Bocchio, M. et al. Hippocampal hub neurons maintain distinct connectivity throughout their lifetime. Nat. commun. 11, 4559. https://doi.org/10.1038/s41467-020-18432-6 (2020). Jim Garys's framework ( Hey, 2009) divides the history of science into four paradigms. Since centuries ago, there have been experimental and theoretical paradigms. Then the phenomena of interest became too complicated to be quantified analytically, so the computational paradigms started with the rise of numerical estimations and simulations. Today, with the bursting advances in recording, storage, and computation capacity of neural signals, neuroscience is now exploring the fourth paradigm of Jim Garys's framework ( Hey, 2009) i.e., data exploration in which the scientific models are fit to the data by learning algorithms.

A dynamic model such as the Neural ODE can be incorporated in an encoder-decoder framework, resembling a Variational Auto-Encoder, as mentioned in Chen et al. (2018). Such models assume that latent variables can capture the dynamics of the observed data. Previous works ( Chen et al., 2018; Kanaa et al., 2019; Rubanova et al., 2019; Yildiz et al., 2019) have successfully used this framework to define and train a generative model on time series data. 3.2.2.3. Stochastic Neural ODEs Ferrante, M., Migliore, M. & Ascoli, G. A. Feed-forward inhibition as a buffer of the neuronal input-output relation. Proc. Natl. Acad. Sci. U S A 106(42), 18004–18009. https://doi.org/10.1073/pnas.0904784106 (2009). Pyka, M., Klatt, S. & Cheng, S. Parametric anatomical modeling: A method for modeling the anatomical layout of neurons and their projections. Fr. Neuroanatom 8, 91. https://doi.org/10.3389/fnana.2014.00091 (2014). While the research on hyper-realistic modeling of many neurons continues, other frameworks focus on simulating the biophysics of the population of neurons. In Section 1.3, we pause on the state of large-scale synaptic simulations to show how a change in computational paradigm helps in overcoming some of the limitations inherent in these models. Models of Neural mass and Wilson-Cowan are examples of such alternatives (see Sections 1.3.1, 1.3.2, respectively). 1.3. Population-Level Models Human Connectome Project: a large-scale structural and functional connectivity map of the human brain (coined as connectome in Sporns et al., 2005; Van Essen et al., 2013).

Contact

The different classes of known mouse hippocampal neurons show a high degree of heterogeneity in structural properties. Nonetheless, geometrical constraints based on morpho-anatomical characteristics can be adopted to generate cell morphologies (see " Neuronal Morphology" in " Methods"). By analyzing the morphological features of experimentally reconstructed CA1 neurons obtained from public repositories (see " Methods"), each neuronal subtype was assigned to a unique morphology. All neurons belonging to a specific class were composed of a combination of ellipsoids and cones whose dimensions were randomly chosen within the normal distributions of dendritic and axonal sizes calculated from experimental morphological features (see Table 1-SM). Pyramidal cells Price, C. J. et al. Neurogliaform neurons form a novel inhibitory network in the hippocampal CA1 area. Neuroscience 25(29), 6775–6786. https://doi.org/10.1523/JNEUROSCI.1135-05.2005 (2005). The orientation vectors were selected according to the directionality of the fibers within CA1 thus, the orientations of probability ellipsoids were modelled starting from specific anatomical landmarks. The first constitutive landmark is represented by the relative positioning of each CA1 neuron with respect to other hippocampal regions. The minimum distance vectors between CA1 neurons and CA3 and subiculum structure meshes allowed the construction of transversal planes in correspondence to each cell (Fig. 3). Udvary, D. et al. The impact of neuron morphology on cortical network architecture. Cell Rep. 39, 110677. https://doi.org/10.1016/j.celrep.2022.110677 (2022). Tominaga, T., Tominaga, Y. & Ichikawa, M. J. Optical imaging of long-lasting depolarization on burst stimulation in area CA1 of rat hippocampal slices. J Neurophysiol. 88(3), 1523–1532. https://doi.org/10.1152/jn.2002.88.3.1523 (2002).

