Constrain synaptic connections in a neural model

As paired recordings between connected cells become more prevalent in the experimental literature, we have a better ability to include detailed, biologically-constrained connectivity in our neural network models. Here I give my strategy for characterizing experimental data about synaptic connections between cells, for use in a detailed, data-driven neural model.

First, consider the type of experimental data available for use in the model. In some cases, there may be multiple experiments available to constrain the model – which should be used?

  • Voltage clamp v. current clamp – for experiments where the postsynaptic cell is clamped, it may be either voltage clamped (where the postsynaptic current response, or PSC, is measured) or current clamped (where the postsynaptic potential response, or PSP, is measured). If there is a choice, it may be better to fit the model connection to PSC response from a voltage clamp. Why? The PSC is mostly affected by the properties of the synapse. In contrast, the PSP is affected by properties at the synapse but also largely influenced by properties of the cell (how that cell transforms currents into potential changes depends on the intrinsic properties of the cell). If a model cell differs substantially from the experimental cell where the recording was made, then it will be more difficult to achieve a similar fit on the synapse using PSP data, and even if  there is a good fit to experimental data, that is no guarantee that the synapse and cell are behaving similarly to those in the experiment unless the model cell has been fitted to single cell data from the experimental cell first.
    One minor point about PSC versus PSP: parameters reported from voltage clamp and current clamp synaptic recordings usually differ slightly. Voltage clamp recordings often report the 10-90% rise time of a PSC, as well as the decay time constant, to give an idea of the kinetics of the response. However, PSP recordings may report the time to peak potential difference from baseline instead of a rise time, and they may report the half-width (or width of the response in time at half of the maximum potential difference from baseline) instead of the decay time constant. However, it is easy to extract any of those parameters from a model cell simulation for comparison to either PSP or PSC data.
  • Type of patch – when characterizing a connection between two cells, which may comprise multiple synapses distributed across the cell, it makes sense to patch the cell in a way that keeps the cell intact, but there can still be variation in whether the cell was patched using whole cell patch configuration or a sharp electrode. When a whole cell patch configuration is used, some of the pipette solution will diffuse into the cell, altering its chemical composition and possibly affecting its behavior. But when sharp electrodes are used, which minimize the transfer of the pipette solution into the cell, there is a much large tip potential at the end of the pipette, which can be a source of noise or confound to the electrical recording. For more information, see Li et al, 2004, Sterratt et al, 2011, or the Scholarpedia entry for intracellular recording.

Beyond these differences in experimental configuration, there are other factors to consider any time a modeler wants to constrain their cell synapses based on experimental data. These factors and some general recommendations are covered below, in the presentation of the synapse-fitting strategy used in the development of the hippocampal ca1 model (Bezaire et al, under review):

Strategy

Start by reading experimental papers that will constrain the model; ideally there would be at least one source characterizing the electrophysiological properties of the connection, and at least 1-2 sources characterizing the anatomical properties of the connection or relevant anatomical data about the axon of the presynaptic cell type and the dendrites or incoming synapse locations of the postsynaptic cell type.

Experimental Constraints

For a publication characterizing the electrophysiological properties of the connection:

  1. From the methods section, look at the concentrations of reagents in the bath and pipette solutions to determine the reversal potential of any ions that can pass through that synapse type.
  2. Also from the methods section, either note their reported junction potential value or, if not reported, attempt to calculate it using the calculator within pClamp (or the stand-alone version available at: http://web.med.unsw.edu.au/phbsoft/JPCalcWin_Demo%20version.htm or an open-source calculator at: http://jljp.sourceforge.net/). If I remember, it may be a bit tedious because the tool requires the activity of each molecule in the bath, not just the concentration.
  3. Track other parameters of the experimental protocol that would be needed to reproduce the same test condition in the model, or that may affect the results: holding potential for recordings done in voltage clamp or baseline current injection for recordings done in current clamp, and also whether the clamp was performed using  whole cell patch clamp, sharp electrode, etc.
  4. Also track other methods and preparation details as necessary, species/strain/sex/age (synapse properties can change quite a bit during development),
  5. In the results section, take note of the reported synaptic amplitude as well as reported kinetics. Usually a rise and a decay time are reported, usually in terms of either 20-80 or 10-90 rise time (time to rise from 10% of max postsynaptic response to 90% of postsynaptic response) and in terms of decay time constant, where the decay of the postsynaptic response was fitted to something like A*exp(-t/taudecay) where A is an amplitude parameter and t is time.

For a publication characterizing the anatomical properties of the connection:

  1. Make note of where on the postsynaptic cell the synapses can be made, and whether the position of the synapses is best characterized relative to the postsynaptic cell (ie, distance from soma, diameter of dendrites at synapse location, or neurite type) or to location within the circuit (such as layer and depth within a layer), or both.

  2. If electron microscopy data are available, note how many boutons usually comprise a connection between two cells of given types (presynaptic cells often provide multiple bouton innervations of a given postsynaptic cell) and, if available, whether the multiple innervations must occur near each other or can be more distributed around the postsynaptic cell.

  3. If information about the axonal extent and/or bouton distribution of the presynaptic cell is available, also note those data.

