Mechanisms of gain control by voltage-gated channels in intrinsically-firing neurons.

This is the final published version. It first appeared at http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0115431.Gain modulation is a key feature of neural information processing, but underlying mechanisms remain unclear. In single neurons, gain can be measured as the slope of the current-frequency (input-output) relationship over any given range of inputs. While much work has focused on the control of basal firing rates and spike rate adaptation, gain control has been relatively unstudied. Of the limited studies on gain control, some have examined the roles of synaptic noise and passive somatic currents, but the roles of voltage-gated channels present ubiquitously in neurons have been less explored. Here, we systematically examined the relationship between gain and voltage-gated ion channels in a conductance-based, tonically-active, model neuron. Changes in expression (conductance density) of voltage-gated channels increased (Ca2+ channel), reduced (K+ channels), or produced little effect (h-type channel) on gain. We found that the gain-controlling ability of channels increased exponentially with the steepness of their activation within the dynamic voltage window (voltage range associated with firing). For depolarization-activated channels, this produced a greater channel current per action potential at higher firing rates. This allowed these channels to modulate gain by contributing to firing preferentially at states of higher excitation. A finer analysis of the current-voltage relationship during tonic firing identified narrow voltage windows at which the gain-modulating channels exerted their effects. As a proof of concept, we show that h-type channels can be tuned to modulate gain by changing the steepness of their activation within the dynamic voltage window. These results show how the impact of an ion channel on gain can be predicted from the relationship between channel kinetics and the membrane potential during firing. This is potentially relevant to understanding input-output scaling in a wide class of neurons found throughout the brain and other nervous systems.This work was supported by the Wellcome Trust- and GSK-funded TMAT programme (085686/ Z/08/C, AXP), the University of Cambridge MB/PhD Programme (AXP), the European Research Council (FP7 starting grant to DB) and the UK Medical Research Council (DB, ref: MC\_UP\_1202/2). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

A wavelet-based estimator of the degrees of freedom in denoised fMRI time series for probabilistic testing of functional connectivity and brain graphs.

Connectome mapping using techniques such as functional magnetic resonance imaging (fMRI) has become a focus of systems neuroscience. There remain many statistical challenges in analysis of functional connectivity and network architecture from BOLD fMRI multivariate time series. One key statistic for any time series is its (effective) degrees of freedom, df, which will generally be less than the number of time points (or nominal degrees of freedom, N). If we know the df, then probabilistic inference on other fMRI statistics, such as the correlation between two voxel or regional time series, is feasible. However, we currently lack good estimators of df in fMRI time series, especially after the degrees of freedom of the "raw" data have been modified substantially by denoising algorithms for head movement. Here, we used a wavelet-based method both to denoise fMRI data and to estimate the (effective) df of the denoised process. We show that seed voxel correlations corrected for locally variable df could be tested for false positive connectivity with better control over Type I error and greater specificity of anatomical mapping than probabilistic connectivity maps using the nominal degrees of freedom. We also show that wavelet despiked statistics can be used to estimate all pairwise correlations between a set of regional nodes, assign a P value to each edge, and then iteratively add edges to the graph in order of increasing P. These probabilistically thresholded graphs are likely more robust to regional variation in head movement effects than comparable graphs constructed by thresholding correlations. Finally, we show that time-windowed estimates of df can be used for probabilistic connectivity testing or dynamic network analysis so that apparent changes in the functional connectome are appropriately corrected for the effects of transient noise bursts. Wavelet despiking is both an algorithm for fMRI time series denoising and an estimator of the (effective) df of denoised fMRI time series. Accurate estimation of df offers many potential advantages for probabilistically thresholding functional connectivity and network statistics tested in the context of spatially variant and non-stationary noise. Code for wavelet despiking, seed correlational testing and probabilistic graph construction is freely available to download as part of the BrainWavelet Toolbox at www.brainwavelet.org.This work was supported by the Wellcome Trust- and GSK-funded Translational Medicine and Therapeutics Programme (085686/Z/08/C, AXP) and the University of Cambridge MB/PhD Programme (AXP). The Behavioral and Clinical Neuroscience Institute is supported by the Wellcome Trust (093875/Z/10/Z) and the Medical Research Council (G1000183). ETB works half-time for GlaxoSmithKline and half-time for the University of Cambridge; he holds stock in GSK.This is the final version of the article. It was first available from Elsevier via http://dx.doi.org/10.1016/j.neuroimage.2015.04.05

Probabilistic thresholding of functional connectomes: Application to schizophrenia.

