Through statistical mechanics we show that helpers do not prompt activation of a sub-group of B-cells: remarkably, the latter are just those broadly interacting in the idiotypic network. Hence Varela theory can finally be reabsorbed into the prevailing framework of the cognate response model. Further, we show how the B-repertoire architecture may emerge, where highly connected clones are self-directed as a natural consequence of ontogenetic learning.
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The basic McCulloch-Pitts design is common to many other living systems, including gene regulatory networks, immune networks, collective intelligence or some aneural systems, such as quorum-sensing decisions in microbial communities.
“Interestingly, the basic McCulloch–Pitts design is common to many other living systems, including gene regulatory networks [256–259], immune networks [260–262], collective intelligence [263–267] or some aneural systems, such as quorum-sensing decisions in microbial communities, where an explicit equivalence has been defined [268].”
From Fundamental constraints to the logic of living systems (2024) · cites this paper as [262]
Cites
Computer Simulation of Liquids
Allen, M. P., & Tildesley, D. J. (2017) · doi:10.1093/oso/9780198803195.001.0001 · Cited by 20,945 · see citing works
Neural networks and physical systems with emergent collective computational abilities.
Hopfield, J. J. (1982) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.79.8.2554 · Cited by 19,270 · see citing works
Computer Simulation of Liquids
P, S., & J, K. (1988) · Journal of Molecular Liquids · doi:10.1016/0167-7322(88)80022-9 · Cited by 16,084 · see citing works
Information theory and statistical mechanics
Jaynes, E. T. (1957) · Physical Review · doi:10.1103/physrev.106.620 · Cited by 12,931 · see citing works
Understanding Molecular Simulation
Frenkel, D., Smit, B., Tobochnik, J., McKay, S. R., & Christian, W. (1997) · Computers in Physics · doi:10.1063/1.4822570 · Cited by 5,395 · see citing works
Metabolic stability and epigenesis in randomly constructed genetic nets
Kauffman, S. A. (1969) · Journal of Theoretical Biology · doi:10.1016/0022-5193(69)90015-0 · Cited by 4,871 · see citing works
Spin Glass Theory and Beyond: An Introduction to the Replica Method and Its Applications
Mezard, M., Parisi, G., & Virasoro, M. (1986) · World Scientific Lecture Notes in Physics · doi:10.1142/0271 · Cited by 3,653 · see citing works
Towards a network theory of the immune system.
Nk, J. (1974) · PubMed · Cited by 3,388 · see citing works
Information Theory and Statistical Mechanics. II
Jaynes, E. T. (1957) · Physical Review · doi:10.1103/physrev.108.171 · Cited by 3,253 · see citing works
Mézard, M., Giorgio Parisi, A., VIRASORO, M. A., & Thouless, D. J. (1988) · Physics Today · doi:10.1063/1.2811676 · Cited by 2,683 · see citing works
The clonal selection theory of acquired immunity
Burnet, F. M. (1959) · Vanderbilt University Press eBooks · doi:10.5962/bhl.title.8281 · Cited by 2,645 · see citing works
Amit, D. J. (1989) · Cambridge University Press eBooks · doi:10.1017/cbo9780511623257 · Cited by 2,279 · see citing works
Computing with Neural Circuits: A Model
Hopfield, J. J., & Tank, D. W. (1986) · Science · doi:10.1126/science.3755256 · Cited by 2,107 · see citing works
Predominant Autoantibody Production by Early Human B Cell Precursors
Wardemann, H., Yurasov, S., Schaefer, A., Young, J. W., Meffre, E., & Nussenzweig, M. C. (2003) · Science · doi:10.1126/science.1086907 · Cited by 2,088 · see citing works
Understanding Molecular Simulation
(2002) · doi:10.1016/b978-0-12-267351-1.x5000-7 · Cited by 2,042 · see citing works
Information, Physics, and Computation
Mézard, M., & Andrea Montanari, A. (2009) · doi:10.1093/acprof:oso/9780198570837.001.0001 · Cited by 1,941 · see citing works
Discrete Choice with Social Interactions
Brock, W. A., & Durlauf, S. N. (2001) · The Review of Economic Studies · doi:10.1111/1467-937x.00168 · Cited by 1,645 · see citing works
Schwartz, R. H. (2003) · Annual Review of Immunology · doi:10.1146/annurev.immunol.21.120601.141110 · Cited by 1,487 · see citing works
Mathematical Foundations of Information Theory.
