Table 1.
Characteristics of in vivo and in vitro MGB responses to periodic stimuli.
Table 2.
Default Model Parameters.
Figure 1.
Intrinsic and Synaptic model characteristics.
A, I-V plot of model responses to current injections. B, IC Input spike probability as a function of inter-click interval. Spike probabilities are close to 1 at high inter-click intervals greater than 25 ms and fall as inter-click intervals are reduced. C, Model responses to 300 pA and -300 pA current injection, which produces a tonic firing response and an offset burst response, respectively. D, Example voltage trace observed from a single trial model simulation. The dots above indicate the 2 individual spike inputs used to produce the voltage response. E, Voltage traces show paired synaptic inputs having interclick interval of 25 and 50 ms. Solid lines are paired EPSPs with 25 ms ICIs and dashed lines are traces with 50 ms ICIs. From top to bottom, left to right: Modeled paired synaptic inputs with no plasticity, AMPA and NMDA exhibiting paired pulse depression (PPD), “Mixed” inputs with AMPA exhibiting depression and NMDA exhibiting facilitation, AMPA and NMDA inputs exhibiting paired pulse facilitation (PPF).
Figure 2.
Model response characteristics produced as a result of adjusting AMPA and NMDA conductance levels.
Y-axis values correspond to AMPA conductance (0 – 20 nS), X-axis values correspond to ratio of NMDA to AMPA conductance (0, .5, 1, 1.5, 2, 2.5, 3). Values of AMPA conductance and NMDA:AMPA ratio chosen for Large and Small IC inputs are identified by a white L and S on the 100 ms color plots, respectively. Regions outlined in white indicate regions where response is statistically calculated to be synchronized (Rayleigh statistic >13.8, p<0.001). As ISIs decrease, the regions of synchronized responses diminish. A, i-iv: Spike rates and vector strength plots for 10 simulation trials at 100 ms interclick intervals, 500 ms duration each trial. From top to bottom: Spike rate and vector strength plots for no plasticity, short-term depression, mixed (AMPA depression + NMDA facilitation), and short-term facilitation do not vary much at large ISIs. B, i-iv: Spike rates and vector strength plots for 10 simulation trials at 25 ms interclick intervals. Synaptic facilitation increases spike rate, while synaptic depression decreases overall spike rates. C, i-iv: Spike rates and vector strength plots for 10 simulation trials at 10 ms interclick intervals. Short-term plasticity greatly affects overall spike rate. With the exception of one conductance pair in the PPD case, regions of synchronized responses only occur in simulations with no plasticity or synaptic facilitation.
Figure 3.
Large jitter values relative to period length desynchronize model responses.
A, Vector strength plot for 4 Small inputs exhibiting AMPA synaptic depression and NMDA synaptic facilitation (Mixed) or AMPA and NMDA facilitation (PPF). Red dots, blue circles and purple squares indicate Mixed input responses with jitter scaled to 10%, 20% and 50% of ICI, respectively. Green dots, pink triangles, and blue stars indicate PPF input responses with jitter scaled to 10%, 20% and 50% of ICI, respectively. Synchronized responses are found in the PPF case with 10% and 20% jitter at ICIs indicated with black symbols. Inset: Spike rates for the parameters described in A. Changes in jitter had little effect on spike rates in the PPF and Mixed case. B, Vector strength plot for 2 Large inputs, exhibiting either synaptic depression (PPD) and no plasticity (None). Red dots, blue circles and purple squares indicate “None” input responses with jitter scaled to 10%, 20% and 50% of ICI, respectively. Green dots, pink triangles, and blue stars indicate PPD input responses with jitter scaled to 10%, 20% and 50% of ICI, respectively. Vector strength increases with reduced jitter, as do the regions of synchronized activity (indicated with black symbols) Inset: Rate curves of the parameters described in B. Changes to input jitter do not affect spike rate curves.
Figure 4.
Large inputs exhibiting PPD produce synchronized, low-pass responses.