Functional connectomes are commonly analysed as sparse graphs, constructed by thresholding cross-correlations between regional neurophysiological signals. Thresholding generally retains the strongest edges (correlations), either by retaining edges surpassing a given absolute weight, or by constraining the edge density. The latter (more widely used) method risks inclusion of false positive edges at high edge densities and exclusion of true positive edges at low edge densities. Here we apply new wavelet-based methods, which enable construction of probabilistically-thresholded graphs controlled for type I error, to a dataset of resting-state fMRI scans of 56 patients with schizophrenia and 71 healthy controls. By thresholding connectomes to fixed edge-specific P value, we found that functional connectomes of patients with schizophrenia were more dysconnected than those of healthy controls, exhibiting a lower edge density and a higher number of (dis)connected components. Furthermore, many participants' connectomes could not be built up to the fixed edge densities commonly studied in the literature (∼5-30%), while controlling for type I error. Additionally, we showed that the topological randomisation previously reported in the schizophrenia literature is likely attributable to "non-significant" edges added when thresholding connectomes to fixed density based on correlation. Finally, by explicitly comparing connectomes thresholded by increasing P value and decreasing correlation, we showed that probabilistically thresholded connectomes show decreased randomness and increased consistency across participants. Our results have implications for future analysis of functional connectivity using graph theory, especially within datasets exhibiting heterogenous distributions of edge weights (correlations), between groups or across participants

Regional expression of the MAPT gene is associated with loss of hubs in brain networks and cognitive impairment in Parkinson disease and progressive supranuclear palsy.

Abnormalities of tau protein are central to the pathogenesis of progressive supranuclear palsy, whereas haplotype variation of the tau gene MAPT influences the risk of Parkinson disease and Parkinson's disease dementia. We assessed whether regional MAPT expression might be associated with selective vulnerability of global brain networks to neurodegenerative pathology. Using task-free functional magnetic resonance imaging in progressive supranuclear palsy, Parkinson disease, and healthy subjects (n = 128), we examined functional brain networks and measured the connection strength between 471 gray matter regions. We obtained MAPT and SNCA microarray expression data in healthy subjects from the Allen brain atlas. Regional connectivity varied according to the normal expression of MAPT. The regional expression of MAPT correlated with the proportionate loss of regional connectivity in Parkinson's disease. Executive cognition was impaired in proportion to the loss of hub connectivity. These effects were not seen with SNCA, suggesting that alpha-synuclein pathology is not mediated through global network properties. The results establish a link between regional MAPT expression and selective vulnerability of functional brain networks to neurodegeneration.Medical Research Council (Grant IDs: G1100464, MR/K020706/1, G0700503), Wellcome Trust (Grant ID: 103838), National Institute for Health Research Cambridge Biomedical Research Centre, Beverley Sackler fellowship scheme, NARSAD Young Investigator Award, Isaac Newton TrustThis is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.neurobiolaging.2016.09.00

Conservative and disruptive modes of adolescent change in human brain functional connectivity.

