Computer simulation of neurone pattern processing

Signal analysis and modelling Computer simulation of neurone pattern processing R.D. Orpwood Bath Institute of Medical Engineering, BA13NG, UK

The Wolfson

Centre,

. Royal United Hospital,

Bath

ABSTRACT Physiological simulation techniques can provide a very useful additional tool with which to explore the behaviour of neurones, especially for probing those areas that are not easily accessible to experimental monitoring techniques such as activity in the dendrites. This paper explores the information processing capabilities of a cerebral cortical pyramidal neurone vringa computer simulation. 77~ computer model simulated two important aspects ofpyramidal cell behaviour: the transient distribution of membranepotential over a proportion of the apical dendritic tree of the cell, and the ability of the receptors in the neurones’ dendritic spines to undergo plastic changes. The simulation of receptor behaviour modelled the ability of receptor regions to increase their sensitivity tfa prior input had occurred when the spine head membrane was depolartid. The model was used to explore the response of the cell to different inputs. It underlined the needfor large amounts of local activity before spinal receptors changed their sensitivity. It also demonstrated the ability of pyramidal cells to both recognize patterns of input and to associate one pattern of inputs with another. It is argued that this pattern association property could be a neuronal bash fbr association learning. Keywords:

Neurone simulation, association learning, neurone pattern association, membrane potential distribution

INTRODUCTION There is much current interest in applying physiological modelling techniques to explore the behaviour of the central nervous system. Simulations of neurone-like elements provide a valuable additional technique for exploring the properties of nervous tissue’. Useful insights into ex erimental findings have been gained from such mo B els2, although much scepticism still remains from some neurobiologists3. However, many of these simulations use neurone models that are rather simple approximations of the real thing. It is felt that there must be many properties of neurones, such as their particular geometry or receptor behaviour, which must have a strong bearing on the way they process information, and that these details should be explored further. In the human brain the cerebral cortex is the site of higher cognitive functions, and the way these properties relate to its structure is an intriguing subject. The human cortex is essentially a twodimensional structure consisting of a sheet of cells about 3mm thick and 0.25m2 in area. Its structure appears to be remarkably uniform throughout the area of the cortex, and the connectivity of its cells, although superficially a tangle of neurones, axons and dendrites, is relatively straightforward on closer examination435. The properties of cortical neurones and the way they process information must have a fundamental bearing on the functioning of the cortex. The main input/output cells in the cortex are the pyramidal. cells 5. They receive inputs over a large Correspondence

and reprint requests to: Mr R.D. Orpwood

0 1992 Butterworth-Heinemann 0141-5425/92/030222-07 222

for BES

J. Biomed. Eng. 1992, Vol. 14, May

distance includin from outside the cortex, and their output axons sen 8 information over similar distances, as well as forming extensive local connections. Figure 7 illustrates the structure of a typical pyramidal cell. These cells have a pivotal role in cortical information recessing and a detailed examination of their ! ehaviour through neuromodelling techniques may provide some useful insights into the way they handle information. There are two aspects that are important to include in a simulation of pyramidal cell behaviour. The first is to model the way information is rapidly communicated throughout the cell. This communication is carried out by means of membrane potential changes. Neurones, like all cells, have an actively maintained potential difference across their cell membranes. Inputs to the cell cause local rapid transient depolarizations and these depolarizations s read throughout the cell. Any model of a yrami c!al cell needs to simulate the transient mem g rane potential distribution. The second aspect that requires modelling is the cell’s response to inputs at its receptor sites. The vast majority of excitatory inputs to pyramidal cells are to dendritic spines (see F@re 7). The cell has the ability to actively control the input sensitivity of the receptor regions. If an input is received whilst the local membrane of the dendritic s ine is depolarized due to activity elsewhere, then 8 a++ ions are admitted into the cell. These ions initiate a train of events that result in an increase in the sensitivity of the receptor. Subsequent in uts to the same receptor cause larger transient mem g rane depolarizations. In this way the cell is able to associate the arrival of an input to the

