Workshop “White matter, axons, and the role of delays – modeling axonal transmission”
31st Annual Computational Neuroscience Meeting
Thomas R. Knösche, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany, email@example.com
July 19th, 2022, 13:30 – 17:00
The microscopic structure of axons in the brain’s white and grey matter governs the transmission of action potentials, and thereby brain dynamics and information processing. This link can be mechanistically quantified using biologically realistic models of axonal transmission. The single axon is characterized by the velocity of action potentials travelling along it, which depends on numerous microstructural parameters, the most important ones being axon diameter, g-ratio (myelination), node and internode lengths. An entire axon bundle is characterized by a multivariate distribution of these parameters, and may additionally feature ephaptic coupling between axons. Distributed delays as well as synchronizations between the action potentials may result.
The formal characterization of the link between microstructural properties of axons and their transmission behavior is key to the understanding of most functional aspects in the brain, both in health and disease. In this symposium, we present the most recent efforts in modeling axons, axon bundles, as well as the effect of axonal properties on brain functionality.
13:30 – 13:45
„Linking non-invasive characterization of white matter and axonal transmission” (Introduction)
Thomas R. Knösche (MPI for Human Cognitive and Brain Science, Leipzig, Germany)
13:45 – 14:15
„Neuronal Structures Determine the Reliability of Spike Generation and Propagation”
Yunliang Zang (Brandeis University, Waltham, Massachusetts, U.S.A.)
Abstract: Despite cell-to-cell variability, biological neurons still have the striking ability to maintain their key firing properties in the face of unpredictable perturbations and stochastic noise. However, the biological strategies that neurons use to reliably maintain their firing properties remain poorly understood. By using a population of compartment models for the lateral pyloric (LP) neuron in the crab stomatogastric ganglion, we explored how the critical pattern of rebound bursting is preserved when the 14 channel conductances in each model undergo random variations. Simulation results suggest that the rebound bursting pattern can be well maintained in many of the neuron models with different ranges of variations, which argues the existence of manifolds for bursting neurons in the 14-dimension parameter space to make this property insensitive to conductance variations. The rebound bursting pattern is more tolerant of individual channel conductance variations, especially those in the soma and neurites. The degree of soma-axon coupling is critical to the ability of the axon to spike during bursts and consequently determines the size of the manifold that corresponds to the bursting models in the whole parameter space. When the soma-axon coupling deviates from the biological range, the neuronal tolerance of conductance variation is significantly lessened. This work suggests that neurons can still find general strategies to enhance their functional reliability, even when they exhibit significant individual variability.
14:15 – 14:30 Short break
14:30 – 15:00
„Ephaptic coupling between axons in central and peripheral white matter”
Helmut Schmidt (Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic)
Abstract: Axonal connections are widely regarded as faithful transmitters of neuronal signals with fixed delays. We challenge this view by providing computational evidence that ephaptic coupling effects can modulate axonal transmission delays in biologically realistic axon bundles. We base our findings on a computationally efficient spike propagation model that allows us to study the effect of extracellular potentials generated by spike volleys in large axonal fibre bundles.
First, we consider fibre bundles in the peripheral nervous system. We lay out the theoretical basis to describe how the spike in an active axon changes the membrane potential of a passive axon. These insights are then incorporated into the spike propagation model, which is calibrated with a biophysically realistic model. The fully calibrated model is then applied to fibre bundles with a large number of axons and different types of axon diameter distributions. One key insight of this study is that the heterogeneity of the axonal diameters has a dispersive effect, and that a higher level of heterogeneity requires stronger ephaptic coupling to achieve full synchronisation between spikes.
Then we shift the focus on fibre bundles in the central nervous system. We demonstrate that, although the extracellular potentials generated by single spikes are of the order of microvolts, the collective extracellular potential generated by spike volleys can reach several millivolts. Interestingly, the resulting depolarisation of the axonal membranes increases the velocity of spikes, and therefore reduces axonal delays between brain areas. Driving a neural mass model with such spike volleys, we further demonstrate that only ephaptic coupling can explain the reduction of stimulus latencies with increased stimulus intensities, as observed in many psychological experiments.