* For hippocampal CA1 area, references to some experimental papers may be found in Bezaire and Soltesz 2013, at the bouton subsection at the end of each cell type section.

Model Design

Now design the model connection to honor the experimental constraints. How the constraints are implemented will depend on the modeler’s judgment and particular strategy as well as goal or question of the model. It may make sense to start by building an anatomically constrained connection and then constrain the electrophysiological behavior of the connection later. One strategy is presented next:

  1. In the model, determine where two cells are close enough to connect (ie, the postsynaptic cell is within the axonal extent of the presynaptic cell or for morphologically detailed models, some appropriate neurites from each cell are within close enough proximity to make a connection).
  2. Establish an appropriate number of synapses between the cells, where the synapses are made onto the appropriate neurites and locations of the postsynaptic cell. For example, my model cells were set up so that I could specify where on the postsynaptic cell a particular cell type usually made its synapses. I would have a max and min for a distance range, where the distance could be relative to the cell’s soma or relative to the layer placement and the cell’s position within the layered network. I also specified whether it connected on only dendrites, soma, or axon as well. Then my model would randomly make the expected number of synapses onto the cell, choosing from the parts of the cell that fit the type and location constraints I specified.
  3. Decide what computational mechanism would best fit (or most efficiently fit) the synaptic kinetics of the experimental preparation. For my model synapses, I almost always used a double exponential model synapse mechanism, so that I could specify the time courses of both the rise and the decay of the synaptic conductance. I would also specify the reversal potential of the synapse, based on which ion types could pass through the synapse.
  4. Actually form the connections. In NEURON, this involved connecting the spike detector of the presynaptic cell to a double exponential point process mechanism on the postsynaptic cell, using a particular weight and axonal conduction delay (the delay may be calculated based on the distance from the presynaptic cell soma to the postsynaptic cell, or perhaps use a constant as a first approximation).

Constraining the Model

Tune the parameters of the synapses to fit the electrophysiological properties of the connection. First, ensure the model and the experimental preparations were exposed to the same conditions. Then execute the simulation. After recording the postsynaptic response, perform the same analysis on the model as was performed on the experimental data.

Design the simulation

  1. Set the reversal potential of the synapses to the potential that the experimental synapses would have experienced with the given bath and pipette solutions (and given the ion types that are expected to pass through the synapse)

  2. Hold the postsynaptic cell at the holding potential reported in the literature (note – if considering junction potential, then hold the cell at the reported holding potential  +  junction potential, unless the experimental paper is reporting a “junction-corrected holding potential”

  3. Specify that the simulator program must report the postsynaptic response from the simulation. In NEURON, that means to set up a recording vector, attached to the soma of the postsynaptic cell (or wherever the experiment patched the cell, but it would usually be on the soma).

  4. Next, fire a spike from the presynaptic cell and record the postsynaptic cell response. Most experimental publications record multiple responses and report the statistics of the response, so it may be a good idea to perform the simulation protocol multiple times in the model as well (for example, on many different possible connections between that pre- and post-synaptic cell type). If running multiple simulations and using NEURON, as I did, make sure to properly initialize the network each time to avoid this issue I ran into at one point.

Analyze the model simulation results in the same way as the experiment:

  1. Find how the experiment treated synaptic failure – did they report a failure rate and/or did they provide an adjusted mean synaptic weight after several trials? Some labs report a mean that is based only on the trials where synaptic transmission actually occurred. Others will average in the failed trials as well and report an “effective mean”. Especially if implementing stochastic synapses with a similar failure rate as to the experiment, make sure to fit the true conductance of the synapse during successful transmission.

  2. Aside from plasticity, most synaptic responses can be well-characterized in terms of the peak conductance, as well as the rise and decay times of the conductance. Many publications will report these properties in terms of a peak current or voltage during the postsynaptic response, a 10-90% (or 20-80%) rise time, and an exponential decay time constant or a half-width of the postsynaptic response. Measure these same properties in the model cell response so that they can be used to tune the time constants in the synaptic mechanism and the synapse weights of the connections.

  3. Multiple iterations may need to be run, such that the model parameters (synaptic weight, time constants of the synaptic mechanism) are adjusted and then the simulation is performed again, and then the synaptic properties are again analyzed and if they do not fit well enough, the whole cycle is repeated. The workflow of this step can be carried out using an optimization/error-minimization program, or in some cases can be hand-tuned if there are few parameters to fit.

As briefly mentioned above, if given a choice of current clamp or voltage clamp experimental data, I prefer to fit the synapses using voltage clamp data, as it is less affected by differences between the intrinsic properties of the model cell and the experimental cell. But one could fit the model connection using experimental current clamp data. Instead of taking care to hold the model cell at the same potential as in a voltage clamp experiment, it would instead be necessary to apply the same current (and look through the experimental methods to see whether they also applied an additional baseline current that needs to be added; sometimes that additional current will be applied at the beginning of the experiment to cause the cell to rest at a pre-determined potential, and will not be provided or mentioned in the rest of the experiment). If it is difficult to fit current clamp data from an experiment, consider that the model cell may need to be (re)tuned before attempting to fit the connection based on current clamp data.

 

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