Computer simulation

Region the

modelled

in

ofneumne paitem

processing: RI?. @wood

‘J-1

simulation )I0

axon IM

Figure 2

The structure of the compartmental model. The diagwm shows the simplest model where adjacent compartments have the same geometry and where no bifurcations occur

Apical Cell body soma

or

spine

current density, Z,, can be expressed as follows:

zm =

a (I$,+ 2(AX)2Ri

Basal

dGdrites Output

axon

Figure 1 Diagram of cerebral cortical pyramidal neurone. All excitatory inputs appear to go to dendritic spines, as indicated. The region modelled in the simulation is enclosed by the dashed line, and includes 30 spines

cell with activity elsewhere. The sensitivity change is long lasting and is felt to be the mechanism underlying neuronal memory. Reviews of these learning mechanisms can be found elsewhere6T7. The variable sensitivity of the receptor regions parallels the variable weights used in artificial neural networks. This paper describes how these two neurone properties were modelled and explores the behaviour of a cell with these properties using a computer simulation.

SIMULATION METHODS Modelling the potential distribution The potential distribution over a non-excitable axon or dendrite can be described by the one-dimensional cable equation:

--CI a2v 2Ri ax2 where Z, V

= local membrane current density = potential difference across the membrane, given as the departure from its resting value = fibre radius ii = s ecific resistance of cytoplasm = 0.8 Corn = B istance along fibre X G, = membrane capacitance = 0.01 F/m2 R, = resistance of unit area of membrane = 0.2 C&m*

q+,-25,

otential, dV/dt, The rate of change of membrane can also be expressed as a simple di P erence equation:

ac_ --

Vj+L

at

Vj

(3)

At

where

Vj Vt+’ /

is the potential difference at the jth compartment at time, t is the potential difference at time, t + At:

When applied to the cable equation an expression can be simply obtained that expresses the membrane potential of compartment, j, at time t + At.

where A2 = aR /2R.1, r = R C This expres:ion appliesm tc? compartments of a dendrite that have the same dimensions and no bifurcations. Similar expressions can be simply obtained for these other situations and the ones used in the simulation are listed in the Appendix. Modelling receptor behaviour The receptor simulation was based on some previous worklo,‘l that modelled the glutamate receptor. This receptor is believed to be the excitatory receptor in pyramidal cells. When an input is received it causes a local transient membrane depoloatization in the spine head. This event was modelled as a transient change in the conductance of the spine head membrane, with a time course as expressed below and with a peak synaptic conductance of 0.4 nanosiemens12. G(t) m texp-l’P

however, it was particularly desired that representative dendritic trees should be used and so a numerical model was derived. The dendritic tree was divided into a large number of small finite compartments. Figure 2 illustrates compartments in a uniform dendrite. The membrane

(5)

where p = peak time = 0.075 ms. In order for the learning behaviour to be modelled, the peak spine head conductance initiated by an input was made variable. Its value was permanently increased by an amount proportional to the spine membrane potential existing at the time of an input. These sensitivity changes were not initiated until the s ine head was depolarized in excess of 30mV. This J e olarization threshold is the value indicated by vo Ptage clamp studies on glutamate receptorsr3.

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Computersimuhtion of nnnwx~ttern

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Orpwood

Membrane potential distributions at different time intervals from the initiation of a single input Tbe shades of grey indicate the potentials of each of the compartments in tbe model, using a logarithmic scale

Figure 3

224 J. Biomed. Eng. 1992, Vol. 14, May

Compuk-rsimulation of wurone pattern ploccssing: R.D. @f~wood well past its peak while the general potential spread