Snell, J. L., Khinchin, A. I., Silverman, R. A., et al. (1959) · American Mathematical Monthly · doi:10.2307/2310044 · Cited by 1,451 · see citing works
Entropy, Large Deviations, and Statistical Mechanics
Ellis, R. S. (1985) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-1-4613-8533-2 · Cited by 1,206 · see citing works
Introduction to Theoretical Neurobiology
Tuckwell, H. C. (1988) · Cambridge University Press eBooks · doi:10.1017/cbo9780511623202 · Cited by 1,174 · see citing works
Entropy, Large Deviations, and Statistical Mechanics
Ellis, R. S. (2006) · Classics in mathematics · doi:10.1007/3-540-29060-5 · Cited by 1,163 · see citing works
Clonal deletion of B lymphocytes in a transgenic mouse bearing anti-MHC class I antibody genes
Nemazee, D. A., & Bürki, K. (1989) · Nature · doi:10.1038/337562a0 · Cited by 1,022 · see citing works
Theory of Financial Risk and Derivative Pricing
Bouchaud, J., & Potters, M. (2003) · Cambridge University Press eBooks · doi:10.1017/cbo9780511753893 · Cited by 879 · see citing works
Random-Energy Model: Limit of a Family of Disordered Models
Derrida, B. (1980) · Physical Review Letters · doi:10.1103/physrevlett.45.79 · Cited by 821 · see citing works
Cellular and genetic mechanisms of self tolerance and autoimmunity
Goodnow, C. C., Sprent, J., Groth, B. F. D. S., & Vinuesa, C. G. (2005) · Nature · doi:10.1038/nature03724 · Cited by 703 · see citing works
Hartley, S. B., Crosbie, J., Brink, R. A., Kantor, A. B., Basten, A., & Goodnow, C. C. (1991) · Nature · doi:10.1038/353765a0 · Cited by 695 · see citing works
Perelson, A. S., & Weisbuch, G. (1997) · Reviews of Modern Physics · doi:10.1103/revmodphys.69.1219 · Cited by 574 · see citing works
Bio-inspired artificial intelligence: theories, methods, and technologies
(2009) · Choice Reviews Online · doi:10.5860/choice.46-4490 · Cited by 498 · see citing works
Control systems and decision making for antibody production
Goodnow, C. C., Vinuesa, C. G., Randall, K. L., Mackay, F., & Brink, R. A. (2010) · Nature Immunology · doi:10.1038/ni.1900 · Cited by 438 · see citing works
High-Throughput Sequencing of the Zebrafish Antibody Repertoire
Weinstein, J. A., Jiang, N. J., White, R. A., III, Fisher, D. S., & Quake, S. R. (2009) · Science · doi:10.1126/science.1170020 · Cited by 432 · see citing works
Allman, D., Ferguson, S. E., Lentz, V. M., & Cancro, M. P. (1993) · The Journal of Immunology · doi:10.4049/jimmunol.151.9.4431 · Cited by 408 · see citing works
Lider, O., Reshef, T., Béraud, E., et al. (1988) · Science · doi:10.1126/science.2447648 · Cited by 397 · see citing works
The molecular basis of antibody formation: a paradox.
Dreyer, W. J., & Bennett, J. (1965) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.54.3.864 · Cited by 392 · see citing works
The cognitive paradigm and the immunological homunculus
Cohen, I. R. (1992) · Immunology Today · doi:10.1016/0167-5699(92)90024-2 · Cited by 379 · see citing works
Perelson, A. S. (1989) · Immunological Reviews · doi:10.1111/j.1600-065x.1989.tb00025.x · Cited by 374 · see citing works
Benedetto, D., Caglioti, E., & Loreto, V. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.048702 · Cited by 359 · see citing works
Transgenic Mice and Analysis of B-Cell Tolerance
Goodnow, C. C. (1992) · Annual Review of Immunology · doi:10.1146/annurev.iy.10.040192.002421 · Cited by 359 · see citing works
The Clonal Selection Theory of Acquired Immunity.
