82 
SIMULATIONS SUGGEST 
INFORMATION PROCESSING ROLES 
FOR THE DIVERSE CURRENTS IN 
HIPPOCAMPAL NEURONS 
Lyle J. Borg-Graham 
Harvard-MIT Division of Health Sciences and Technology and 
Center for Biological Information Processing, 
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 
ABSTRACT 
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- 
sistent description for this cell type. The model presently includes descrip- 
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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- 
tivity, synapses, morphometrics 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 
83 
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- 
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- 
marily affecting the action potential shape. Other channels have longer ki- 
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- 
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- 
ulation results. Model simulations qualitatively or quantitatively reproduce 
a wide range of somatic electrical behavior in HPCs, and explicitly demon- 
strate possible functional roles for the various currents [1]. 
The model presently includes descriptions of eleven non-linear somatic 
currents, including three putative Na + currents - INa-t-ig, INa-rep, and 
INa-t,it; six K + currents that have been reported in the literature - IDa 
(Delayed Rectifier), IA, Ic, 1.4Hp (After-hyperpolarization), IM, and IQ; 
and two Ca 2+ currents, also reported previously - Ic, and 
The electrotonic structure of the HPC is modelled with a soma/short- 
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 Rail conditions [3]), the Zi, 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. 
84 
In part this paper will address the following question: if neural nets 
are realizable using elements that have simple integrarive all-or-nothing re- 
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- 
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- 
sumptions as to how information is encoded in neuronal output. The clas- 
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. 
 Spike shape. 
Note that these variables apply to patterns of repetitive firing 1. The 
relative phase of different inputs to a single cell is very important at low 
firing rates, but becomes less so as firing frequency approaches the time 
constant of the postsynaptic membrane or some other rate-limiting process 
in the synaptic transduction (e.g. neurotransmitter release or post synap- 
tic channel activation/deactivation kinetics). Frequency modulation during 
bursts/spike trains may be important in the interaction of a given axon's 
output with other inputs at the target neuron. Cessation of firing due to 
mechanisms intrinsic to the cell (as opposed to the end of input) may be 
Single spikes may be considered as degenerate cases of repetitive firing responses. 
85 
important, for example, in that cell's transmission function. Finally, modu- 
lation of spike shape may have several consequences, which will be discussed 
later. 
4 Physiological Modulation of HPC Currents 
In order for modulation of HPC currents to be considered as potential in- 
formation processing mechanisms in vivo, it is necessary to identify physio- 
logical modulators. For several of the currents described here such factors 
have been identified. For example, there is evidence that IM is inhibited 
by muscarinic (physiologically, cholinergic) agonists [2], that 1,4 is inhib- 
ited by acetylcholine [6], and that 1.4HP is inhibited by noradrenaline [5]. 
In fct, the list of neurotransmitters which are active non-synaptically is 
growing rapidly. It remains to be seen whether there are as yet undiscov- 
ered mechanisms for modulating other HPC currents, for example the three 
Na + currents proposed in the present model. Some possible consequences 
of such mechanisms will be discussed later. 
5 HPC Currents and Information Processing 
The role of a given channel on the HPC electrical response depends on its 
temporal characteristics as a function of voltage, intracellular messengers, 
and other variables. This is complicated by the fact that the opening and 
closing of channels is equivalent to varying conductances, allowing both lin- 
ear and non-linear operations (e.g. [4] and [7]). In particular, a current 
which is activated/deactivated over a period of hundreds of milliseconds 
will, to a first approximation, act by slowly changing the time constant of 
the membrane. At the other extreme, currents which activate/deactivate 
with sub-millisecond time constants act by changing the trajectory of the 
membrane voltage in complicated ways. The classic example of this is the 
role of Na + currents underlying the action potential. 
To investigate how the different HPC currents may contribute to the 
information processing of this neuron, we have looked at how each current 
shapes the HPC response to a simple repertoire of inputs. At this stage 
in our research the inputs have been very basic - short somatic current 
steps that evoke single spikes, long lasting somatic current steps that evoke 
spike trains, and current steps at the distal end of the dendritic cable. By 
examining the response to these inputs the functional roles of the HPC 
86 
Current [[ Spike Shape Spike Threshold tin/Frequency-Intensity 
IN- t,.ig + -]--]-+ - 
INa-rep + ++ +++ 
ICa -(++) -(+) q- (+-t-q-) 
IDR ++ + ++ 
1.4 + ++ ++ 
Ic + - +++ 
IAHP - q-q- +q-q- 
IM - q- q- 
Table 1: Putative functional roles of HPC somatic currents. Entries in 
parentheses indicate secondary role, e.g. Ca 2+ activation of K + current. 
currents can be tentatively grouped into three (non-exclusive) categories: 
 Modulation of spike shape. 