Adolescent changes in human brain function are not entirely understood. Here, we used multiecho functional MRI (fMRI) to measure developmental change in functional connectivity (FC) of resting-state oscillations between pairs of 330 cortical regions and 16 subcortical regions in 298 healthy adolescents scanned 520 times. Participants were aged 14 to 26 y and were scanned on 1 to 3 occasions at least 6 mo apart. We found 2 distinct modes of age-related change in FC: "conservative" and "disruptive." Conservative development was characteristic of primary cortex, which was strongly connected at 14 y and became even more connected in the period from 14 to 26 y. Disruptive development was characteristic of association cortex and subcortical regions, where connectivity was remodeled: connections that were weak at 14 y became stronger during adolescence, and connections that were strong at 14 y became weaker. These modes of development were quantified using the maturational index (MI), estimated as Spearman's correlation between edgewise baseline FC (at 14 y, [Formula: see text]) and adolescent change in FC ([Formula: see text]), at each region. Disruptive systems (with negative MI) were activated by social cognition and autobiographical memory tasks in prior fMRI data and significantly colocated with prior maps of aerobic glycolysis (AG), AG-related gene expression, postnatal cortical surface expansion, and adolescent shrinkage of cortical thickness. The presence of these 2 modes of development was robust to numerous sensitivity analyses. We conclude that human brain organization is disrupted during adolescence by remodeling of FC between association cortical and subcortical areas

Tuning Low-Voltage-Activated A-Current for Silent Gain Modulation

Modulation of stimulus-response gain and stability of spontaneous (unstimulated) firing are both important for neural computation. However, biologically plausible mechanisms that allow these distinct functional capabilities to coexist in the same neuron are poorly defined. Low-threshold, inactivating (A-type) K(+) currents (I(A)) are found in many biological neurons and are historically known for enabling low-frequency firing. By performing simulations using a conductance-based model neuron, here we show that biologically plausible shifts in I(A) conductance and inactivation kinetics produce dissociated effects on gain and intrinsic firing. This enables I(A) to regulate gain without major changes in intrinsic firing rate. Tuning I(A) properties may thus represent a previously unsuspected single-current mechanism of silent gain control in neurons

The effects of modulating voltage- and Ca²⁺-gated K⁺ conductances on gain.

<p>(A) Examples of firing responses of the model neuron with different values of A-type channel maximal specific conductance (</p><p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><mi>A</mi><p></p><p></p><p></p>). The input stimuli driving the firing rate are shown schematically below the traces: current for the tonic input model (upper panel) and membrane potential for the synaptic input model (lower panel). Positive values of tonic driving current represent depolarizing input. <i>λ</i> is the mean interval between impulses in the synaptic input model (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115431#sec002" target="_blank">Methods</a>). (B) The left panel shows current-frequency (input-output) relationships obtained with different values of <p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><mi>A</mi><p></p><p></p><p></p> in the model neuron (maximal specific conductance densities, in mS·cm⁻², are given near the corresponding tuning curves) when stimulated with different tonic driving current magnitudes. The right panel shows data in the left panel re-plotted as maximal gain (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115431#sec002" target="_blank">Methods</a>) against <p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><mi>A</mi><p></p><p></p><p></p> for the tonic driving input (dotted line) and the fluctuating synaptic input (solid line). (C) The same analysis shown in panel B, for the delayed-rectifier K⁺ channel, and (D) the Ca²⁺-activated K⁺ channel. Increasing maximal specific conductances of all three K⁺ channels reduced neuronal gain in response to both tonic and fluctuating inputs.<p></p

The effect of changing Ca²⁺-activated K⁺ and voltage-gated Ca²⁺ conductances on the current-voltage relationship.

<p>(A) The left upper panel shows a plot of Ca²⁺-activated K⁺ (<i>I</i>_<i>KCa</i>) current against membrane potential over 4 seconds of firing (I-V loop). This relationship was plotted at different <i>I</i>_<i>KCa</i> channel maximal specific conductances (</p><p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><p><mi>K</mi><mi>C</mi><mi>a</mi></p><p></p><p></p><p></p>) in the presence or absence of a tonic, depolarizing, driving current. The grey traces show the effect of uncoupling the <i>I</i>_<i>KCa</i> channel from changes in intracellular [Ca²⁺]. <p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><p><mi>K</mi><mi>C</mi><mi>a</mi></p><p></p><p></p><p></p> and driving current values are given above the plot. The left middle panel shows histograms of the percentage time (% time) the membrane spent at various potentials over these 4 seconds. Firing rates were matched by changing the driving input magnitudes in order to separate the effects of changing <p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><p><mi>K</mi><mi>C</mi><mi>a</mi></p><p></p><p></p><p></p> (what we were interested in), from the confounding effects of changes in firing rate as a result of changing <p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><p><mi>K</mi><mi>C</mi><mi>a</mi></p><p></p><p></p><p></p>. The <p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><p><mi>K</mi><mi>C</mi><mi>a</mi></p><p></p><p></p><p></p> and driving current values for the histograms are given to the right of the plot. The lower left panel shows the voltages at which the channels were active (y axis: <i>m</i>_∞ × <i>h</i>_∞ / <i>τ</i>_<i>m</i> × <i>τ</i>_<i>h</i>). The right panel shows action potential and inter-spike interval (upper) and current (lower) traces for the same <p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><p><mi>K</mi><mi>C</mi><mi>a</mi></p><p></p><p></p><p></p> / driving current combinations shown in the histograms. (B) The same as panel A for the voltage-gated Ca²⁺ (<i>I</i>_<i>CaS</i>) channel.<p></p

