Nonlinear-dynamics theory of up-down transitions in neocortical neural networks
The neurons of the neocortex show ∼1-Hz synchronized transitions between an active up state and a quiescent down state. The up-down state transitions are highly coherent over large sections of the cortex, yet they are accompanied by pronounced, incoherent noise. We propose a simple model for the up-down state oscillations that allows analysis by straightforward dynamical systems theory. An essential feature is a nonuniform network geometry composed of groups of excitatory and inhibitory neurons with strong coupling inside a group and weak coupling between groups. The enhanced deterministic noise of the up state appears as the natural result of the proximity of a partial synchronization transition. The synchronization transition takes place as a function of the long-range synaptic strength linking different groups of neurons.
PDFs: Non-linear dynamics theory.pdf
JPEGs: levine_nonlineardynamics.jpg (319.59 KB)
Research categories: Neuroscience, Nonequilibrium physics

Frequency dependent changes in NMDAR-dependent synaptic plasticity
A. Kumar & M. R. Mehta, ‘Frequency dependent changes in NMDAR-dependent synaptic plasticity’, Frontiers in Computational Neuroscience 5 (2011).
Arvind Kumar and Mayank R. Mehta
The NMDAR-dependent synaptic plasticity is thought to mediate several forms of learning, and can be induced by spike trains containing a small number of spikes occurring with varying rates and timing, as well as with oscillations. We computed the influence of these variables on the plasticity induced at a single NMDAR containing synapse using a reduced model that was analytically tractable, and these findings were confirmed using detailed, multi-compartment model. In addition to explaining diverse experimental results about the rate and timing dependence of synaptic plasticity, the model made several novel and testable predictions. We found that there was a preferred frequency for inducing long-term potentiation (LTP) such that higher frequency stimuli induced lesser LTP decreasing as 1/f, when the number of spikes in the stimulus was kept fixed. Among other things, the preferred frequency for inducing LTP varied as a function of the distance of the synapse from the soma. In fact, same stimulation frequencies could induce LTP or long-term depression depending on the dendritic location of the synapse. Next, we found that rhythmic stimuli induced greater plasticity then irregular stimuli. Furthermore, brief bursts of spikes significantly expanded the timing dependence of plasticity. Finally, we found that in the ∼5–15-Hz frequency range both rate- and timing-dependent plasticity mechanisms work synergistically to render the synaptic plasticity most sensitive to spike timing. These findings provide computational evidence that oscillations can have a profound influence on the plasticity of an NMDAR-dependent synapse, and show a novel role for the dendritic morphology in this process.
JPEGs: Frequency-dependent changes in NMDAR-dependent.jpg (602.98 KB)
PDFs: fncom-05-00038.pdf (11.30 MB)
Research categories: Neuroscience

Speed Controls the Amplitude and Timing of the Hippocampal Gamma Rhythm
Zhiping Chen, Evgeny Resnik, James M. McFarland, Bert Sakmann, Mayank R. Mehta
Cortical and hippocampal gamma oscillations have been implicated in many behavioral tasks. The hippocampus is required for spatial navigation where animals run at varying speeds. Hence we tested the hypothesis that the gamma rhythm could encode the running speed of mice. We found that the amplitude of slow (20–45 Hz) and fast (45–120 Hz) gamma rhythms in the hippocampal local field potential (LFP) increased with running speed. The speed-dependence of gamma amplitude was restricted to a narrow range of theta phases where gamma amplitude was maximal, called the preferred theta phase of gamma. The preferred phase of slow gamma precessed to lower values with increasing running speed. While maximal fast and slow gamma occurred at coincident phases of theta at low speeds, they became progressively more theta-phase separated with increasing speed. These results demonstrate a novel influence of speed on the amplitude and timing of the hippocampal gamma rhythm which could contribute to learning of temporal sequences and navigation.
JPEGs: Speed Controls the Amplitude and Timing.jpg (326.56 KB)
PDFs: journal.pone.0021408.pdf (15.35 MB)
Research categories: Neuroscience

Cortico-hippocampal interaction during up-down states and memory consolidation
Mayank R Mehta
Sleep may promote the transfer of memories from hippocampus to cortex. New work shows that experiences are replayed during sleep in both brain regions and that replay in these two areas occurs synchronously.
JPEGs: Cortico-hippocampal interaction.jpg (699.52 KB)
PDFs: Cortico-hippocampal interaction during up-down states and memory consolidation.pdf (5.85 MB)
Research categories: Neuroscience

Phase-locking of hippocampal interneurons’ membrane potential to neocortical up-down states
Thomas T G Hahn, Bert Sakmann & Mayank R Mehta
During quiet wakefulness and sleep, and under anesthesia, the membrane potentials of neocortical pyramidal neurons show synchronous, slow oscillations, so-called up-down states (UDS), that can be detected in the local field potential (LFP). The influence of this synchronized, spontaneous neocortical activity on the hippocampus is largely unknown. We performed the first in vivo whole-cell recordings from hippocampal dorsal CA1 interneurons and found that their membrane potentials were phase-locked to neocortical up-down states with a small delay. These results provide strong evidence for cortico-hippocampal interaction and suggest that neocortical activity drives hippocampal interneurons during UDS.
JPEGs: Phase-locking of hippocampal.jpg (599.50 KB)
PDFs: Phase-locking of hippocampal.pdf (1.66 MB)

Cooperative LTP can map memory sequences on dendritic branches
Mayank R. Mehta
Hebbian synaptic learning requires co-activation of presynaptic and postsynaptic neurons. However, under some conditions, information regarding the postsynaptic action potential, carried by backpropagating action potentials, can be strongly degraded before it reaches the distal dendritic synapse. Can these synapses still exhibit Hebbian long-term potentiation (LTP)? Recent results show that LTP can indeed occur at synapses on distal dendrites of hippocampal CA1 neurons, even in the absence of a postsynaptic somatic spike. Instead, local dendritic spikes contribute to the depolarization required to induce LTP. Here, a dendritically constrained synaptic learning rule is proposed, which suggests that nearby synapses can encode temporally contiguous events.
JPEGs: Cooperative LTP.jpg (239.23 KB)
PDFs: Cooperative LTP.pdf (1.06 MB)
Research categories: Neuroscience