 Modulation of firing threshold, both for single and repetitive spikes. 
 Modulation of semi-steady-state membrane time constant. 
 Modulation of repetitive firing, specifically the relationship between 
strength of tonic input and frequency of initial burst and later "steady 
state" spike train. 
Table I summarizes speculative roles for some of the HPC currents as 
suggested by the simulations. Note that while all four of the listed char- 
acteristics are interrelated, the last two are particularly so and are lumped 
togetler in Table 1. 
5.1 Possible Roles for Modulation of F! Characteristic 
Again, it has been traditionally assumed that neural information is encoded 
by (steady-state) frequency modulation, e.g. the number of spikes per second 
over some time period encodes the output information of a neuron. For 
example, muscle fiber contraction is approximately proportional to the spike 
frequency of its motor neuron 2 If the physiological inhibition of a specific 
2In fact, where action potential propagation is a stereotyped phenomena, such as in 
long axons, then the timing of spikes is the only parameter that may be modulated. 
87 
Stimulus Intensity (Constant Current) 
Figure 1: Classical relation between total neuronal input (typically tonic 
current stimulus) and spike firing frequency [solid line] and (qualitative) 
biological relationships [dashed and dotted lines]. The dotted line applies 
when INa-rp is blocked. 
current changes the FI characteristic, this allows one way to modulate that 
neuron's information processing by various agents. 
Figurel contrasts the classical input-output relation of a neuron and 
more biological input-output relations. The relationships have several fea- 
tures which can be potentially modulated either physiologically or patho- 
logically, including saturation, threshold, and shape of the curves. Note in 
particular the cessation of output with increased stimulation, as the alepo- 
larizing stimulus prevents the resetting of the transient inward currents. 
For the HPC, simulations show (Figure 2 and Figure 3) that blocking the 
putative INa-rep has the effect of causing the cell to "latch-up" in response 
to tonic stimulus that would otherwise elicit stable spike trains. Both de- 
polarizing currents and repolarizing currents play a role here. First, spike 
upstroke is mediated by both IN-p and the lower threshold IN-tig; at 
high stimuli repolarization between spikes does not get low enough to reset 
INa-trig. Second, spikes due to only one of these Na + currents are weaker 
and as a result do not activate the repolarizing K + currents as much as 
normal because a) reduced time at depolarized levels activates the voltage- 
dependent K + currents less and b) less Ca 2+ influx with smaller spikes 
reduces the Ca2+-dependent activation of some K + currents. The net re- 
sult is that repolarization between spikes is weaker and, again, does not reset 
INa-trig, 
Although the current being modulated here (IN-ep) is theoretical, the 
88 
99.9 
2 n $tnulus Hornml  
olta9e (nV) Tne (sec) ( 1.Be-3) 
ta9e (nV) Ttne (sec) (M 1.Be-3) 
Figure 2: Simulation of repetitive firing in response to constant current 
injection into the soma. In this series, with the "normal" cell, a stimulus 
of about 8 nA (not shown) will cause to cell to fire a short burst and then 
cease firing. 
possibility of selective blocking of INa-?ep allows a mechanism for shifting 
the saturation of the neuron's response to the left and, as can be seen by 
comparing Figures 2 and 3, making the FI curve steeper over the response 
range. 
5.2 Possible Roles for Modulation of Spike Threshold 
The somatic firing threshold determines the minimal input for eliciting a 
spike, and in effect change the sensitivity of a cell. As a simple example, 
blocking INa-t?ig in the HPC model raises threshold by about 10 millivolts. 
This could cause the cell to ignore input patterns that would otherwise 
generate action potentials. 
There are two aspects of the firing "threshold" for a cell - static and 
dynamic. Thus, the rate at which the soma membrane approaches thresh- 
old is important along with the magnitude of that threshold. In general 
the threshold level rises with a slower depolarization for several reasons, in- 
cluding partial inactivation of inward currents (e.g. INa-trig) and partial 
activation of outward currents (e.g. IA [8]) at subthreshold levels. 