BEAN, W. B. (1960) · Archives of Internal Medicine · doi:10.1001/archinte.1960.00270180151020 · Cited by 340 · see citing works
Second generation immune networks
Varela, F. J., & Coutinho, A. (1991) · Immunology Today · doi:10.1016/s0167-5699(05)80046-5 · Cited by 335 · see citing works
Maximum entropy models for antibody diversity
Mora, T., Walczak, A. M., Bialek, W., & Callan, C. G. (2010) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1001705107 · Cited by 313 · see citing works
Statistical inference of the generation probability of T-cell receptors from sequence repertoires
Murugan, A., Mora, T., Walczak, A. M., & Callan, C. G. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1212755109 · Cited by 292 · see citing works
Melamed, D., Benschop, R. J., Cambier, J. C., & Nemazee, D. A. (1998) · Cell · doi:10.1016/s0092-8674(00)80912-5 · Cited by 232 · see citing works
Natural regulatory T cells and self-tolerance
Schwartz, R. H. (2005) · Nature Immunology · doi:10.1038/ni1184 · Cited by 231 · see citing works
Idiotypic-anti-idiotypic regulation of antibody synthesis in rabbits.
Cazenave, P. (1977) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.74.11.5122 · Cited by 218 · see citing works
The Art of the Probable: System Control in the Adaptive Immune System
Germain, R. N. (2001) · Science · doi:10.1126/science.1062946 · Cited by 215 · see citing works
Urbain, J., Wikler, M., Franssen, J.-D., & Collignon, C. (1977) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.74.11.5126 · Cited by 209 · see citing works
The cognitive principle challenges clonal selection
Cohen, I. R. (1992) · Immunology Today · doi:10.1016/0167-5699(92)90071-e · Cited by 206 · see citing works
How can statistical mechanics contribute to social science?
Durlauf, S. N. (1999) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.96.19.10582 · Cited by 199 · see citing works
Efroni, S., Harel, D., & Cohen, I. R. (2003) · Genome Research · doi:10.1101/gr.1215303 · Cited by 158 · see citing works
A B-cell receptor-specific selection step governs immature to mature B cell differentiation
Levine, M. H., Haberman, A. M., Sant’Angelo, D. B., Hannum, L. G., Cancro, M. P., Janeway, C. A., & Shlomchik, M. J. (2000) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.050552997 · Cited by 154 · see citing works
On the equivalence of Hopfield networks and Boltzmann Machines
Adriano Barra, A., Bernacchia, A., Santucci, E., et al. (2012) · Neural Networks · doi:10.1016/j.neunet.2012.06.003 · Cited by 137 · see citing works
How the thymus designs antigen-specific and self-tolerant T cell receptor sequences
Košmrlj, A., Jha, A., Huseby, E. S., Mehran Kardar, A., & Chakraborty, A. K. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0808081105 · Cited by 136 · see citing works
Evidence for a functional idiotypic network among natural antibodies in normal mice.
Lundkvist, I., Coutinho, A., Varela, F. J., et al. (1989) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.86.13.5074 · Cited by 122 · see citing works
Multitasking Associative Networks
Agliari, E., Adriano Barra, A., Galluzzi, A., Guerra, F., & Moauro, F. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.268101 · Cited by 121 · see citing works
Self-citationReal and artificial immune systems: computing the state of the body
Cohen, I. R. (2007) · Nature reviews. Immunology · doi:10.1038/nri2102 · Cited by 118 · see citing works
The cytokine network and immune functions
Thèze, J. (1999) · Oxford University Press eBooks · Cited by 116 · see citing works
Theory of neural information processing systems
Coolen, A. C. C., Kühn, R., & Peter Sollich, A. (2006) · Choice Reviews Online · doi:10.5860/choice.43-4068 · Cited by 106 · see citing works
A simple model for the immune network.