The effects of passive membrane conductances on gain.

<p>(A) Examples of firing responses of the model neuron with different maximal specific conductance densities of the passive (non-voltage-gated) inhibitory channel (</p><p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><mi>i</mi><p></p><p></p><p></p>). The current step (tonic depolarizing current input) is of the same amplitude in the two traces, but the baselines were shifted to points giving the same firing rates for visual clarity. (B) The left panel shows current-frequency (input-output) relationships obtained with different values of <p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><mi>i</mi><p></p><p></p><p></p> when stimulated with an increasing tonic driving current. Inward, depolarizing, driving currents are represented as positive values. Maximal specific conductance densities, in <i>μ</i>S·cm⁻², are given near the corresponding tuning curves. The right panel shows data in the left panel re-plotted as maximal gain (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115431#sec002" target="_blank">Methods</a>) against <p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><mi>i</mi><p></p><p></p><p></p> for the tonic driving input (dotted line) and for the fluctuating synaptic input (solid line). (C) The same analysis shown in panel B for the passive excitatory channel. Increasing <p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><mi>e</mi><p></p><p></p><p></p> or <p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><mi>i</mi><p></p><p></p><p></p> appeared to have no effect on gain in response to both tonic and fluctuating inputs.<p></p

The role of Ca²⁺-dependent coupling between voltage-gated Ca²⁺ and K⁺ currents.

<p>(A) The left panel shows current-frequency (input-output) relationships obtained when varying the maximal specific conductance of the Ca²⁺-activated K⁺ channel (</p><p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><p><mi>K</mi><mi>C</mi><mi>a</mi></p><p></p><p></p><p></p>) when uncoupled from changes in intracellular [Ca²⁺]. The input was a tonic driving current where positive values of the current represent depolarizing input. The right panel shows data from the left panel re-plotted as maximal gain (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115431#sec002" target="_blank">Methods</a>) against <p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><p><mi>K</mi><mi>C</mi><mi>a</mi></p><p></p><p></p><p></p> in the uncoupled (solid line) and the default coupled (dashed line) state. (B) This panel shows the effects of uncoupling the <i>I</i>_<i>KCa</i> channel from [Ca²⁺] on the voltage-gated Ca²⁺ channel (<i>I</i>_<i>CaS</i>). The analysis conducted was the same as in panel A, but while varying the maximal conductance of the <i>I</i>_<i>CaS</i> channel (<p></p><p></p><p></p><p><mi>G</mi><mo>‾</mo></p><p><mi>C</mi><mi>a</mi><mi>S</mi></p><p></p><p></p><p></p>). (C) Firing responses of the neuron under different coupling strengths (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115431#sec002" target="_blank">Methods</a>). The input (tonic) driving current is shown schematically below the traces. (D) The left panel shows current-frequency relationships in response to a tonic driving current, where the <i>I</i>_<i>KCa</i> and <i>I</i>_<i>CaS</i> channels were coupled by different strengths (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115431#sec002" target="_blank">Methods</a>). The right panel shows data in the left panel re-plotted as maximal gain (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115431#sec002" target="_blank">Methods</a>) against the strength of coupling between the two channels.<p></p