skip to main content

Title: A case study in the functional consequences of scaling the sizes of realistic cortical models.
Neuroscience models come in a wide range of scales and specificity, from mean-field rate models to large-scale networks of spiking neurons. There are potential trade-offs between simplicity and realism, versatility and computational speed. This paper is about large-scale cortical network models, and the question we address is one of scalability: would scaling down cell density impact a network’s ability to reproduce cortical dynamics and function? We investigated this problem using a previously constructed realistic model of the monkey visual cortex that is true to size. Reducing cell density gradually up to 50-fold, we studied changes in model behavior. Size reduction without parameter adjustment was catastrophic. Surprisingly, relatively minor compensation in synaptic weights guided by a theoretical algo- rithm restored mean firing rates and basic function such as orientation selectivity to models 10-20 times smaller than the real cortex. Not all was normal in the reduced model cortices: intracellular dynamics acquired a character different from that of real neurons, and while the ability to relay feedforward inputs remained intact, reduced models showed signs of defi- ciency in functions that required dynamical interaction among cortical neurons. These findings are not confined to models of the visual cortex, and modelers should be aware more » of potential issues that accompany size reduction. Broader implications of this study include the importance of homeostatic maintenance of firing rates, and the functional consequences of feedforward versus recurrent dynamics, ideas that may shed light on other species and on systems suffering cell loss. « less
; ; ;
Tao, L
Award ID(s):
Publication Date:
Journal Name:
PLoS computational biology
Page Range or eLocation-ID:
Sponsoring Org:
National Science Foundation
More Like this
  1. Rubin, Jonathan (Ed.)
    Constraining the many biological parameters that govern cortical dynamics is computationally and conceptually difficult because of the curse of dimensionality. This paper addresses these challenges by proposing (1) a novel data-informed mean-field (MF) approach to efficiently map the parameter space of network models; and (2) an organizing principle for studying parameter space that enables the extraction biologically meaningful relations from this high-dimensional data. We illustrate these ideas using a large-scale network model of the Macaque primary visual cortex. Of the 10-20 model parameters, we identify 7 that are especially poorly constrained, and use the MF algorithm in (1) to discover the firing rate contours in this 7D parameter cube. Defining a “biologically plausible” region to consist of parameters that exhibit spontaneous Excitatory and Inhibitory firing rates compatible with experimental values, we find that this region is a slightly thickened codimension-1 submanifold. An implication of this finding is that while plausible regimes depend sensitively on parameters, they are also robust and flexible provided one compensates appropriately when parameters are varied. Our organizing principle for conceptualizing parameter dependence is to focus on certain 2D parameter planes that govern lateral inhibition: Intersecting these planes with the biologically plausible region leads to very simplemore »geometric structures which, when suitably scaled, have a universal character independent of where the intersections are taken. In addition to elucidating the geometry of the plausible region, this invariance suggests useful approximate scaling relations. Our study offers, for the first time, a complete characterization of the set of all biologically plausible parameters for a detailed cortical model, which has been out of reach due to the high dimensionality of parameter space.« less
  2. Abstract Neurons in the association cortices are particularly vulnerable in cognitive disorders such as schizophrenia and Alzheimer’s disease, while those in primary visual cortex remain relatively resilient. This review proposes that the special molecular mechanisms needed for higher cognitive operations confer vulnerability to dysfunction, atrophy, and neurodegeneration when regulation is lost due to genetic and/or environmental insults. Accumulating data suggest that higher cortical circuits rely on magnified levels of calcium (from NMDAR, calcium channels, and/or internal release from the smooth endoplasmic reticulum) near the postsynaptic density to promote the persistent firing needed to maintain, manipulate, and store information without “bottom-up” sensory stimulation. For example, dendritic spines in the primate dorsolateral prefrontal cortex (dlPFC) express the molecular machinery for feedforward, cAMP–PKA–calcium signaling. PKA can drive internal calcium release and promote calcium flow through NMDAR and calcium channels, while in turn, calcium activates adenylyl cyclases to produce more cAMP–PKA signaling. Excessive levels of cAMP–calcium signaling can have a number of detrimental effects: for example, opening nearby K + channels to weaken synaptic efficacy and reduce neuronal firing, and over a longer timeframe, driving calcium overload of mitochondria to induce inflammation and dendritic atrophy. Thus, calcium–cAMP signaling must be tightly regulated, e.g., bymore »agents that catabolize cAMP or inhibit its production (PDE4, mGluR3), and by proteins that bind calcium in the cytosol (calbindin). Many genetic or inflammatory insults early in life weaken the regulation of calcium–cAMP signaling and are associated with increased risk of schizophrenia (e.g., GRM3 ). Age-related loss of regulatory proteins which result in elevated calcium–cAMP signaling over a long lifespan can additionally drive tau phosphorylation, amyloid pathology, and neurodegeneration, especially when protective calcium binding proteins are lost from the cytosol. Thus, the “genie” we need for our remarkable cognitive abilities may make us vulnerable to cognitive disorders when we lose essential regulation.« less