The in-degree and out-degree distributions of connections among only pyramidal cells showed the expected shapes (Fig. 7A,B) and the shapes were conserved when inhibitory connections were included in the distributions, albeit the model predicts that the peaks of the in-degree distributions shift to higher values, suggesting a prominent role of inhibitory interneurons as hub neurons (Fig. 7A–C). Network validationScaling compute power does not suffice for leveling up to the whole-brain models. Another challenge is the integration of time delays that become significant at the whole-brain level. In local connections, the time delays are small enough to be ignored ( Jirsa et al., 2010) the transmission happens in a variety of finite speeds from 1 to 10 m per second. As a result of this variation, time delays between different brain parts are no longer negligible. Additional spatial features emerge by the implementation of this heterogeneity ( Jirsa and Kelso, 2000; Petkoski and Jirsa, 2019). Knowles, W. D. & Schwartzkroin, P. A. Axonal ramifications of hippocampal Ca1 pyramidal cells. J. Neurosci. 1(11), 1236–1241. https://doi.org/10.1523/JNEUROSCI.01-11-01236.1981 (1981). DCM is, in fact, a method for testing hypotheses and guiding experiments, not a predictive or generative model by itself. Models of the intra-connected regions can be built based on the earlier subsections, e.g., neural mass model, neural fields, or conductance-based models. For a review of such hybrid approaches, see Moran et al. (2013).

The independence from prior knowledge sounds interesting as it frees the methodology from inductive biases and makes the models more generalizable by definition. However, this virtue comes at the cost of a need for large training sets. In other words, the trade-off of bias and computation should be considered: Applying lots of prior knowledge and inductive biases result in a lesser need for data and computation. In contrast, little to no inductive bias calls for a great need for big and curated data. It is true that with the advancement of recording techniques, the scarcity of data is less of a problem than it was before, but even with all these advances, having clean and sufficiently large medical dataset that helps with the problem in hand is not guaranteed. In this scenario, the advent of High-Performance Computing, coupled with a huge amount of experimental data, boosted the development of extended data-driven spiking neural network models 16, 17, 18, 19. Irrespective of the single cell model employed and the level of electrophysiological detail, the connectivity strategy remains a critical determinant in the construction of networks 20. Glasser, M. F. et al. The human connectome project’s neuroimaging approach. Nat. Neurosci. 19(9), 1175–1187. https://doi.org/10.1038/nn.4361 (2016). Winnubst, J. et al. Reconstruction of 1000 projection neurons reveals new cell types and organization of long-range connectivity in the mouse brain. Cell https://doi.org/10.1016/j.cell.2019.07.042 (2019).Romani, A., Schürmann, F., Markram, H. & Migliore, M. Reconstruction of the Hippocampus. In Computational Modelling of the Brain Advances in Experimental Medicine and Biology Vol. 1359 (eds Giugliano, M. et al.) (Springer, 2022). https://doi.org/10.1007/978-3-030-89439-9_11.

Mahta Ramezanian-Panahi 1,2 * Germán Abrevaya 1,3 Jean-Christophe Gagnon-Audet 1,2 Vikram Voleti 1,2 Irina Rish 1,2 Guillaume Dumas 1,2,4 The 21 st century has been the bursting era of large-scale brain initiatives. The objective of the simulation partly justifies this multitude. As it was previously mentioned, the notion simulation is highly versatile in meaning depending on the goal of the project ( de Garis et al., 2010), i.e., where it sits on the Figure 3. Some of the projects of this spectrum are listed below.Billeh, Y. N. et al. Systematic integration of structural and functional data into multi-scale models of mouse primary visual cortex. Neuron 106(3), 388-403.e18. https://doi.org/10.1016/j.neuron.2020.01.040 (2020). Furthermore, latent ODE models can add another layer of abstraction. The observed data is assumed to be regularly/irregularly sampled from a continuous stream of data, following the dynamics described by a continuously changing hidden state. Both the dynamics of the hidden state and the relationship between the interpolated observations and the hidden state can be described by neural networks. Such systems are called Neural Control Differential Equations (Neural CDE) ( Kidger et al., 2020). Broadly speaking, they are the continuous equivalent of RNNs. 3.2.3. Differential Equations Enhanced by Deep Neural Networks