We studied the impact of a dynamical threshold on the f-I curve-the relationship between the input and the firing rate of a neuron-in the presence of background synaptic inputs. First, we found that, while the leaky integrate-and-fire model cannot reproduce the f-I curve of a cortical neuron, the leaky integrate-and-fire model with dynamical threshold can reproduce it very well. Second, we found that the dynamical threshold modulates the onset and the asymptotic behavior of the f-I curve. These results suggest that a cortical neuron has an adaptation mechanism and that the dynamical threshold has some significance for the computational properties of a neuron.
When attention is directed into the receptive field of a V4 neuron, its contrast response curve is shifted to lower contrast values (Reynolds et al, 2000, Neuron 26:703). Attention also increases the coherence between neurons responding to the same stimulus (Fries et al, 2001, Science 291:1560). We studied how the firing rate and synchrony of a densely interconnected cortical network varied with contrast and how they were modulated by attention. We found that an increased driving current to the excitatory neurons increased the overall firing rate of the network, whereas variation of the drivin…
The importance of self-feedback autaptic transmission in modulating spike-time irregularity is still poorly understood. By using a biophysical model that incorporates autaptic coupling, we here show that self-innervation of neurons participates in the modulation of irregular neuronal firing, primarily by regulating the occurrence frequency of burst firing. In particular, we find that both excitatory and electrical autapses increase the occurrence of burst firing, thus reducing neuronal firing regularity. In contrast, inhibitory autapses suppress burst firing and therefore tend to improve the r…
Grid-cell firing fields lack local sixfold symmetry
Faculty of Biology, Ludwig-Maximilians-Universität München（慕尼黑大学动物学系）；Graduate School of Systemic Neurosciences (GSN), Ludwig-Maximilians-Universität München（慕尼黑大学系统神经科学研究生院）；Bernstein Center for Computational Neuroscience Munich（慕尼黑贝恩斯坦计算神经科学中心）
Recordings from area V4 of monkeys have revealed that when the focus of attention is on a visual stimulus within the receptive field of a cortical neuron, two distinct changes can occur: The firing rate of the neuron can change and there can be an increase in the coherence between spikes and the local field potential in the gamma-frequency range (30-50 Hz). The hypothesis explored here is that these observed effects of attention could be a consequence of changes in the synchrony of local interneuron networks. We performed computer simulations of a Hodgkin-Huxley type neuron driven by a constan…
Many neurons in the visual cortex are orientation-selective, increase their firing rate with contrast and are modulated by attention. What is the cortical circuit that underlies these computations? We examine how synchrony can be modulated by the excitability of interneurons, in a model layer 4 network displaying contrast-invariant orientation-tuning. We did not find parameter settings for which the standard ring model (Somers et al, 1995), which contains only cells with simple receptive fields (RF), behaved appropriately. Only when interneurons with complex receptive fields were included, sim…
Neurons process information by transforming barrages of synaptic inputs into spiking activity. Synaptic inhibition suppresses the output firing activity of a neuron, and is commonly classified as having a subtractive or divisive effect on a neuron's output firing activity. Subtractive inhibition can narrow the range of inputs that evoke spiking activity by eliminating responses to non-preferred inputs. Divisive inhibition is a form of gain control: it modifies firing rates while preserving the range of inputs that evoke firing activity. Since these two "modes" of inhibition have distinct impac…
Fast-spiking (FS) interneurons in the brain are self-innervated by powerful inhibitory GABAergic autaptic connections. By computational modelling, we investigate how autaptic inhibition regulates the firing response of such interneurons. Our results indicate that autaptic inhibition both boosts the current threshold for action potential generation as well as modulates the input-output gain of FS interneurons. The autaptic transmission delay is identified as a key parameter that controls the firing patterns and determines multistability regions of FS interneurons. Furthermore, we observe that n…