89 
Time (sec) ( 1.Be-3) 
2 n8 Stimulus, u/o I-Ha-ReD 
I o.ba9e (mY) Time (sec) ( 1.Be-3) 
I" ' ?' ' ' 2' 
4 n8 Stimuluss w/o I-Na-Rep 
tm9e (mV) Time (sec) 
6 nFt Stimulus, w/o I-lm-Rep 
Figure 3: Blocking one of the putative Na + currents (IN,-r,p) causes the 
HPC repetitive firing response to fail at lower stimulus than "normal". This 
corresponds to the leftward shift in the saturation of the response curve 
shown in Figure 1. 
Thus it is possible, for example, that I helps to distinguish tonic den- 
dritic distal synaptic input from proximal input. For input that eventually 
will supply the same depolarizing current at the soma, dendritic input will 
have a slower onset due to the cable properties of the dendrites. This slow 
onset could allow I to delay the onset of the spike or spikes. A simi- 
lar depolarizing current applied more proximally would have a faster onset. 
Sub-threshold activation of I on the depolarizing phase would then be in- 
sufficient to delay the spike. 
5.3 Possible Roles for Modulation of Somatic Spike Shape 
How important is the shape of an individual spike generated at the soma? 
First, we can assume that spike shape, in particular spike width, is unimpor- 
tant at the soma spike-generating membrane - once the soma fires, it fires. 
However, the effect of the spike beyond the soma may or may not depend 
on the spike shape, and this is dependent on both the degree which spike 
propagation is linear and on the properties of the pre-synaptic membrane. 
Axon transmission is both a linear and non-linear phenomena, and the 
shorter the axon's electrotonic length, the more the shape of the somatic 
9O 
action potential will be preserved at the distal pre-synaptic terminal. At 
one extreme, an axon could transmit the spike a purely non-linear fashion 
- once threshold was reached, the classic "all-or-nothing" response would 
transmit a stereotyped action potential whose shape would be independent 
of the post-threshold soma response. At the other extreme, i.e. if the axonal 
membrane were purely linear, the propagation of the somatic event at any 
point down the axon would be a linear convolution of the somatic signal 
and the axon cable properties. It is likely that the situation in the brain lies 
somewhere between these limits, and will depend on the wavelength of the 
spike, the axon non-linearities and the axon length. 
What role could be served by the somatic action potential shape modu- 
lating the pre-synaptic terminal signal? There are at least three possibilities. 
First, it has been demonstrated that the release of transmitter at some pre- 
synaptic terminals is not an "all-or-nothing" event, and in fact is a function 
of the pre-synaptic membrane voltage waveform. Thus, modulation of the 
somatic spike width may determine how much transmitter is released down 
the line, providing a mechanism for changing the effective strength of the 
spike as seen by the target neuron. Modulation of somatic spike width could 
be equivalent to a modulation of the "loudness" of a given neuron's message. 
Second, pyramidal cell axons often project collateral branches back to the 
originating soma, forming axo-somatic synapses which result in a feedback 
loop. In this case, modulation of the somatic spike could affect this feedback 
in complicated ways, particularly since the collaterals are typically short. 
Finally, somatic spike shape may also play a role in the transmission of 
spikes at axonal branch points. For example, consider a axonal branch point 
with an impedance mismatch and two daughter branches, one thin and one 
thick. Here a spike that is too narrow may not be able to alepolarize the 
thick branch sufficiently for transmission of the spike down that branch, with 
the spike propagating only down the thin branch. Conversely, a wider spike 
may be passed by both branches. Modulation of the somatic spike shape 
could then be used to direct how a cell's output is broadcast, some times 
allowing transmission to all the destinations of an HPC, and at other times 
inhibiting transmission to a limited set of the target neurons. 
For HPCs much evidence has been obtained which implicate the roles 
of various HPC currents on modulating somatic spike shape, for example 
the 'a2+-dependent K + current Ic [9]. Simulations which demonstrate 
the effect of Ic on the shape of individual action potentials are shown in 
Figure 4. 