  3. Manto, Mario (Ed.)
    Background Cerebellar electrical stimulation has shown promise in improving motor recovery post-stroke in both rodent and human studies. Past studies have used motor evoked potentials (MEPs) to evaluate how cerebellar stimulation modulates ongoing activity in the cortex, but the underlying mechanisms are incompletely understood. Here we used invasive electrophysiological recordings from the intact and stroke-injured rodent primary motor cortex (M1) to assess how epidural cerebellar stimulation modulates neural dynamics at the level of single neurons as well as at the level of mesoscale dynamics. Methods We recorded single unit spiking and local field potentials (LFPs) in both the intact and acutely stroke-injured M1 contralateral to the stimulated cerebellum in adult Long-Evans rats under anesthesia. We analyzed changes in the firing rates of single units, the extent of synchronous spiking and power spectral density (PSD) changes in LFPs during and post-stimulation. Results Our results show that post-stimulation, the firing rates of a majority of M1 neurons changed significantly with respect to their baseline rates. These firing rate changes were diverse in character, as the firing rate of some neurons increased while others decreased. Additionally, these changes started to set in during stimulation. Furthermore, cross-correlation analysis showed a significant increase in coincidentmore »firing amongst neuronal pairs. Interestingly, this increase in synchrony was unrelated to the direction of firing rate change. We also found that neuronal ensembles derived through principal component analysis were more active post-stimulation. Lastly, these changes occurred without a significant change in the overall spectral power of LFPs post-stimulation. Conclusions Our results show that cerebellar stimulation caused significant, long-lasting changes in the activity patterns of M1 neurons by altering firing rates, boosting neural synchrony and increasing neuronal assemblies’ activation strength. Our study provides evidence that cerebellar stimulation can directly modulate cortical dynamics. Since these results are present in the perilesional cortex, our data might also help explain the facilitatory effects of cerebellar stimulation post-stroke.« less
  4. Dendritic spikes in thin dendritic branches (basal and oblique dendrites) are traditionally inferred from spikelets measured in the cell body. Here, we used laser-spot voltage-sensitive dye imaging in cortical pyramidal neurons (rat brain slices) to investigate the voltage waveforms of dendritic potentials occurring in response to spatially restricted glutamatergic inputs. Local dendritic potentials lasted 200–500 ms and propagated to the cell body, where they caused sustained 10- to 20-mV depolarizations. Plateau potentials propagating from dendrite to soma and action potentials propagating from soma to dendrite created complex voltage waveforms in the middle of the thin basal dendrite, comprised of local sodium spikelets, local plateau potentials, and backpropagating action potentials, superimposed on each other. Our model replicated these voltage waveforms across a gradient of glutamatergic stimulation intensities. The model then predicted that somatic input resistance ( R in ) and membrane time constant (tau) may be reduced during dendritic plateau potential. We then tested these model predictions in real neurons and found that the model correctly predicted the direction of R in and tau change but not the magnitude. In summary, dendritic plateau potentials occurring in basal and oblique branches put pyramidal neurons into an activated neuronal state (“prepared state”), characterizedmore »by depolarized membrane potential and smaller but faster membrane responses. The prepared state provides a time window of 200–500 ms, during which cortical neurons are particularly excitable and capable of following afferent inputs. At the network level, this predicts that sets of cells with simultaneous plateaus would provide cellular substrate for the formation of functional neuronal ensembles. NEW & NOTEWORTHY In cortical pyramidal neurons, we recorded glutamate-mediated dendritic plateau potentials with voltage imaging and created a computer model that recreated experimental measures from dendrite and cell body. Our model made new predictions, which were then tested in experiments. Plateau potentials profoundly change neuronal state: a plateau potential triggered in one basal dendrite depolarizes the soma and shortens membrane time constant, making the cell more susceptible to firing triggered by other afferent inputs.« less
  5. Recent advances in modeling oxygen supply to cortical brain tissue have begun to elucidate the functional mechanisms of neurovascular coupling. While the principal mechanisms of blood flow regulation after neuronal firing are generally known, mechanistic hemodynamic simulations cannot yet pinpoint the exact spatial and temporal coordination between the network of arteries, arterioles, capillaries and veins for the entire brain. Because of the potential significance of blood flow and oxygen supply simulations for illuminating spatiotemporal regulation inside the cortical microanatomy, there is a need to create mathematical models of the entire cerebral circulation with realistic anatomical detail. Our hypothesis is that an anatomically accurate reconstruction of the cerebrocirculatory architecture will inform about possible regulatory mechanisms of the neurovascular interface. In this article, we introduce large-scale networks of the murine cerebral circulation spanning the Circle of Willis, main cerebral arteries connected to the pial network down to the microcirculation in the capillary bed. Several multiscale models were generated from state-of-the-art neuroimaging data. Using a vascular network construction algorithm, the entire circulation of the middle cerebral artery was synthesized. Blood flow simulations indicate a consistent trend of higher hematocrit in deeper cortical layers, while surface layers with shorter vascular path lengths seem tomore »carry comparatively lower red blood cell (RBC) concentrations. Moreover, the variability of RBC flux decreases with cortical depth. These results support the notion that plasma skimming serves a self-regulating function for maintaining uniform oxygen perfusion to neurons irrespective of their location in the blood supply hierarchy. Our computations also demonstrate the practicality of simulating blood flow for large portions of the mouse brain with existing computer resources. The efficient simulation of blood flow throughout the entire middle cerebral artery (MCA) territory is a promising milestone towards the final aim of predicting blood flow patterns for the entire brain.« less