Parisi, G. (1990) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.87.1.429 · Cited by 104 · see citing works
The idiotypic network in autoimmunity: antibodies that bind antibodies that bind antibodies
Shoenfeld, Y. (2003) · Nature Medicine · doi:10.1038/nm0104-17 · Cited by 96 · see citing works
Bio-inspired artificial intelligence
Floreano, D. (2008) · Cited by 82 · see citing works
Emergent Dynamics of Thymocyte Development and Lineage Determination
Efroni, S., Harel, D., & Cohen, I. R. (2007) · PLoS Computational Biology · doi:10.1371/journal.pcbi.0030013 · Cited by 82 · see citing works
Discriminating self from nonself with short peptides from large proteomes
Burroughs, N. J., de Boer, R. J., & Keşmir, C. (2004) · Immunogenetics · doi:10.1007/s00251-004-0691-0 · Cited by 73 · see citing works
Information, physics, and computation
Kak, S. C. (1996) · Foundations of Physics · doi:10.1007/bf02058892 · Cited by 72 · see citing works
The mathematical theory of minority games : statistical mechanics of interacting agents
Coolen, A. C. C. (2005) · Cited by 68 · see citing works
B-cell tolerance: mechanisms and implications
Basten, A., & Silveira, P. A. (2010) · Current Opinion in Immunology · doi:10.1016/j.coi.2010.08.001 · Cited by 62 · see citing works
Immune networks: multitasking capabilities near saturation
Agliari, E., Annibale, A., Barra, A., Coolen, A. C. C., & Tantari, D. (2013) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/46/41/415003 · Cited by 52 · see citing works
Self-citationBernabé, R. R., Coutinho, A., Cazenave, P., & Forni, L. (1981) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.78.10.6416 · Cited by 52 · see citing works
Stewart, J. R., Varela, F. J., & Coutinho, A. (1989) · Journal of Autoimmunity · doi:10.1016/0896-8411(89)90113-3 · Cited by 47 · see citing works
A Model of the Immune Network with B-T Cell Co-operation. I—Prototypical Structures and Dynamics
Carneiro, J., Coutinho, A., Faro, J., et al. (1996) · Journal of Theoretical Biology · doi:10.1006/jtbi.1996.0192 · Cited by 46 · see citing works
Thymic Selection of T-Cell Receptors as an Extreme Value Problem
Košmrlj, A., Chakraborty, A. K., Mehran Kardar, A., et al. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.068103 · Cited by 46 · see citing works
Immune networks: multitasking capabilities near saturationPreprint
Agliari, E., Annibale, A., Adriano Barra, A., Coolen, A. C. C., & Tantari, D. (2013) · Cited by 44 · see citing works
Self-citationNetwork Theory Analysis of Antibody-Antigen Reactivity Data: The Immune Trees at Birth and Adulthood
Madi, A., Kenett, D. Y., Bransburg‐Zabary, S., et al. (2011) · PLoS ONE · doi:10.1371/journal.pone.0017445 · Cited by 43 · see citing works
Identifying essential genes in Escherichia coli from a metabolic optimization principle
Martelli, C., Martino, A. D., Marinari, E., Matteo Marsili, A., & Castillo, I. P. (2009) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0813229106 · Cited by 41 · see citing works
A thermodynamic perspective of immune capabilities
Agliari, E., Adriano Barra, A., Guerra, F., & Moauro, F. (2011) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2011.07.027 · Cited by 40 · see citing works
Self-citationImmune network theory: a role for parallel distributed processing?
