Parameter estimation for connectome generative models: Accuracy, reliability, and a fast parameter fitting method

A generative model of the connectome with dynamic axon growth

Connectome generative models, otherwise known as generative network models, provide insight into the wiring principles underpinning brain network organization. While these models can approximate numerous statistical properties of empirical networks, they typically fail to explicitly characterize an important contributor to brain organization-axonal growth. Emulating the chemoaffinity-guided axonal growth, we provide a novel generative model in which axons dynamically steer the direction of propagation based on distance-dependent chemoattractive forces acting on their growth cones. This simple dynamic growth mechanism, despite being solely geometry-dependent, is shown to generate axonal fiber bundles with brain-like geometry and features of complex network architecture consistent with the human brain, including lognormally distributed connectivity weights, scale-free nodal degrees, small-worldness, and modularity. We demonstrate that our model parameters can be fitted to individual connectomes, enabling connectome dimensionality reduction and comparison of parameters between groups. Our work offers an opportunity to bridge studies of axon guidance and connectome development, providing new avenues for understanding neural development from a computational perspective.

Geometric Scaling Law in Real Neuronal Networks

We investigate the synapse-resolution connectomes of fruit flies across different developmental stages, revealing a consistent scaling law in neuronal connection probability relative to spatial distance. This power-law behavior significantly differs from the exponential distance rule previously observed in coarse-grained brain networks. We demonstrate that the geometric scaling law carries functional significance, aligning with the maximum entropy of information communication and the functional criticality balancing integration and segregation. Perturbing either the empirical probability model's parameters or its type results in the loss of these advantageous properties. Furthermore, we derive an explicit quantitative predictor for neuronal connectivity, incorporating only interneuronal distance and neurons' in and out degrees. Our findings establish a direct link between brain geometry and topology, shedding lights on the understanding of how the brain operates optimally within its confined space.

A generative model of the connectome with dynamic axon growth

Connectome generative models, otherwise known as generative network models, provide insight into the wiring principles underpinning brain network organization. While these models can approximate numerous statistical properties of empirical networks, they typically fail to explicitly characterize an important contributor to brain organization - axonal growth. Emulating the chemoaffinity guided axonal growth, we provide a novel generative model in which axons dynamically steer the direction of propagation based on distance-dependent chemoattractive forces acting on their growth cones. This simple dynamic growth mechanism, despite being solely geometry-dependent, is shown to generate axonal fiber bundles with brain-like geometry and features of complex network architecture consistent with the human brain, including lognormally distributed connectivity weights, scale-free nodal degrees, small-worldness, and modularity. We demonstrate that our model parameters can be fitted to individual connectomes, enabling connectome dimensionality reduction and comparison of parameters between groups. Our work offers an opportunity to bridge studies of axon guidance and connectome development, providing new avenues for understanding neural development from a computational perspective.

The adaptive stochasticity hypothesis: Modeling equifinality, multifinality, and adaptation to adversity

Neural phenotypes are the result of probabilistic developmental processes. This means that stochasticity is an intrinsic aspect of the brain as it self-organizes over a protracted period. In other words, while both genomic and environmental factors shape the developing nervous system, another significant-though often neglected-contributor is the randomness introduced by probability distributions. Using generative modeling of brain networks, we provide a framework for probing the contribution of stochasticity to neurodevelopmental diversity. To mimic the prenatal scaffold of brain structure set by activity-independent mechanisms, we start our simulations from the medio-posterior neonatal rich club (Developing Human Connectome Project, n = 630). From this initial starting point, models implementing Hebbian-like wiring processes generate variable yet consistently plausible brain network topologies. By analyzing repeated runs of the generative process (>107 simulations), we identify critical determinants and effects of stochasticity. Namely, we find that stochastic variation has a greater impact on brain organization when networks develop under weaker constraints. This heightened stochasticity makes brain networks more robust to random and targeted attacks, but more often results in non-normative phenotypic outcomes. To test our framework empirically, we evaluated whether stochasticity varies according to the experience of early-life deprivation using a cohort of neurodiverse children (Centre for Attention, Learning and Memory; n = 357). We show that low-socioeconomic status predicts more stochastic brain wiring. We conclude that stochasticity may be an unappreciated contributor to relevant developmental outcomes and make specific predictions for future research.

Simulation-based inference for efficient identification of generative models in computational connectomics

Recent advances in connectomics research enable the acquisition of increasing amounts of data about the connectivity patterns of neurons. How can we use this wealth of data to efficiently derive and test hypotheses about the principles underlying these patterns? A common approach is to simulate neuronal networks using a hypothesized wiring rule in a generative model and to compare the resulting synthetic data with empirical data. However, most wiring rules have at least some free parameters, and identifying parameters that reproduce empirical data can be challenging as it often requires manual parameter tuning. Here, we propose to use simulation-based Bayesian inference (SBI) to address this challenge. Rather than optimizing a fixed wiring rule to fit the empirical data, SBI considers many parametrizations of a rule and performs Bayesian inference to identify the parameters that are compatible with the data. It uses simulated data from multiple candidate wiring rule parameters and relies on machine learning methods to estimate a probability distribution (the 'posterior distribution over parameters conditioned on the data') that characterizes all data-compatible parameters. We demonstrate how to apply SBI in computational connectomics by inferring the parameters of wiring rules in an in silico model of the rat barrel cortex, given in vivo connectivity measurements. SBI identifies a wide range of wiring rule parameters that reproduce the measurements. We show how access to the posterior distribution over all data-compatible parameters allows us to analyze their relationship, revealing biologically plausible parameter interactions and enabling experimentally testable predictions. We further show how SBI can be applied to wiring rules at different spatial scales to quantitatively rule out invalid wiring hypotheses. Our approach is applicable to a wide range of generative models used in connectomics, providing a quantitative and efficient way to constrain model parameters with empirical connectivity data.

Early adversity changes the economic conditions of mouse structural brain network organization

Early adversity can change educational, cognitive, and mental health outcomes. However, the neural processes through which early adversity exerts these effects remain largely unknown. We used generative network modeling of the mouse connectome to test whether unpredictable postnatal stress shifts the constraints that govern the organization of the structural connectome. A model that trades off the wiring cost of long-distance connections with topological homophily (i.e., links between regions with shared neighbors) generated simulations that successfully replicate the rodent connectome. The imposition of early life adversity shifted the best-performing parameter combinations toward zero, heightening the stochastic nature of the generative process. Put simply, unpredictable postnatal stress changes the economic constraints that reproduce rodent connectome organization, introducing greater randomness into the development of the simulations. While this change may constrain the development of cognitive abilities, it could also reflect an adaptive mechanism that facilitates effective responses to future challenges.