Implementation of model The region simulated in the model consisted of four terminal apical dendrites and their connection to the cell body, as shown in Figure 7. It thro incluYhed 30 s ines spread evenly over the terminal dendrites, wi tK each spine head having an input receptor. The region modelled was divided into 118

compartments, with separate corn artments being

used for each of the spine heads an B the spine necks. The cell’s response to an input was modelled by initiating a depolarization in a spine head compartment at time t = 0, using equation (5) to map its time course. The membrane potential difference at each of the 118 compartments was then computed using the appropriate compartmental equation. The computations were re ated at At time intervals following the input until t.Pe cell compartments returned to their resting potential levels. In order to maintain stability, the At interval used was 5 X l@ms. Any input received when the spine head membrane was depolarized in excess of 30mV initiated the sensitivity changes described above. All 30 spine head receptors were able to undergo these sensitivity rogram was implemented on an increases. The Acorn Archim edpes computer and written in BASIC. A typical 1Orns simulation took about 25min to run. In order to follow the potential changes, an image of the dendritic tree was displayed on the VDU with the potential of each of the compartments displayed as different colours or shades of grey. In addition, the time course of the potential changes in any of the compartments could be plotted.

RESULTS Response to single input Following a single input into the distal apical dendrites, the potential change throughout the cell could be displayed. Figure 3 shows six frames from a sequence lasting 1Oms from the initiation of the depolarization, with the membrane depolarization for each compartment indicated by shades of grey. The depolarization local to the input is very rapid and 0.16

40

0

0

1

2

3

4

5

had caused little change in the soma. By the time the soma depolarization has reached its peak at about 4ms, the apical dendrites have almost returned to their resting potential levels. Figure 4 plots the predicted potential changes in several regions of the cell. The potential spread throughout the cell to the soma is very slow compared to the rapid transient in the spine and its magnitude is very much smaller. It is not currently possible to directly measure potential changes in fine dendrites, but microelectrodes can be used to impale cell bodies and record the changes occurring there. Following conditions that cause a single input to a pyramidal cell, the soma potential changes experimentally recorded are similar to those predicted in the simulation’4~15. This result gave confidence that the model was sufficientl realistic to be used to explore the pyramidal ce G behaviour.

Soma response to trains of inputs The effect of applying a train of inputs to the same dendritic spine was explored. At low frequencies (~50 Hz) the soma response had time to return to resting levels between inputs. At higher frequencies a degree of summation of soma responses took place. Figure5 shows the response in the spine and the soma at two high frequencies, and shows the soma summation that occurred. The effect of a single input to each of two adjacent spines was explored. As shown in Figurn 6, a peak soma res onse occurred when the two inputs were separate B by 1 ms. The peak response was 7.6% higher than that obtained with no separation. This result is not due to receptor sensitivity changes as there would not have been time for these to occur between inputs. It is due to the dynamics of the depolarization process.

Spine response

to adjacent

activity

The learning behaviour of the spine head depends on the degree of depolarization that exists when it receives an input. As discussed above, the leaming behaviour does not take place until the local membrane is depolarized by more than 30mV.

0

Time Ims) Figure 4 predicted time course of membrane potential changes at several points within the new-one, following a single input to an apical dendritic spine

8

12

bo

Time (ms)

Figure 5 The effect of trains of inputs to a single spine head showing the summation of soma depolarization that occurs

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Computerrimuhtion of ncumnc pattern processing:RD. Orpwood 40

30

20

10

1 Time

Figure 6

2 between

The soma depolarization

inputs

(ms) 0

of two adjacent spine heads, with a small time delay between them

A study was subsequently carried out to explore the depolarization caused by activity in ad’acent spines. Two variables were explored: the num k er of spines. activated, and the distance of those spines from the one being monitored. In real neurones, the density of s ines is very high and their separation is variable. In tKe simulation, the spines were regularly spaced at 20pm intervals. In order to evaluate the impact of distance when more than one spine was being activated, the depolarization of the monitored spine was plotted against the mean distance from the activated spines. F&W 7 shows the results obtained. As can be seen the critical 30mV depolarization was only achieved when there was a lot of activity very close to the sample spine.