15:00 – 15:30
„Effects of myelin distribution on axonal conduction”
Afroditi Talidou (University of Ottawa, Canada)
Abstract: The generation and propagation of action potentials in white matter are influenced by a fatty substance, called myelin, wrapping around axons. Myelin is formed by glial cells -- oligodendrocytes -- and allows action potentials to transmit faster and without attenuation. An important feature of myelin is its impact on conduction delays, that is, the time it takes for action potentials to reach their destination. Conduction delays play an important role in brain function due to the dependence of neural communication on spike timing. Thus studying conduction delays is of the utmost importance. Previous studies examining action potential propagation along myelinated axons are based on stereotyped cases based on the assumption that myelin sheaths are periodically located along axons and are thus very symmetric. The question we aim to answer is: do changes in myelin segment distribution, length and thickness, not only along the same axon but also along different axons, influence conduction delays and neural communication across the white matter? We are making a step forward to answer this question and estimate conduction delays and the corresponding conduction velocity in the more general case where myelin sheaths of different longitudinal lengths and widths are randomly distributed along single axons. The lengths of nodes of Ranvier, namely the gaps between two consecutive myelin, will also change. How will this impact the propagation of action potentials? What are other parameters affecting conduction delays? We approach the problem using a mathematical model and provide both computational and mathematical analysis whenever possible.
15:30 – 16:00 Coffee break
16:00 – 16:30
„Impact of axonal delay on receptive field development in a multi-layer network”
Katie Davey (University of Melbourne)
Abstract: The mechanisms underlying how neural plasticity in the visual pathway gives rise to features in the primary visual cortex was provided by Linsker in a seminal, three-paper series. Owing to the complexity of multi-layer models, an implicit assumption in Linsker’s and subsequent papers has been that propagation delay is homogeneous, playing little functional role in neural behaviour. We relax this assumption to examine the impact of distance-dependent axonal propagation delay on neural learning. We show that propagation delay induces low-pass filtering by dispersing arrival times of spikes from presynaptic neurons, providing a natural correlation cancellation mechanism for distal connections. The cut-off frequency decreases as radial propagation delay within a layer increases relative to propagation delay between layers, introducing an upper limit on temporal resolution. Given that the postsynaptic potential acts as a low-pass filter, we show that the effective time constant of each should enable processing of similar scales of temporal information. This has implications for the visual system, in which receptive field size and, thus, propagation delay, increases with eccentricity. Furthermore, network response is frequency dependent since higher frequencies require increased input amplitude to compensate for attenuation. This concords with frequency-dependent contrast sensitivity.
16:30 – 17:00
„A mathematical model of ephaptic interactions in neuronal fiber pathways”
Hiba Sheheitli (Aix-Marseille Université, France)
Abstract: While numerous studies of ephaptic interactions have focused on either axons of peripheral nerves or on cortical structures, no attention has been given to the possibility of ephaptic interactions in white matter tracts. Inspired by the highly organized, tightly packed geometry of axons in fiber pathways, we investigate the potential effects of ephaptic interactions along these structures that are resilient to experimental probing. We derive a minimal model of a sheet of N ephaptically coupled axons and demonstrate that ephaptic interactions can lead to local phase locking between adjacent traveling impulses, such as traveling impulses, and can possibly trigger new impulses along adjacent axons, resulting in finite size traveling fronts. For strong enough coupling, complex spatiotemporal patterns of activity emerge. This calls for a careful examination of assumptions behind modeling fiber pathways as simple relays of signals between different brain regions in large-scale brain network models; brain fiber tracts can instead act as a dynamic active medium in the presence of significant ephaptic interactions.