Nonlinear functions in the dendritic tree

[Michael Hucka]

>>>>> On 12 Sep 94, lcw at ukc.ac.uk (L.C.Walton) said:

  lcw> Can somebody provide me with a reference to the kinds of
  lcw> non-linearities observed in dendritic trees. In particular, I'm
  lcw> interested to find out if there are any effects determined by the
  lcw> number of times a dendrite has branched, i.e. if a bifurcation is
  lcw> close to the cell body, the function is mainly additive whereas at the
  lcw> extremities, the function is more multiplicative.  Please email
  lcw> replies.

I'm not an expert in this, but as a starting point I suggest looking at work
by Idan Segev, Wilfrid Rall, Gordon Shepherd, and Christof Koch, in
particular under the topics of cable theory and dendritic computation.

If I remember correctly, the chapter by Gordon Shepherd and Christof Koch in
the following excellent book addresses your question:
 
@BOOK{shepherd:90,
       EDITOR = {Gordon M. Shepherd},
	TITLE = {The Synaptic Organization of the Brain},
    PUBLISHER = {Oxford University Press},
	 YEAR = 1990,
      ADDRESS = {New York},
      EDITION = {Third Edition}
}

The following chapters also discuss electrical properties of dendritic trees
and are more oriented towards computational accounts:

@INCOLLECTION{koch:87a,
       AUTHOR = {Christof Koch and Tomaso Poggio},
        TITLE = {Biophysics of Computation:  Neurons, Synapses, and Membranes},
    BOOKTITLE = {Synaptic Function},
       EDITOR = {Gerald M. Edelman and W. Einar Gall and W. Maxwell Cowan},
    PUBLISHER = {Wiley},
      ADDRESS = {New York},
         YEAR = 1987
}

@INCOLLECTION{koch:90,
       AUTHOR = {Christof Koch},
        TITLE = {Biophysics of Computation:  Toward the Mechanisms Underlying
                 Information Processing in Single Neurons},
    BOOKTITLE = {Computational Neuroscience},
    PUBLISHER = {MIT Press},
         YEAR = 1990,
       EDITOR = {Eric L. Schwartz},
      CHAPTER = 9,
        PAGES = {97--113}
}

A good book that includes a couple of chapters on cable theory and
compartmental models of dendrites (among other things) is:

@BOOK{koch:89,
       EDITOR = {Christof Koch and Idan Segev},
	TITLE = {Methods in Computational Neuroscience},
    PUBLISHER = {MIT Press},
	 YEAR = 1989,
      ADDRESS = {Cambridge, Mass.}
}

The following article also discusses models of dendritic properties:

@ARTICLE{segev:92,
       AUTHOR = {Idan Segev},
        TITLE = {Single Neurone Models:  Oversimple, Complex and Reduced},
      JOURNAL = {Trends in Neuroscience},
         YEAR = 1992,
       VOLUME = 15,
       NUMBER = 11,
        PAGES = {414--421}
}

There is a lot more out there, but hopefully this will help you.

Mike
--
-- Mike Hucka (michael.hucka at umich.edu)
   University of Michigan, Ann Arbor, Mich.