explaination of code creating dendritic spines

[citron]

Hello, I am trying to understand this piece of code from a model by Z. F. Mainen and T. J. Sejnowski (1996):

Code: Select all

spine_dens = 1
spine_area = 0.83 

proc add_spines() { local a
  forsec dendritic {
    a =0
    for(x) a=a+area(x)

    F = (L*spine_area*spine_dens + a)/a

    L = L * F^(2/3)
    for(x) diam(x) = diam(x) * F^(1/3)
  }
}
 

It should include spines into dendrites by increasing their membrane area by a factor of 0.83. Can anyone please explain, why did authors choose ale the steps in procedure add_spines() ? I understand the code until the line for(x) a=a+area(x).

[Raj]

Code: Select all

 for(x) a=a+area(x)

This bit of code iterates over all segments in the current section and adds up the contribution from each segment to calculate the area as specified by the pyramidal cell reconstruction.

Code: Select all

F = (L*spine_area*spine_dens + a)/a

Calculate with which factor the area needs to be increased to account for the membrane surface in the spines. The spine density is specified here in terms of the number of spines per unit of length (i.e. per um) , as opposed to the number of spines per surface area (um^2).

Code: Select all

    L = L * F^(2/3)
    for(x) diam(x) = diam(x) * F^(1/3)

Include the extra area in the cell by adjusting diameter and length but keep the axial resistance constant. Axial resistance is proportional to L divided by diam^2. Note: there is extra leak current and extra capacitance so the electrotonic length of the section so equiped with spines does change!

[ted]

Good explanation, Raj.

An alternative strategy for representing the effects of spines on the electrical properties
of neurites is to multiply specific membrane capacitance and channel densities by a factor
that specifies the contribution of spine membrane to neurite surface area.

These two strategies, which might be called "anatomical rescaling" and "biophysical
rescaling," have their own pros and cons--

Anatomical rescaling automatically affects all inserted mechanisms that have density
parameters, so is easy to use with models that have spatially inhomogeneous properties
(as long as it is correct to assume that channel density in spines is identical to channel
density in the adjacent neurite). However, since it changes L, it distorts shape plots and
range variable plots (plots of the spatial variation of range variables along sections).

Biophysical rescaling does not distort shape or range variable plots. However, each
inserted mechanism's density must be individually rescaled in each segment. This can
be tedious if there are many mechanisms, especially when there are subsets of sections
that have different inserted mechanisms. The trick is to use conditional statements of the
form
if ismembrane("suffix") for (x,0) gbar_suffix*=factor
where
suffix is the "name" of an inserted mechanism
gbar_suffix is its density parameter
factor is a number > 1 that specifies the effect of spines on effective neurite surface
area.

Food for thought:

1. There are several published studies of spine density in various neurons. Some present
results as spines per unit length, others as spines per unit area. Most data indicate that
spine density is not constant over the surface of a cell, but varies with distance from the
soma. Density per unit area tends to be more uniform than density per unit length.

2. No neurites are cylindrical. Electron micrographs reveal that irregular outlines are
the rule, and some profiles are even convex on one side and concave on the other.
Variation along the length of a neurite can be striking, so that apparent neurite diameter
as seen in light microscopy may have little relationship to the actual surface area or the
cross-sectional area of the neurite's contents. Ideally one would like to have a
quantitative description of these relationships, but I am not aware of any systematic
study of neurite profiles of any of the commonly investigated neuron classes, or any
paper that reports "form factors" that could be applied to light microscopy measurements
for the purpose of improving the estimate of neurite surface and cross section area.

[CCohen]

Hello,

I have trouble understanding how these two lines of code work:

L = L * F^(2/3)
for(x) diam(x) = diam(x) * F^(1/3)

1. Why does making L longer by a factor of F^(2/3), and making diam(x) bigger by a factor of F^(1/3), add spines to the dendritic section at a density of 1 spine/um, for an individual spine area of 0.83 um^2. Basically I do not understand why F^(2/3) and F^(1/3).

2. How does increasing the diameter of dendritic compartments by a factor greater than 1 (F^(1/3)) affect Ri in the dendritic compartments? Ri is defined as the cytoplasmic resistivity of 1 cm^3 of cytoplasm, in units of ohm-cm. I expect ri to be affected (=Ri/pi*diameter of a dendritic process), but what about Ri? Is it not supposed to be independent of surface area or diameter? How does NEURON compute Ri? Does NEURON use diameter or surface area to compute Ri? Because if it does not, then I see no affect on Ri via the computation above, as mentioned above.

[ted]

I have trouble understanding how these two lines of code work

The approach is explained in the papers written by proponents of anatomical rescaling. Those were published decades ago--early to mid 1980s as I recall. Almost nobody uses that approach any more.

2. How does increasing the diameter of dendritic compartments by a factor greater than 1 (F^(1/3)) affect Ri in the dendritic compartments? Ri is defined as the cytoplasmic resistivity of 1 cm^3 of cytoplasm, in units of ohm-cm.

You may call cytoplasmic resistivity Ri, but in NEURON it is called Ra. Ra is unaffected by anatomical rescaling. ri will not be affected if one does anatomical rescaling properly, i.e. scales both length and diameter.

How does NEURON compute Ri?

From the specified geometry and Ra. See chapter 5 of The NEURON Book. If you don't have that, see
Hines, M.L. and Carnevale, N.T.
The NEURON simulation environment.
Neural Computation 9:1179-1209, 1997
which is available from a link at http://www.neuron.yale.edu/neuron/nrnpubs

It can be informative to explore the relationship between ri, the anatomical and biophysical specification of a model neurite, and the discretization parameter nseg, by constructing toy models and comparing simulation results with ones own calculations.