Various classes of neurons alternate between high-frequency discharges and silent intervals. This phenomenon is called burst firing. To analyze burst activity in an insect system, grasshopper auditory receptor neurons were recorded in vivo for several distinct stimulus types. The experimental data show that both burst probability and burst characteristics are strongly influenced by temporal modulations of the acoustic stimulus. The tendency to burst, hence, is not only determined by cell-intrinsic processes, but also by their interaction with the stimulus time course. We study this interaction…
When two stimuli are present in the receptive field of a V4 neuron, the firing rate response is between the weakest and strongest response elicited by each of the stimuli alone (Reynolds et al, 1999, Journal of Neuroscience 19:1736-1753). When attention is directed towards the stimulus eliciting the strongest response (the preferred stimulus), the response to the pair is increased, whereas the response decreases when attention is directed to the other stimulus (the poor stimulus). These experimental results were reproduced in a model of a V4 neuron under the assumption that attention modulates…
We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn. The theory is complemented by a description of a numerical procedure for solving the mean-field equations quantitatively. With our treatment, we can determine self-consistently both the firing rates and the firing correlations, without being restricted to specific neuron models. Here, we solve the analytically derived mean-field equations numerically for integrate-and-fire neurons. Several known key properties of orientation selective cortical neurons emerge naturally from the descript…
We show that the stochastic Morris-Lecar neuron, in a neighborhood of its stable point, can be approximated by a two-dimensional Ornstein-Uhlenbeck (OU) modulation of a constant circular motion. The associated radial OU process is an example of a leaky integrate-and-fire (LIF) model prior to firing. A new model constructed from a radial OU process together with a simple firing mechanism based on detailed Morris-Lecar firing statistics reproduces the Morris-Lecar Interspike Interval (ISI) distribution, and has the computational advantages of a LIF. The result justifies the large amount of atten…
In many cases, the computation of a neural system can be reduced to a receptive field, or a set of linear filters, and a thresholding function, or gain curve, which determines the firing probability; this is known as a linear/nonlinear model. In some forms of sensory adaptation, these linear filters and gain curve adjust very rapidly to changes in the variance of a randomly varying driving input. An apparently similar but previously unrelated issue is the observation of gain control by background noise in cortical neurons: the slope of the firing rate vs current (f-I) curve changes with the va…
The baroreceptor neurons serve as the primary transducers of blood pressure for the autonomic nervous system and are thus critical in enabling the body to respond effectively to changes in blood pressure. These neurons can be separated into two types (A and C) based on the myelination of their axons and their distinct firing patterns elicited in response to specific pressure stimuli. This study has developed a comprehensive model of the afferent baroreceptor discharge built on physiological knowledge of arterial wall mechanics, firing rate responses to controlled pressure stimuli, and ion chan…
To thrive in dynamic environments, animals must be capable of rapidly and flexibly adapting behavioral responses to a changing context and internal state. Examples of behavioral flexibility include faster stimulus responses when attentive and slower responses when distracted. Contextual or state-dependent modulations may occur early in the cortical hierarchy and may be implemented via top-down projections from cortico-cortical or neuromodulatory pathways. However, the computational mechanisms mediating the effects of such projections are not known. Here, we introduce a theoretical framework to…
Extracellular recordings of single neurons in primary and secondary somatosensory cortices of monkeys in vivo have shown that their firing rate can increase, decrease, or remain constant in different cells, as the external stimulus frequency increases. We observed similar intrinsic firing patterns (increasing, decreasing or constant) in rat somatosensory cortex in vitro, when stimulated with oscillatory input using conductance injection (dynamic clamp). The underlying mechanism of this observation is not obvious, and presents a challenge for mathematical modelling. We propose a simple principl…