Vertosick, F. T., & Kelly, R. H. (1989) · PubMed · Cited by 38 · see citing works
Statistical Mechanical Concepts in Immunology
Chakraborty, A. K., & Košmrlj, A. (2010) · Annual Review of Physical Chemistry · doi:10.1146/annurev.physchem.59.032607.093537 · Cited by 37 · see citing works
A statistical mechanics approach to autopoietic immune networks
Barra, A., & Agliari, E. (2010) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2010/07/p07004 · Cited by 31 · see citing works
Self-citationImmune networks: multi-tasking capabilities at medium load
Agliari, E., Annibale, A., Adriano Barra, A., Coolen, A. C. C., & Tantari, D. (2013) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/46/33/335101 · Cited by 31 · see citing works
Self-citationA Model of the Immune Network with B-T Cell Co-operation. II—The Simulation of Ontogenesis
Carneiro, J., Coutinho, A., & Stewart, J. R. (1996) · Journal of Theoretical Biology · doi:10.1006/jtbi.1996.0193 · Cited by 28 · see citing works
Stochastic dynamics for idiotypic immune networks
Adriano Barra, A., & Agliari, E. (2010) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2010.09.004 · Cited by 27 · see citing works
Self-citationCoolen, A. C. C. (2005) · Cited by 24 · see citing works
Parallel processing in immune networks
Agliari, E., Adriano Barra, A., Bartolucci, S., Galluzzi, A., Guerra, F., & Moauro, F. (2013) · Physical Review E · doi:10.1103/physreve.87.042701 · Cited by 23 · see citing works
Self-citationPatterns in randomly evolving networks: Idiotypic networks
Brede, M., & Behn, U. (2003) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.67.031920 · Cited by 22 · see citing works
Cell cycle 'check points' T cell anergy
Rudd, C. E. (2006) · Nature Immunology · doi:10.1038/ni1106-1130 · Cited by 17 · see citing works
Architecture of idiotypic networks: Percolation and scaling Behavior
Brede, M., & Behn, U. (2001) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.64.011908 · Cited by 17 · see citing works
Organization and evolution of synthetic idiotypic networks
Agliari, E., Asti, L., Adriano Barra, A., et al. (2012) · Physical Review E · doi:10.1103/physreve.85.051909 · Cited by 12 · see citing works
Self-citationRabello, S., Coolen, A. C. C., Vicente, C. J. P., & Fraternali, F. (2008) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/41/28/285004 · Cited by 12 · see citing works
Randomly evolving idiotypic networks: Structural properties and architecture
Schmidtchen, H., Thüne, M., & Behn, U. (2012) · Physical Review E · doi:10.1103/physreve.86.011930 · Cited by 10 · see citing works
Self-nonself Recognition through B-Cell Antigen Receptor
Kitamura, D. (2008) · Springer eBooks · doi:10.1007/978-4-431-73884-8_4 · Cited by 3 · see citing works
Short peptides sensitize target cells to CTL specific for the MHC class Ib molecule, H2-M3
Dabhi, V. M., & Fischer Lindahl, K. (1998) · European Journal of Immunology · doi:10.1002/(sici)1521-4141(199811)28:11
Flagged first, then by citations
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Towards the development of human immune-system-on-a-chip platforms
Polini, A., del Mercato, L. L., Adriano Barra, A., Zhang, Y. S., Calabi, F., & Gigli, G. (2018) · Drug Discovery Today · doi:10.1016/j.drudis.2018.10.003 · Cited by 98 · see citing works
“Microfluidic systems could also provide experimental tools to validate theoretical models whereby the balance between an effective immune response to foreign antigens and the suppression of autoimmunity depends on the degree of connectivity of the B cell network [65] or on collective decisions by the T cell population…”
BackgroundOrgans on chip approach: a tool to evaluate cancer -immune cells interactions
Biselli, E., Agliari, E., Barra, A., Bertani, F. R., Gerardino, A., De Ninno, A., Mencattini, A., Di Giuseppe, D., Mattei, F., Schiavoni, G., et al. (2017) · Scientific Reports · doi:10.1038/s41598-017-13070-3 · Cited by 91 · see citing works
Self-citationRobustness of weighted networks
Bellingeri, M., & Cassi, D. (2017) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2017.07.020 · Cited by 75 · see citing works
Statistical physics of liquid brains
Piñero, J., & Solé, R. (2019) · Philosophical Transactions of the Royal Society B: Biological Sciences · doi:10.1098/rstb.2018.0376 · Cited by 39 · see citing works
Fundamental constraints to the logic of living systems
Solé, R., Kempes, C. P., Corominas-Murtra, B., De Domenico, M., Kolchinsky, A., Lachmann, M., Libby, E., Saavedra, S., Smith, E., & Wolpert, D. (2024) · Interface Focus · doi:10.1098/rsfs.2024.0010 · Cited by 34 · see citing works
Non-convex Multi-species Hopfield Models
Agliari, E., Migliozzi, D., & Tantari, D. (2018) · Journal of Statistical Physics · doi:10.1007/s10955-018-2098-6 · Cited by 32 · see citing works
“which may have zero entries [33, 34, 35, 36, 37, 38], Gaussian patterns [39, 40, 41, 42, 43], weighted patterns [44].”
