### Increased computational accuracy in multi-compartmental cable models (Lindsay et al. 2005)

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Accession:129149
Compartmental models of dendrites are the most widely used tool for investigating their electrical behaviour. Traditional models assign a single potential to a compartment. This potential is associated with the membrane potential at the centre of the segment represented by the compartment. All input to that segment, independent of its location on the segment, is assumed to act at the centre of the segment with the potential of the compartment. By contrast, the compartmental model introduced in this article assigns a potential to each end of a segment, and takes into account the location of input to a segment on the model solution by partitioning the effect of this input between the axial currents at the proximal and distal boundaries of segments. For a given neuron, the new and traditional approaches to compartmental modelling use the same number of locations at which the membrane potential is to be determined, and lead to ordinary differential equations that are structurally identical. However, the solution achieved by the new approach gives an order of magnitude better accuracy and precision than that achieved by the latter in the presence of point process input.
Reference:
1 . Lindsay AE, Lindsay KA, Rosenberg JR (2005) Increased computational accuracy in multi-compartmental cable models by a novel approach for precise point process localization. J Comput Neurosci 19:21-38 [PubMed]
Model Information (Click on a link to find other models with that property)
 Model Type: Neuron or other electrically excitable cell; Brain Region(s)/Organism: Cell Type(s): Channel(s): I Na,t; I K; Gap Junctions: Receptor(s): Gene(s): Transmitter(s): Simulation Environment: NEURON; C or C++ program; Model Concept(s): Methods; Implementer(s):
Search NeuronDB for information about:  I Na,t; I K;
 / LindsayEtAl2005 readme.txt 03-192.pdf AnalyseResults.c BitsAndPieces.c CellData.dat CompareSpikeTrain.c Ed04.tex ExactSolution.dat GammaCode Gen.tex Gen1.tex Gen2.tex Gen3.tex Gen4.tex Gen5.tex Gen6.tex GenCom.c GenCom1.c GenCom2.c GenComExactSoln.c GenerateInput.c GenerateInputText.c GenRan.ran GetNodeNumbers.c Info100.dat Info20.dat Info200.dat Info30.dat Info300.dat Info40.dat Info400.dat Info50.dat Info500.dat Info60.dat Info70.dat Info80.dat Info90.dat InputCurrents.dat InputDendrite.dat JaySpikeTrain.c JayTest1.dat JayTest100.dat KenSpikeTrain.c KenTest1.dat * KenTest10.dat KenTest100.dat * KenTest10p.dat KenTest1p.dat * KenTest2.dat KenTest2p.dat KenTest3.dat KenTest3p.dat KenTest4.dat KenTest4p.dat KenTest5.dat KenTest5p.dat KenTest6.dat KenTest6p.dat KenTest7.dat KenTest7p.dat KenTest8.dat KenTest8p.dat KenTest9.dat KenTest9p.dat LU.c Mean50.dat Mean500.dat mosinit.hoc NC.pdf NC.tex NC1.tex NC2.tex NC3.tex NC4.tex NC5.tex NC6.tex NCFig2.eps * NCFig3.eps * NCFig4.eps * NCFig5a.eps * NCFig5b.eps * NCFig6.eps * NCPics.tex NeuronDriver.hoc NewComExactSoln.c NewComp.pdf NewComp.ps NewComp.tex NewComp.toc NewComp1.tex NewComp2.tex NewComp3.tex NewComp4.tex NewComp5.tex NewComp6.tex NewCompFig1.eps NewCompFig2.eps * NewCompFig3.eps * NewCompFig4.eps * NewCompFig5a.eps * NewCompFig5b.eps * NewCompFig6.eps * NewCompPics.tex NewComSpikeTrain.c NewRes.dat NewRes60.dat NewRes70.dat NewRes80.dat NewSynRes40.dat NewTestCell.d3 NResults.res OldComExactSoln.c out.res principles_01.tex rand Ratio.dat RelErr.dat ReviewOfSpines.pdf SpikeTimes.dat TestCell.d3 TestCell1.d3 TestCell2.d3 TestCell3.d3 TestCell4.d3 testcellnew2.hoc TestCGS.c TestGen1.c TestSim.hoc TestSim020.hoc TestSim030.hoc TestSim040.hoc TestSim050.hoc TestSim060.hoc TestSim070.hoc TestSim080.hoc TestSim090.hoc TestSim1.hoc TestSim100.hoc TestSim200.hoc TestSim300.hoc TestSim400.hoc TestSim500 TestSim500.hoc
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\title{\LARGE\bf Increased computational accuracy in
multi-compartmental cable models by a novel approach for precise
point process localization}
\author{\Large\bf A.E. Lindsay\\
Department of Mathematics, University of Edinburgh,\\
Edinburgh EH9 3JZ \\[10pt]
\Large\bf K.A. Lindsay \\
Department of Mathematics, University of Glasgow,\\
Glasgow G12 8QQ \\[10pt]
\Large\bf J.R. Rosenberg$^\dagger$\\
Division of Neuroscience and Biomedical Systems,\\
University of Glasgow, Glasgow G12 8QQ}

