Animal Handling and Seizure Induction

C57/Bl6 mice were injected intraperitoneally at P13–P15 with 2 mg/kg picrotoxin. This treatment induced tonic-clonic seizures (80% of animals); only animals experiencing such seizures were used for analysis. Animals seized for approximately 20–40 minutes after injection. Picrotoxin injection did not subsequently produce spontaneous seizures, and 24 hours after the initial event, animals were behaviorally indistinguishable from control littermates, which served as electrophysiological controls. Animals were killed for electrophysiology 24 hours after treatment, between P13 and P15 (mean control: 14.2 and postseizure: 14.4 days).

Preparation of Brain Slices

Animals were anesthetized with isoflurane, decapitated, and their brains quickly removed. Coronal slices (400 *μ*m) were prepared in ice-cold artificial cerebrospinal fluid (ACSF) saturated with 95% O_{2}–5% CO_{2} containing (in mM): 119 NaCl, 2.5 KCl, 1.0 NaH_{2}PO_{4}, 1.3 MgCl_{2}, 2.5 CaCl_{2}, 26.2 NaHCO_{3}, and 11 glucose. After preparation of slices, tissue was maintained at room temperature in this solution.

Electrophysiology

Layer 2/3 pyramidal neurons in the barrel cortex were targeted for whole-cell recording. Sixteen animals were used for the seizure condition and 13 for the control condition. Typically, each cell was recorded from a separate brain slice. In all analysis, *n* refers to the number of cells (Current clamp—control: 35, postseizure: 33; Voltage clamp—control: 18, postseizure: 15) or the number of Up states (Current clamp—control: 278, postseizure: 352; Voltage clamp—control: 157, postseizure: 100) or Down states (control: 313; post-seizure: 385).

Experiments were performed at room temperature in a modified ACSF (

Maffei et al., 2004) with a physiologic calcium concentration (

Fishman, 1992) to facilitate spontaneous activity containing (in mM): 0.5 MgCl

_{2}, 1 CaCl

_{2}, 119 NaCl, 2.5 KCl, 1.0 NaH

_{2}PO

_{4}, 26.2 NaHCO

_{3}, and 11 glucose. The patch pipette contained a solution composed of (in mM): 125 K-gluconate, 10 HEPES, 2 KCl, 4 Mg-ATP, 0.25 Na-GTP, 0.05 Alexa-568. Pyramidal cell identity was confirmed

*post hoc* by morphology and dendritic arborization and by the presence of dendritic spines under fluorescence microscopy. Neurons were held under current clamp with a steady-state holding current to depolarize neurons to a target membrane potential of −50 mV to normalize the ionic driving forces across neurons (). Signals were acquired using a Multi-clamp 700B amplifier (Axon Instruments) and digitized at 10 kHz using a PCI-6036 A/D board (National Instruments). Data were acquired and analyzed using custom functions (written by R.C.G.) for Igor Pro (Wavemetrics, Lake Oswego, OR).

Identification of Up and Down states

A hallmark of network bistability is that Up states are characterized by an enhancement in the amplitude and/or rate of synaptic input compared with the Down state, and that both the membrane potential and its variability are increased (

Shu et al., 2003;

Zou et al., 2005). The algorithm developed here to detect transitions between Up and Down states exploits this by continuously estimating the mean and variance of the membrane potential and using these estimates to establish a threshold in a two-dimensional space that marks statistically significant changes in both quantities.

Determining what constitutes a significant change in membrane potential is challenging because the statistics that govern membrane potential time series during the Down state are not homogenous across time, cells, and contexts (). For a threshold method to be consist and robust, the membrane potential signal must be transformed to a homogeneous, stationary time series. This transformation is achieved by expressing the membrane potential during the Down state as:

The membrane potential *Y*_{t} is determined by the underlying mean *μ*_{t}, standard deviation *σ*_{t}, and a homogeneous, stationary, zero mean, unit variance noise term *W*_{t}. After applying the transformation *Y* → *W* (), observation of a fixed threshold crossing, *ŵ*_{t} > *Q* (), would identify moments when the observed value *ŵ*_{t} was unlikely given the unit normal distribution of *ŵ*. Such a crossing would either be (a) a chance occurrence (false positive), or (b) an indication that the membrane potential was dictated by a new state, the Up state. To eliminate fast time-scale correlations and ensure that *W*_{t} during the Down state satisfies the above criteria, the recorded signal was decimated using bins with a width of the membrane time constant (~10 milliseconds), to generate a working signal *y*.

Computation of Mean and Variance

For each time point

*t*, estimates are made for both the mean

_{t} and variance

that instantaneously describe the membrane potential at that time, using an exponential filter, the simplest linear recursive filter:

where

*T* = 1 second and the initial estimate

_{0} is set equal to

*y*_{0}. The membrane potential variance estimate

is computed with an analogous update equation. To ensure that this variance estimate was independent of trends in the data that might be on the order of

*T*,

was computed based on the time series

*y*′, given by

Using

*y*′ () obviates the need for a computational intensive detrending step. Because variance can be expressed as a summation, the same kind of recursive exponential filter can be used to estimate the variance over a recent period of time:

Finally,

is equal to

, reducing the actual number of estimation steps from 4 to 3. To identify states, a state variable

*S* is initialized to zero. At every time step in

*y*(

*t*), the estimates (

_{t},

) and (

) are computed as above, as well as:

which is the solution of

Eq. 1 for

*W* (, and analogously for

*W*′, ). The threshold for transition from a Down state to an Up state is given by a single parameter,

*Q*, which is a constant = 2. When both

*ŵ*_{t} and

exceed

*Q*, the computation of (

_{t},

) and (

) is suspended, and

*S* is set to 1 (). For every successive sample

*y*_{t}, the inequalities are examined again. If both are no longer satisfied,

*S* is set to 0 and the updating of (

_{t},

) and (

) resumes. Otherwise,

*S* remains equal to 1. Thus, the resultant time series

*S*(

*t*) is equal to 1 when the evidence for an Up state exceeds a threshold level

*Q*, and 0 otherwise. To consolidate 1-dense regions into Up states, and 0-dense regions into Down states,

*S*(

*t*) is median smoothed using a window of width

*T*_{smooth} = 1 second. Contiguous segments of the time series after this smoothing which remain equal to 1 are then classified as Up states. The entire algorithm can be implemented online with the exception of the final consolidation step, which improves accuracy (using a subjective inspection of the signal as the ground truth).