Pattern association It was predicted that pyramidal cells would have the ability to associate one pattern of inputs with another and this property was explored using the pyramidal cell model. Two patterns of four inputs were used. The first pattern was one that went to receptors with a higher than normal sensitivity. It was assumed this pattern was one that the neurone had seen before and, through prior experience, had learnt to be significant. The second pattern was a test pattern that the neurone had not seen before and went to rece tars whose sensitivity was at the nominal starting revel. The test pattern was initially put into the dendrites to measure the time course of the soma response. A learning procedure was then used in which the significant pattern was put into the dendrites, followed within a millisecond by the test pattern. The significant pattern caused a depolariza-

226

300

200

100

caused by two inputs, one to each

J. Blamed. Eng. 1992, Vol. 14, May

Mean

distance

from

spine

(urn)

Figure 7 The effect on spine head depolarization of two variables: the number of other spines activated, and their mean distance away. To achieve the 30 mV depolarization threshold required for Ca’ + entry, and therefore sensitivity changes, several spine heads need to be activated within a short distance

Significant input pattern

80

0.B Test input

60

pattern 0.6

i\

9 E

40

*p

20

0-

0

1

2

3

4

5

Time (ms)

Figure 8 Pattern association in the pyramidal neurone. The cell diagrams indicate the patterns used far the significant input and the test input: a, the depolarization in one of the spine heads and in the soma, both prior to any learning and b, the depolarization in the same regions following 5 learning sequences in which the test input was put in just after the significant input. The depolarizations shown are caused by the test input pattern on ib own

Computer simulation of neuronepattern processing:R.D. Orpwood

tion in the spines that were subsequently activated by the test pattern. The receptors activated by the test pattern therefore increased in sensitivity. Figure 8 illustrates the soma response produced by the test pattern both before and after five learning procedures. After the learning rocedures, the soma response had been increase cf by 45%. The cellular behaviour demonstrated by this computer experiment parallels classical conditioning.

DISCUSSION Monitoring of the electrical activity of neurones is currently limited to measurements of soma potential changes. The dendrites are just too fine to insert microelectodes into them. However, much of the neurones’ processing capabilities must involve the dendritic tree and at the present time measurement techniques are unable to probe it in detail. Simulation techniques such as that described in this paper, based on the known electrical properties and anatomy of the dendrites, provide a means of exploring the behaviour of dendritic activity. The display of transient membrane potential distributions, as shown in Figwe 3, provide a graphic visualization of activity in the dendritic region and the ability of being able to plot the time course of potential changes provides a very useful tool with which to explore the information processing properties of the cell. One of the crucial factors in the learning behaviour of pyramidal cells is the level of depolarization in a spine at the time of receiving an input. The results imply that the 30mV needed before any learning takes place, is quite difficult to achieve and requires the simultaneous activation of a number of spines in the same vicinity. In a real neurone, of course, it is likely that far more inputs than the four used in the study would be received, but the result does underline the importance of the 30 mV threshold measured in experimental studies and the stringent conditions needed for learning to take place. The results demonstrated the ability of pyramidal cells to recognize and associate patterns of input. This result has an important bearing on the role of pyramidal cells in the information processing of the cortex. All information coming into the cortex is in the form of patterns of activity and it might be expected that pyramidal cells would be able to recognize components of these attems. The interesting property demonstrated by IFie simulation was the ability to associate one pattern with another. If a yramidal cell had learnt to recognize one particular tL‘nd of in ut pattern then any other input attem that hap ene cf to occur at the same time woul CFeventually lea cf to a large soma response on its own. Pattern association may well be the way that the pyramidal cell increases its repertoire of stored memories. Association of events in the real world enables new memories to be formed. These events are communicated to the cortex as large patterns of activity and transmitted to millions of pyramidal cells. Each pyramidal cell just sees a pattern of inputs representing a tiny component of the overall cortical input. If these tiny corn one& can associate with each other on the cellu Par level and lead to new

patterns bein stored, then this property may well be underlying association the neurona P mechanism learning.