BackgroundSelf-citationHierarchical neural networks perform both serial and parallel processing
Agliari, E., Adriano Barra, A., Galluzzi, A., et al. (2015) · Neural Networks · doi:10.1016/j.neunet.2015.02.010 · Cited by 26 · see citing works
Self-citationCentrality metrics and localization in core-periphery networks
Barucca, P., Tantari, D., & Lillo, F. (2016) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2016/02/023401 · Cited by 25 · see citing works
“In particular, centrality is a pivotal topic in network theory because it encompasses all dierent scales in networks: central nodes often play important roles in systems’ growth [2, 3], cascade eects [4], information and epidemic spreading [5].”
BackgroundSelf-citationNotes on stochastic (bio)-logic gates: computing with allosteric cooperativityPreprint
Agliari, E., Altavilla, M., Adriano Barra, A., et al. (2014) · arXiv (Cornell University) · doi:10.1038/srep09415 · Cited by 18 · see citing works
Self-citationBellingeri, M., Lu, Z., Cassi, D., et al. (2018) · Modern Physics Letters B · doi:10.1142/s0217984918500677 · Cited by 18 · see citing works
Retrieving infinite numbers of patterns in a spin-glass model of immune networks
Agliari, E., Annibale, A., Adriano Barra, A., Coolen, A. C. C., & Tantari, D. (2017) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/117/28003 · Cited by 16 · see citing works
Self-citationComplete integrability of information processing by biochemical reactions
Agliari, E., Barra, A., Schiavo, L. D., et al. (2016) · Scientific Reports · doi:10.1038/srep36314 · Cited by 15 · see citing works
Self-citationAgliari, E., Barra, A., Galluzzi, A., et al. (2014) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/48/1/015001 · Cited by 15 · see citing works
“Recently, a generalization of this paradigm, i.e. the multitasking associative network [21], appeared as a candidate mean-field network able to perform spontaneously parallel retrieval [22, 23, 24, 25, 26, 27], that is to retrieve more patterns at once (without falling into spurious states) [28, 29].”
Self-citationAgliari, E., Adriano Barra, A., Galluzzi, A., Guerra, F., Tantari, D., & Tavani, F. (2014) · Cited by 14 · see citing works
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Alemanno, F., Camanzi, L., Manzan, G., et al. (2023) · Applied Mathematics and Computation · doi:10.1016/j.amc.2023.128253 · Cited by 13 · see citing works
Self-citationAgliari, E., Barra, A., & Tirozzi, B. (2019) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/ab02ef · Cited by 13 · see citing works
Self-citationComplete integrability of information processing by biochemical reactions
Agliari, E., Adriano Barra, A., Dello Schiavo, L., et al. (2016) · Northumbria Research Link (Northumbria University) · Cited by 12 · see citing works
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Agliari, E., Adriano Barra, A., Galluzzi, A., et al. (2015) · Physical Review E · doi:10.1103/physreve.91.062807 · Cited by 10 · see citing works
“Another observable closely related to the coupling matrix J is the weighted degree w [11].”
BackgroundSelf-citationAn Evolutionary Game Theory Model of Spontaneous Brain Functioning
Madeo, D., Talarico, A., Pascual‐Leone, Á., Mocenni, C., & Santarnecchi, E. (2017) · Scientific Reports · doi:10.1038/s41598-017-15865-w · Cited by 10 · see citing works
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Landmann, S., Preuss, N., & Behn, U. (2017) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2017.05.004 · Cited by 6 · see citing works
Vitality of Neural Networks under Reoccurring Catastrophic Failures
Sardi, S., Goldental, A., Amir, H., et al. (2016) · Scientific Reports · doi:10.1038/srep31674 · Cited by 5 · see citing works
The role of idiotypic interactions in the adaptive immune system: a belief-propagation approach
Bartolucci, S., Mozeika, A., & Annibale, A. (2016) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2016/08/083402 · Cited by 4 · see citing works
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Agliari, E., Adriano Barra, A., Landolfi, G., Murciano, S., & Perrone, S. (2018) · Complexity · doi:10.1155/2018/7423297 · Cited by 4 · see citing works
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Javarone, M. A., & O’Connor, J. A. (2021) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2021.0282 · Cited by 3 · see citing works
Fine-grained Construction of Semantic Technology Network for Technology Evolution Analysis
Li, X., Song, H., Zhang, X., et al. (2019) · International Conference on Computer Science and Application Engineering (CSAE) · doi:10.1145/3331453.3361638 · Cited by 3 · see citing works
“In immune networks, the weight of the link indicates the amount of exchanging chemical signals between lymphocytes and proteins such as cytokines or antibodies[13,14]; In ecological networks, describing species and trophic interactions among them, link’s weight indicates the amount of energy and material passing among…”
BackgroundIlan, Y. (2025) · Immunology Letters · doi:10.1016/j.imlet.2025.107085 · Cited by 2 · see citing works
Wang, H., & Song, J. (2019) · Symmetry · doi:10.3390/sym11030416 · Cited by 2 · see citing works
Can the Immune System Perform a t-Test?
