Part of Neural Information Processing Systems 0 (NIPS 1987)
A computer model of the hippocampal pyramidal cell (HPC) is described
which integrates data from a variety of sources in order to develop a con(cid:173) sistent description for this cell type. The model presently includes descrip(cid:173) tions of eleven non-linear somatic currents of the HPC, and the electrotonic structure of the neuron is modelled with a soma/short-cable approximation. Model simulations qualitatively or quantitatively reproduce a wide range of somatic electrical behavior i~ HPCs, and demonstrate possible roles for the various currents in information processing.
1 The Computational Properties of Neurons
There are several substrates for neuronal computation, including connec(cid:173) tivity, synapses, morphometries of dendritic trees, linear parameters of cell membrane, as well as non-linear, time-varying membrane conductances, also referred to as currents or channels. In the classical description of neuronal function, the contribution of membrane channels is constrained to that of generating the action potential, setting firing threshold, and establishing the relationship between (steady-state) stimulus intensity and firing frequency. However, it is becoming clear that the role of these channels may be much more complex, resulting in a variety of novel "computational operators" that reflect the information processing occurring in the biological neural net.
© American Institute of Physics 1988
2 Modelling Hippocampal Neurons
Over the past decade a wide variety of non-linear ion channels, have been described for many excitable cells, in particular several kinds of neurons. One such neuron is the hippocampal pyramidal cell (HPC). HPC chan(cid:173) nels are marked by their wide range of temporal, voltage-dependent, and chemical-dependent characteristics, which results in very complex behavior or responses of these stereotypical cortical integrating cells. For example, some HPC channels are activated (opened) transiently and quickly, thus pri(cid:173) marily affecting the action potential shape. Other channels have longer ki(cid:173) netics, modulating the response of HPCs over hundreds of milliseconds. The measurement these channels is hampered by various technical constraints, including the small size and extended electrotonic structure of HPCs and the diverse preparations used in experiments. Modelling the electrical behavior of HPCs with computer simulations is one method of integrating data from a variety of sources in order to develop a consistent description for this cell type.
In the model referred to here putative mechanisms for voltage-dependent
and calcium-dependent channel gating have been used to generate simula(cid:173) tions of the somatic electrical behavior of HPCs, and to suggest mechanisms for information processing at the single cell level. The model has also been used to suggest experimental protocols designed to test the validity of sim(cid:173) ulation results. Model simulations qualitatively or quantitatively reproduce a wide range of somatic electrical behavior in HPCs, and explicitly demon(cid:173) strate possible functional roles for the various currents .
The model presently includes descriptions of eleven non-linear somatic currents, including three putative N a+ currents - INa-trig, INa-rep, and INa-tail; six K+ currents that have been reported in the literature - IDR (Delayed Rectifier), lA, Ie, IAHP (After-hyperpolarization), 1M, and IQ; and two Ca2+ currents, also reported previously - lea and leas.
The electrotonic structure of the HPC is modelled with a soma/short(cid:173)
cable approximation, and the dendrites are assumed to be linear. While the conditions for reducing the dendritic tree to a single cable are not met for HPC (the so-called Rall conditions ), the Zin of the cable is close to that of the tree. In addition, although HPC dendrites have non-linear membrane, it assumed that as a first approximation the contribution of currents from this membrane may be ignored in the somatic response to somatic stimulus. Likewise, the model structure assumes that axon-soma current under these conditions can be lumped into the soma circuit.
In part this paper will address the following question: if neural nets
are realizable using elements that have simple integrative all-or-nothing re(cid:173) sponses, connected to each other with regenerative conductors, then what is the function for all the channels observed experimentally in real neurons? The results of this HPC model study suggest some purpose for these com(cid:173) plexities, and in this paper we shall investigate some of the possible roles of non-linear channels in neuronal information processing. However, given the speculative nature of many of the currents that we have presented in the model, it is important to view results based on the interaction of the many model elements as preliminary.
3 Defining Neural Information Coding is the First
Step in Describing Biological Computations
Determination of computational properties of neurons requires a priori as(cid:173) sumptions as to how information is encoded in neuronal output. The clas(cid:173) sical description assumes that information is encoded as spike frequency. However, a single output variable, proportional to firing frequency, ignores other potentially information-rich degrees of freedom, including:
• Relative phase of concurrent inputs.
• Frequency modulation during single bursts.
• Cessation of firing due to intrinsic mechanisms.