CONCLUSIONS Neuronal simulations provide an extra techni ue for exploring the properties of neurones especi 9 ly for the dendritic areas that are difficult to explore experimentally. The simulation described in the paper showed the high level of dendritic acitivity needed for the receptor sensitivity changes that underlie memory to occur. It also showed that cortical pyramidal cells would be expected to be able to recognize patterns amongst their inputs and to associate one pattern of inputs with another. Pyramidal pattern association may well be the neuronal mechanism underlying association learning.

REFERENCES 1. Traub RD, Miles R, Wong RKS. Model of the origin of rhythmic population oscillations in the hippocampal slice. Science 1989; 243: 1319-1325. 2. Zipser D, Anderson RA. A back-propagation programmed network that simulates response properties of a subset of posterior parietal neurons. Nature 1988; 331: 679-684. 3. Crick F. The recent excitement about neural networks. Nature 1989; 337: 129-132. 4. Shepherd GM. A basic circuit of cortical organisation. In: Gazzaniga MS, ed. Perspectives in Memory Research. Cambridge: MIT Press, 1988; 93-134. 5. Shepherd GM. TI%E Synaptic Organisation of the Brain. New York: Oxford University Press, 1979. 6. Brown TH, Kairiss EW, Keman CC. Hebbian synapses: biophysical mechanisms and algorithms. Ann Rev Neurosci 1990; 13: 475-511. 7. Madison DV, Malenka RS, Nicoll RA. Mechanisms underlying long-term potentiation of synaptic transmission. Ann Rev Neurosci 1991; 14: 379-397. 8. Dodge FA, Cooley JW. Action potentials of the motorneuron. IBMJRes Dev 1973; 17: 219-229. 9. Rall W. Core conduction theory and cable properties of neurons. In: Kandel ER, ed. Handbook of Physiology, The Nervous System, Section 1, Vol. 1, The Cellular Biology of Neurons. Bethesda: American Physiological Society, 1977; 39-97. 10. Orpwood RD. Basic module for an adaptive control system based on neurone information processing. JBiomed Eng 1988; 10: 201-205. 11. Orpwood RD. Mechanisms of association learning in the post-synaptic neurone. J X&-or Biol 1990; 143: 145-162. 12. Rall W, Segev I. Excitable dendritic spine clusters: nonlinear synaptic processing. In: Cottrill RMJ, ed. Computer Simulation in Brain Science. Cambridge, UK: Cambridge University Press, 1988; 26-43. 13. Mayer ML, Westbrook GL, Guthrie PB. Voltage dependent block by Mg++ of NMDA receptors in spinal cord neurones. Nature 1984; 309: 261-263. 14. Barrionuevo G, Kelso SR, Johnson D, Brown TH. Conductance mechanisms responsible for long term potentiation in monosynaptic and isolated excitatory synaptic inputs to hippocampus. J Neurophysiol 1986; 55: 540-550. 15. Anderson P. Synaptic integration in hippocampal CA1 pyramids. In: StormMathisen J, Zimmer J, Ottersen OP, eds. Progressin Brain Research. Amsterdam: Elsevier, 1990; 83: 215-222.

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& S

i

j+l

“J

a

C

6’ i-1

d

Ql10 1

2

fF i

“J

S

i+l

Figure 9 The various component geometriesused for the compartmental model

e

f

APPENDIX derivation of the basic compartmental model used for the simulation was described in the section on ‘Modelling the potential distribution’. This Ap endix lists the numerical equations used for the various other component geometries, as shown in Figure 9. TlYese include the modelling of the dendritic spines and situations where bifurcations occur.

The

(b)

V:+‘=(

where

&)2

t

S 7

A2 = s,

[ (2-a)

V/+(2-P)

I$+,),+

T= R,G,

I a=

2

‘=

f2Ax

l+-

G = G(t)

228 J. Biomed. Eng. 1992, Vol. 14, May

0a,

s

Ax

V[j+1)2- V: 6-2P-a+ (

111

Ax 2 7 ( S

+ Vi