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$^\dagger$  & \textbf{Corresponding author} \\[5pt]
& J.R. Rosenberg \\
& West Medical Building \\
& Division of Neuroscience and Biomedical Systems \\
& University of Glasgow \\
& Glasgow G12 8QQ \\
& Scotland UK \\[5pt]
& Tel\quad(+44) 141 330 6589 \\
& Fax\quad(+44) 141 330 2923 \\
& Email \verb$j.rosenberg@bio.gla.ac.uk$\\[10pt]
& \textbf{Keywords} \\[5pt]
& Compartmental models, Dendrites, Cable Equation
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\multicolumn{1}{c}{\textbf{Abstract}}\\[10pt]

Compartmental models of dendrites are the most widely used tool
for investigating their electrical behaviour. Traditional models
assign a single potential to a compartment. This potential is
associated with the membrane potential at the centre of the
segment represented by the compartment. All input to that segment,
independent of its location on the segment, is assumed to act at
the centre of the segment with the potential of the compartment.
By contrast, the compartmental model introduced in this article
assigns a potential to each end of a segment, and takes into
account the location of input to a segment on the model solution
by partitioning the effect of this input between the axial
currents at the proximal and distal boundaries of segments. For a
given neuron, the new and traditional approaches to compartmental
modelling use the same number of locations at which the membrane
potential is to be determined, and lead to ordinary differential
equations that are structurally identical. However, the solution
achieved by the new approach gives an order of magnitude better
accuracy and precision than that achieved by the latter in the
presence of point process input.
\end{tabular}
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Compartmental models have become important tools for investigating
the behaviour of neurons to the extent that a number of packages
exist to facilitate their implementation (\emph{e.g.} Hines and
Carnevale \cite{Hines97}; Bower and Beeman \cite{Bower97}). Their
use is motivated by the desire to reduce the mathematical
complexity inherent in a continuum description of a neuron. This
simplification is achieved by replacing the partial differential
equations defining the continuum description of a neuron by a
compartmental model of the neuron in which its behaviour is
described by the solution of a set of ordinary differential
equations (Rall, \cite{Rall64}).

The traditional approach to compartmental modelling, introduced by
Rall (\cite{Rall64}), assumes that a lump of membrane becomes a
compartment; the rate constants governing exchange between
compartments are proportional to the series conductance between
them". Rall's definition of a compartmental model thus
distinguishes between the input acting on a localised region of
neuronal membrane (the compartment) and the resistive properties
of the axoplasm which determines the conductances linking
compartments in his model. Other authors (\emph{e.g.} Segev and
Burke, \cite{Segev98}) treat the neuronal segment, including the
membrane and axoplasm, as the compartment. Both definitions,
however, associate a single potential with a compartment, and
assume that all input falling on the segment that is represented
by the compartment will act with this potential. For this reason
these compartments are iso-potential, and indeed Segev and Burke
(\cite{Segev98}) state this explicitly. Of course, iso-potential
compartments are a feature of the model and \emph{should not be
confused} with the true potential distribution within segments.

Compartmental models in which a compartment has a single potential
are aesthetically unsatisfactory since a compartment of this type
cannot act as the fundamental unit in the construction of a model
dendrite for two reasons. First, compartments defined by a single
potential must coexist in pairs in order to support axial current
flow, and second, half compartments are required to represent
branch points and dendritic terminals (\emph{e.g.}, Segev and
Burke, \cite{Segev98}). In the new approach to compartmental
modelling presented in this article, two potentials are assigned
to each compartment --- one to represent the membrane potential at
the proximal boundary of the segment and the other to represent
the membrane potential at its distal boundary. The new compartment
can exist as an independent entity without the need to introduce
half compartments, and can therefore function as the basic
building block of a multi-compartmental neuronal model. The new
compartments more accurately describe the influence of point
current and synaptic input to the segments they represent than
those of a traditional compartmental model.

The accuracy of the new and traditional approaches to
compartmental modelling is first assessed by calculating the error
in the somal potential of a test neuron when each approach is used
to calculate this potential ten milliseconds after the initiation
of large scale point current input. In a second comparison, the
accuracy of the two approaches is assessed by comparing the
statistics of the spike train output generated by each type of
compartmental model of the test neuron when subjected to large
scale synaptic input.


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