91 
Uoltage ('nU) 'Volt'9 e' (nU') ......... 
line (sec) (x 1.0e-8) line (sec) (x 
_--80.8 -88.0 
Current (nR) o., ICurrent (nR)F, 
lie!() i..ee-) lie (ec) (-...ee-) 
. .e ?_? 2.'e-.,_.__-:,5.e .e .p. ,3.e ,.e ,5.e 
19 9 .-19.9 I-Ha-Trig 
 I-DR 
Figure 4: Role of Ic during repolarization of spike. In the simulation on the 
left, Ic is the largest repolarizing current. In the simulation on the right, 
blocking Ic results in an wider spike. 
6 
The Assumption of Somatic Vs. Non-Somatic 
Currents 
In this research the somatic response of the HPC has been modelled under 
the assumption that the data on HPC currents reflect activity of channels 
localized at the soma. However, it must be considered that all channel pro- 
teins, regardless of their final functional destination, are manufactured at 
the soma. Some of the so-called somatic channels may therefore be ves- 
tiges of channels intended for dendritic, axonal, or pre-synaptic membrane. 
For example, if the spike-shaping channels are intended to be expressed for 
pre-synaptic membrane, then modulation of these channels by endogenous 
factors (e.g. ACh) takes place at target neuron. This may seem disarlvan- 
tageous if a factor is to act selectively on some afferent tract. On the other 
hand, in the dendritic field of a given neuron it is possible only some affer- 
ents have certain channels, thus allowing selective response to modulating 
agents. These possibilities further expand the potential roles of membrane 
channels for computation. 
92 
7 
Other Possible Roles of Currents for Modulat- 
ing HPC Response 
There are many other potential ways that HPC currents may modulate the 
HPC response. For example, the relationship between intracellular Ca 2+ 
and the Ca2+-dependent K + currents, Ic and IAHp, may indicate possible 
information processing mechanisms. 
Intracellular Ca 2+ is an important second messenger for several intracel- 
lular processes, for example muscular contraction, but excessive [Ca2+]in is 
noxious. There are at least three negative feedback mechanisms for limiting 
the flow of Ca 2+: voltage-dependent inactivation of Ca 2+ currents; reduc- 
tion of Eta (and thus the Ca 2+ driving force) with Ca 2+ influx; and the just 
mentioned Ca2+-mediation of repolarizing currents. A possible information 
processing mechanism could be by modulation of IAHp, which plays an im- 
portant role in limiting repetitive firing 3. Simulations suggest that blocking 
this current causes Ic to step in and eventually limit further repetitive fir- 
ing, though after many more spikes in a train. Blocking both these currents 
may allow other mechanisms to control repetitive firing, perhaps ones that 
operate independently of [Ca2]i n. Conceivably, this could put the neuron 
into quite a different operating region. 
8 
Populations of Neurons Vs. Single Cells: Im- 
plications for Graded Modulation of HPC Cur- 
rents 
In this paper we have considered the all-or-nothing contribution of the var- 
ious channels, i.e. the entire population of a given channel type is either 
activated normally or all the channels are disabled/blocked. This descrip- 
tion may be oversimplified in two ways. First, it is possible that a blocking 
mechanism for a given channel may have a graded effect. For example, it is 
possible that cholinergic input is not homogeneous over the soma membrane, 
or that at a given time only a portion of these afferents are activated. In 
either case it is possible that only a portion of the cholinergic receptors are 
bound, thus inhibiting a portion of channels. Second, the result of channel 
inhibition by neuromodulatory projections must consider both single cell 
3The slowing down of the spike trains in Figure 2 and Figure 3 is mainly due to the 
buildup of [Ca2+]i,, which progressively activates more IAHr. 
93 
response and population response, the size of the population depending on 
the neuro-architecture of a cortical region and the afferents. For example, 
activation of a cholinergic tract which terminates in a localized hippocampal 
region may effect thousands of HPCs. Assuming that the IM of individual 
HPCs in the region may be either turned on or off completely with some 
probability, the behavior of the population will be that of a graded response 
of IM inhibition. This graded response will in turn depend on the strength 
of the cholinergic tract activity. 
The key point is that the information processing properties of isolated 
neurons may be reflected in the behavior of a population, and vica-versa. 
While it is likely that removal of a single pyramidal cell from the hippocam- 
pus will have zero functional effect, no neuron is an island. Understand- 
ing the central nervous system begins with the spectrum of behavior in its 
functional units, which may range from single channels, to specific areas of 
a dendritic tree, to the single cell, to cortical or nuclear subfields, on up 
through the main subsystems of CNS. 
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