Faria, B. F., Mostardinha, P., & de Abreu, F. V. (2017) · PLoS ONE · doi:10.1371/journal.pone.0169464 · Cited by 2 · see citing works
“Considerable high quality theoretical work has been done on different formulations, such as self nonself discrimination models [6, 8], idiotypic networks [16, 17], clonal expansion models [22, 23], and models following the danger hypothesis [24].”
BackgroundOu, C. (2016) · Applied Mathematical Modelling · doi:10.1016/j.apm.2016.07.011 · Cited by 1 · see citing works
Ferromagnetic Models for Cooperative Behavior: Revisiting Universality in Complex Phenomena
Agliari, E., Adriano Barra, A., Galluzzi, A., et al. (2014) · Springer INdAM series · doi:10.1007/978-3-319-02657-2_6
Self-citationSepsis and Autoimmune Disease: Pathology, Systems Medicine, and Artificial Intelligence
Jendrek, S. T., Lai, X., Riemekasten, G., Vera, J., Schmeck, B., & Bertrams, W. (2020) · Elsevier eBooks · doi:10.1016/b978-0-12-801238-3.11643-5
Ultrametric identities in glassy models of natural evolution
Agliari, E., Alemanno, F., Aquaro, M., et al. (2023) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/acf101
Self-citation
- Authors
- Agliari, E., Barra, A., Del Ferraro, G., Guerra, F., & Tantari, D.
- Affiliations
- Sapienza University of Rome (IT)
- Venue
- Journal of Theoretical Biology
- Publisher
- Elsevier BV
- Published
- 2015-06
- Volume
- 375
- Pages
- 21-31
- ISSN
- 0022-5193 (ISSN-L)
- OpenAlex
- W2037431582
- Cited by
- 34
- References
- 91
- Citations by year
- 2025: 1 · 2024: 1 · 2023: 2 · 2021: 1 · 2020: 1 · 2019: 4 · 2018: 5 · 2017: 6 · 2016: 6 · 2015: 3 · 2014: 4
- FWCI
- 2.89
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Theoretical Biology (publishedVersion)
- PubMed (publishedVersion)
- KTH Publication Database DiVA (KTH Royal Institute of Technology) (submittedVersion, other-oa)
- Archivio istituzionale della ricerca (Alma Mater Studiorum Università di Bologna) (submittedVersion)
- Florence Research (University of Florence) (submittedVersion)
- IRIS Research product catalog (Sapienza University of Rome) (submittedVersion)
- AIRUS (submittedVersion)
- Scuola Normale Superiore di Pisa (submittedVersion, other-oa)
- Funders
- FIRB (RBFR08EKEV)
- Netadis Project (290038)
- Topics
- Life Sciences › Immunology and Microbiology › Immunology › T-cell and B-cell Immunology
- Physical Sciences › Engineering › Biomedical Engineering › Artificial Immune Systems Applications
- Life Sciences › Immunology and Microbiology › Immunology › Immune Response and Inflammation
- Keywords
- anergy, B cells, clonal deletion, idiotypic network, T helper cells, network connectivity
- MeSH terms
- Algorithms, Epitopes, B-Lymphocytes, Computer Simulation, Enzyme-Linked Immunosorbent Assay, Humans, Immune System, Immune Tolerance, Models, Biological, Stochastic Processes, T-Lymphocytes, Models, Statistical, Clonal Anergy
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