In this letter to MIT cognitive neuroscientist Tomaso Poggio, written in anticipation of a meeting of the Neurosciences Research
Program at the Salk Institute October 14-17, 1981, Crick discussed current ideas about dendritic spines developed by himself
as well as by his collaborator, California Institute of Technology computational neuroscientist Christof Koch.
Item is a photocopy.
Number of Image Pages:
4 (390,227 Bytes)
1981-10-06 (October 6, 1981)
Original Repository: Wellcome Library for the History and Understanding of Medicine. Francis Harry Compton Crick Papers
Thank you so much for your long and helpful letter, the manuscripts and the paper from TINS. I discovered yesterday that
the latter idea is not entirely new, since it is fairly clearly stated in the discussion (p. 332) in Peters and Kaiserman-Abramof,
Am. J. Anat. (1970), 127:321-356. I enclose a copy. They make the point, which I think Nick Swindale missed, that if the
scheme is to work the spines must, in some sense, "reach out to the axon", otherwise, as far as I can see, nothing
is gained. In the simplest scheme this would imply that the spines only formed after the axons were there. I will check
with Max Cowan if this is the case. However one could always argue that the spines in the critical period are constantly
disappearing (when not used) and others reforming, in which case they could reach out at that stage.
Now as to the main points of your letter. Both Graeme and I had concluded, with you, that the rhythm idea should be left
out. In fact I have cut the last page almost entirely. I note your point about the multiplicative term but notice that for
two excitatory synapses, each on a spine, this term, in the simple case, is negative. For rapid modification we need a positive
term (i.e., the two synapses should reinforce each other), so some special mechanism is needed.
Now about Rall. I don't really like your division into the two terms, A and S, since both depend on the dimensions of
the spine. It seems to me you are making heavy weather of a simple problem. As I see it you have
[handwritten scientific formulas]
Now since K25 depends very little on the shape of the spine, for any given position of the spine on the dendrite, we can consider
it independent of g and R.
Now Rall wished to express the condition that the (absolute) change in Vs was a maximum for a given percentage change in R.
Thus we need
to be a maximum. As far as I can see this implies that
R = 1/g + K22
As you rightly point out, if g is large, this gives us
R = K22
which is Rall's impedence-matching condition. As one can see, if g is smaller, the condition is a little different, but
in the same direction, as Rall points out by giving numerical examples. Cristof's notes (pp 10 and 11) come to the same
general conclusion; his figures for optimal spine dimensions (p. 11) seem to me to be in the same ballpark as what is observed.
(Though I suspect that the dimensions of spines are a little bigger and the specific resistance of the spine neck cytoplasm
a little higher.) However I am not clear what value of g Cristof assumed for these calculations, though several values are
given in his Fig. 6.
The other factor is "range compression." To avoid this, as you say, you must have gK11 (which is g(R+K22) small compared
to unity. Another way of looking at it is to ask that the absolute change in Vs be a maximum for a given percentage change
in g, keeping R and K22 fixed. This assumed that memory is at last partly coded by changes in the value of g. Then one obtains
(as one might expect from the symmetry of the problem)
1/g = R + K22
Clearly one cannot satisfy both this condition and the previous one
R = 1/g + K22
unless K22 is much smaller than the other terms and Rg = 1. In other words, R must be big and g must be small, for any given
K22. However R must not be made enormous or the approximation that
K15 = K25
breaks down, because appreciable current will leak out through the spine membrane.
We can reasonably ask, what is the diminution factor produced by the spine. If the synapse were on the dendritic shaft, we
have (putting R=0 in our usual equation)
Vs = (gK25E)/(1 + gK22)
Thus the diminution factor is
(1 + gK22)/(1 + gK22 + gR)
If we obey the condition for maximum change due to R (Rg = 1 + gK22) thus becomes l/2. That is, the synapse on the spine
is half as effective as a corresponding one on the dendrite. This is not too bad.
Unfortunately the condition that g is small means that the punch of the synapse (in either position) is also small, so that
some compromise is necessary. For example, we might take
R = 2K22
gK22 = 1/2
so that gR = 1
thus gives a diminutive factor of 0.6. Whether these values are reasonable I don't know since I have not fully digested
Cristof's notes. The value of g is really an unknown but I suspect that the ratio of R to K22 is largely a geometrical
factor (i.e., it doesn't depend too much on the choices for Rm and Ri). Christof must have data on this.
As you can see, the two requirements conflict, in that for R to have any effect it must be large enough to choke back the
input and, if it does do this, some range-compression is inevitable.
This all assumes that one wants Vs to vary as g varies. However if long-term memory is in the neck of the spine (and more
or less independent of the value of g, provided g is large enough) then there is no conflict, although the system is "wasteful"
in that the synaptic punch is not fully used, but then that is often Nature's way. It would also have the advantage that
statistical variations in g (due to random fluctuations in the number of packets of transmitter released) would be smoothed
out. However this leaves us with the problem of how to preserve long-term memory for a long time in the face of metabolic
fluctuations, etc. To approach this we have to know what molecular structure determines the shape of the neck of the spine.
I suppose another solution is to assume that long-term memory is represented by all the synapses without spines. On pyramidal
cells, these are all inhibitory ones. On non-spiney stellates (most of which produce inhibition) they can be either on the
soma or on the dendrites. This would imply that long-term memory is especially tied to inhibitory effects, leaving the spines
to handle ultra-short memory. I can't say I feel happy with any of this.
I have not yet had time to think carefully about the active membrane case, though I can see I shall have to.
I don't know quite what to say about the old spine note. It comes to much the same conclusion as Rall's but it could
be expressed perhaps a little more clearly. Perhaps we should talk about this.
I am still hoping you will be coming to the NRP meeting at La Jolla, but just in case you don't I am sending this to MIT.
I'll keep an extra copy here in case you arrive here without having seen it.
Graeme and I are having some fun speculating about sleep and dreams but still too early to say much about it.
Odile is in fine form. We have had an ex-au-pair girl (now 40) staying with us for a few weeks. She is very vivacious so
it's been a lively time.
Our love to Barbara and Martino,
F. H. C. Crick
P.S. Another way to alter synaptic weight is to alter alpha, the time course of synaptic activity. I think this gets over
the difficulty that the choking back effect, needed to make the neck of the spine have some effect, reduces the effect of