The gain of neurons' responses in the auditory cortex is sensitive to contrast changes in the stimulus within a spectrotemporal range similar to their receptive fields, which can be interpreted to represent the tuning of the input to a neuron. This indicates a local mechanism of contrast gain control, which we explore with a minimal mechanistic model here. Gain control through noisy input has been observed in vitro and in a range of computational models. We investigate the behaviour of the simplest of such models to showcase gain control, a stochastic leaky integrate-and-fire (sLIF) neuron, wh…
Periodically modulated traveling waves in integrate-and-fire networks: recursive speed law and propagation failure
Georgia State University（佐治亚州立大学）；Norcliffe Foundation Center for Integrative Brain Research, Seattle Children’s Research Institute（西雅图儿童医院研究所整合脑研究中心）；Perimeter College, Georgia State University（佐治亚州立大学边界学院）；Universal Alloy Corporation（通用合金公司）；Pyrsquare Analytics（Pyrsquare分析公司）；Transylvanian Institute of Neuroscience（特兰西瓦尼亚神经科学研究所）
Phase transitions and critical behavior are crucial issues both in theoretical and experimental neuroscience. We report analytic and computational results about phase transitions and self-organized criticality (SOC) in networks with general stochastic neurons. The stochastic neuron has a firing probability given by a smooth monotonic function $Φ(V)$ of the membrane potential $V$, rather than a sharp firing threshold. We find that such networks can operate in several dynamic regimes (phases) depending on the average synaptic weight and the shape of the firing function $Φ$. In particular, we enc…
A major goal of neuroscience, statistical physics and nonlinear dynamics is to understand how brain function arises from the collective dynamics of networks of spiking neurons. This challenge has been chiefly addressed through large-scale numerical simulations. Alternatively, researchers have formulated mean-field theories to gain insight into macroscopic states of large neuronal networks in terms of the collective firing activity of the neurons, or the firing rate. However, these theories have not succeeded in establishing an exact correspondence between the firing rate of the network and the…
Adaptive whitening with fast gain modulation and slow synaptic plasticity
Center for Computational Neuroscience, Flatiron Institute（Flatiron Institute计算神经科学中心）；Center for Neural Science, New York University（纽约大学神经科学中心）；Neuroscience Institute, NYU Langone Medical School（纽约大学朗格尼医学院神经科学研究所）
The role of gain neuromodulation in layer-5 pyramidal neurons
Neural Circuits Laboratory, Biosciences Institute, Faculty of Medical Sciences, Newcastle University（神经回路实验室、生物科学学院、医学科学学院、新castle大学）；Brain and Mind Center, The University of Sydney（脑与心智中心、悉尼大学）；Center for Complex Systems, The University of Sydney（复杂系统中心、悉尼大学）；IT:U Interdisciplinary Transformation University Austria（奥地利 interdisciplinary transformation university Austria）；International Research Center for Neurointelligence, The University of Tokyo（神经智能国际研究中心、东京大学）；Department of Anatomy, University of Quebec in Trois-Rivieres（解剖学系、魁北克三河大学）；Theoretical Sciences Visiting Program (TSVP), Okinawa Institute of Science and Technology Graduate University（理论科学访问计划（TSVP）、冲绳科学技术大学院大学）
In self-organized criticality (SOC) models, as well as in standard phase transitions, criticality is only present for vanishing external fields $h \to 0$. Considering that this is rarely the case for natural systems, such a restriction poses a challenge to the explanatory power of these models. Besides that, in models of dissipative systems like earthquakes, forest fires, and neuronal networks, there is no true critical behavior, as expressed in clean power laws obeying finite-size scaling, but a scenario called "dirty" criticality or self-organized quasi-criticality (SOqC). Here, we propose s…
We show that dynamical gain modulation of neurons' stimulus response is described as an information-theoretic cycle that generates entropy associated with the stimulus-related activity from entropy produced by the modulation. To articulate this theory, we describe stimulus-evoked activity of a neural population based on the maximum entropy principle with constraints on two types of overlapping activities, one that is controlled by stimulus conditions and the other, termed internal activity, that is regulated internally in an organism. We demonstrate that modulation of the internal activity rea…