A, Spike rate curves from simulations using 2 Large inputs with 1 ms jitter. Rates are given in spikes/cycle. Inset: Rate gain curves calculated from model spike rates and input spike times. Spike rates do not change with plasticity at ICIs≥50 ms. PPF inputs (purple) greatly increases rate gain, Mixed inputs (blue) slightly increases gain. Inputs exhibiting PPD (green) reduces gain. B, Spike rate (solid lines) and vector strength (dashed line) curves of 2 Large inputs. Red lines with “+” have no added synaptic plasticity, green lines indicate responses using PPD. Synchrony is indicated with black symbols. C, Measured First Spike Latency (FSL) of the Large PPD (Green ovals) and Large None (Red “+”) responses. At ICIs>10 ms, FSL is measured to be ∼7 ms, after which FSL increases due to decreased spike probability.
Figure 5.
Small inputs exhibiting either PPF of Mixed plasticity produce band-pass, non-synchronized responses.
A, Spike rate curves from simulations using 4 Small inputs with 1 ms jitter. Rates are given in spikes/cycle. Simulations with PPD produced subthreshold activity. Inset: Rate gain curves calculated from model spike rates and input spike times. Spike rates do not change with plasticity at ICIs≥100 ms. Purple lines with triangles mark PPF, blue lines with circles indicate Mixed, and Red lines with plus symbols indicated no synaptic plasticity. B, Spike rate (solid lines) and vector strength (dashed lines) curves of 4 Small inputs. Synchronized responses were only found in the PPF case between 10 and 50 ms ICI, marked in black symbols. C, FSL curves for Small None, Mixed and PPF inputs. Dashed line shows FSL curve of 2 Large PPD inputs for comparison. Subthreshold responses were observed at ICIs≥100 ms and therefore no FSL was measured. FSL values reduced with ICI until a minimum is reached at an ICI of 10 ms, after which FSL increases due to decreased input spike probability.
Figure 6.
Reduction of NMDA receptor mediated current shifts responses rates and synchronization regions.
A, Model rate responses for 2 Large PPD Inputs with 1 ms jitter. Red lines show 0% NMDA, green lines show 50%, blue lines show 150% and purple lines show 200% NMDA. B, Vector strength curves for the same parameters as in A. Reduced NMDA reduces regions of spiking, which occurs at high ICIs where the effects of synaptic depression diminishes or at low ICIs where summation of EPSPs may occur. At low ICIs, typically only an onset response is observed followed by weak sustained or subthreshold activity. Synchronized responses are indicated with black symbols. C, Model rate responses for 4 Small Mixed Inputs with 1 ms jitter. Colors and symbols indicate percent of NMDA conductance used as described in A. D, Vector strength curves for the same parameters as in C. Synchronized responses are found only at high ICIs with increased NMDA. E, Model rate responses for 4 Small PPF Inputs with 1 ms jitter. F, Vector strength curves for the same parameters as in E. Although high vector strength values are observed at ICIs≥100 ms for trials with increased NMDA, these responses produce small spike rates and were not found to be synchronized. Reduced NMDA does produce synchronized responses between ICIs of 10 – 20 ms.
Figure 7.
Changes in membrane potential affect response rates and synchronization boundaries.
Plus, circle and diamond symbols indicate simulations run at -55 mV, -65 mV, and -75 mV, respectively. A, Vector strength responses for trials using 4 Small Mixed inputs with 1 ms jitter. At -55 mV, synchronized responses were observed at ICIs≥50 ms. At more hyperpolarized membrane potentials, responses at these ICIs were subthreshold. Synchronized responses are observed at 20 – 25 ms. Inset: Spike rate responses for parameters used in A. At more depolarized membrane potentials, response rate is elevated. At hyperpolarized membrane potentials, rate is reduced. B, Vector strength responses for trials using 2 Large inputs and 1 ms jitter without synaptic plasticity. Synchronized responses were found at ICIs≥8.5 ms at all membrane potentials. Inset: Spike rate responses for B. C, Vector strength responses for 4 Small PPF Inputs with 1 ms jitter. Responses are synchronized at ICIs between 10 – 25 ms at all membrane potentials used. At -55 mV, synchronized responses are found at ICIs≥50 ms. At these ICIs responses are subthreshold at -65 and -75 mV.