A study of cortical network models with realistic connectivity
- Autores: Marina Vegué Llorente
- Directores de la Tesis: Alexander Roxin (dir. tes.)
- Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2018
- Idioma: español
- Tribunal Calificador de la Tesis: Jaime de la Rocha Vázquez (presid.), Gemma Huguet Casades (secret.), Srdjan Ostojic (voc.)
- Programa de doctorado: Programa de Doctorado en Matemática Aplicada por la Universidad Politécnica de Catalunya
- Materias:
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- Resumen
Structure is fundamental in shaping the types of computations that neuronal circuits can perform. Explaining the laws that determine the connectivity properties of brain networks and their implications in neuronal dynamics is therefore an important step in the understanding of how brains operate. The local circuits of cortex, which are considered to carry out the basic and essential computations for brain functioning, exhibit a highly stereotyped and organized architecture, which is, in very general terms, conserved across different species, brain areas and individuals. An appropriate way to mathematically represent this family of networks is by means of models defined by a set of connectivity laws that include a certain degree of randomness. These laws reflect the common structural scaffold, whereas the randomness should be interpreted as the variability across the different networks in the ensemble. There is growing experimental evidence that the local circuits of cerebral cortex are far from the simplest random model, according to which connections appear independently with a fixed probability. This evidence is based on a set of observed features that have been collectively called the "nonrandomness" of the cortical circuitry. In this thesis we have explored to what extent several alternative architectures (clustered networks, networks with distance-dependent connectivity and networks that exhibit a given in/out-degree distribution) could be compatible with the reported nonrandom features. We showed that all these structural models can explain the experimental observations, which implies that these nonrandom properties do not provide much information about the underlying organization. This is mainly due to the fact that real data are collected from sparse neuronal samples due to experimental limitations. We sought a local measure that can nevertheless help to distinguish between different alternatives, and we found it in the "sample degree correlation" (SDC), or the correlation coefficient between in- and out-degrees in small groups of neurons. The analysis of the SDC in real data suggests that cortical microcircuits are heterogeneous in structure and possibly shaped through a mixture of distance-dependent and non-symmetrical organizational principles. We finally explored some of the dynamical consequences of imposing a heterogeneous structure in models of neuronal activity. This heterogeneity appears through an arbitrary joint in/out-degree distribution in the entire network. By means of both mean-field approximations and spectral analysis, we demonstrate that broad and positively correlated degree distributions can have an important effect on neuronal dynamics, which suggests that this particular type of structural heterogeneity might allow for richer network computations as compared to standard random models.
