A summary of the findings with respect to expression and standard aggregate statistics is shown in Table . Before examining the patterns presented a brief discussion of the analyses and their limitations is in order.
Table 1 Summary of findings with respect to molecular aggregation in response to agrin, LN1, and combination stimuli. AL, agrin and laminin. Sequential administrations were similar to the AL combination and have been omitted for clarity. + indicates significant (more ...)
With respect to average expression of AChRs and α-DG, the approach assumes these molecules are uniformly distributed along the z-axis (one sample of which – the cell meridian – is sampled). Confocal sections support this generalization (not shown) so that these samples of the cell surface can be taken as representative measures of overall expression.
There are additional subtleties involved in measuring aggregate size and number. The presented data represent aggregates detected or observed per cell image, so as to provide for ready comparison to other published work. These values are quite different from the best estimates of the number of aggregates actually present on a per cell basis. Assuming aggregates are uniformly distributed along the z axis, and that they are globular in shape (well approximated by circles on average), the probability of detecting an aggregate of diameter d on a cell of diameter D is
This means that estimates of the true aggregate number per cell are a larger multiple of the number observed when the aggregates are small. This can be grasped qualitatively by imagining optical sections near (along the z axis) to those presented. By uniformity these would appear on average quite similar in aggregates detected to the meridian samples, but a larger fraction of these would be new sections of previously detected aggregates as their size increased. Thus for example the data presented in Figure (4.69 ± .21, controls; 6.65 ± .25, agrin) are corrected to 296 ± 16 (controls) and 357 ± 21 (agrin) estimated aggregates per cell. The trends presented (Results) are thus somewhat diminished (a 20% increase instead of a 42% increase), but the increases and their statistical significance remain.
As with aggregate number the observed size is not the best estimate of actual aggregate size; because many aggregates detected are actually slightly above or below the meridian their size in cross section will be underestimated. Geometrical considerations, given the assumptions outlined above, lead to the conclusion that observed aggregate size is reduced from actual size by about 21%. This estimate is not sensitive to aggregate size (it would be completely independent given perfect optical sectioning) and therefore has no effect on the trends reported.
The estimates presented for the increase in number of receptor aggregates induced by agrin are considerably smaller than those in previous studies (reviewed in [25
]). This may in part be due to the algorithms used: previous studies have depended upon the human observer to count aggregates defined as fluorescent regions above some threshold in size, while the approach described here utilizes software which is equally sensitive to very small aggregates. Alternatively, it may be that spherical muscle cell cultures, attached to the substrate by a small percentage of the membrane area, are intrinsically different in their response to agrin due perhaps to less organized cytoskeleton.
The distributions of aggregate sizes reveal additional information about the induction of aggregation (Figure ). In the case of AChRs, we see that agrin actually reduces the population of intermediate size aggregates (1–2 μm) in favor of larger aggregates (Figure left). Laminin similarly increases the frequency of large aggregates, but also increases the number of intermediate size aggregates (Figure left). Together the two stimuli broaden out the distribution, further increasing both intermediate and larger sized aggregates (Figure left). Amongst the α-DG aggregate distributions there is no difference between controls and cells stimulated with agrin while LN1 alone or with agrin increases both intermediate and larger αDG aggregates (Figure , right).
Figure 6 Aggregate size distributions following the various stimulation protocols. Each left-right pair represents the frequency histograms of aggregate size for AChRs (left) and α-DG (right). A, controls (no stimulus). B, agrin. C, laminin. D, agrin and (more ...)
The significant patterns emerging from the data are as follows (see Table ). First, receptor expression was increased by both agrin, laminin, and their combinations. This means that mass action effects of greater receptor expression could in principle account for some of the changes in aggregate parameters as discussed below. It is of further significance that the effects seem to be additive, suggesting that the mechanisms involved are independent. α-DG expression is also increased with agrin, while the expression in laminin stimulated cells could not be determined.
Second, there is a reversal in the roles of agrin and laminin induction with respect to the numbers of receptor and αDG aggregates per cell. Agrin increases the number of receptor aggregates but LN1 does not, while the reverse is true of α-DG aggregates.
Third, aggregate size is reversed for AChRs and αDG following stimulation by agrin. Agrin increases aggregate size for receptors, but decreases it for α-DG. This is consistent with a recent finding that receptor aggregate size increased in α-DG-deficient myotubes[23
Finally, receptor aggregate size was increased by all stimulus combinations, but the number of aggregates per cell and the aggregate density is reversed for agrin and LN1; the former increases aggregate number but not density, while the latter increases aggregate density but not number in the standard protocols. This similarity in aggregate size (agrin vs. LN1) contradicts previous findings in C2 myotubes, while increase in aggregate density via LN1 stimulation is in agreement with this report[1
]. We should also note however that these measures of density are averaged over the micron scale and are not inconsistent with lowered density on the nanometer scale as previously reported[6
Correlation of aggregates
This is the first report in which entire slices of membrane have been compared in their entirety for correlation of AChR and α-DG distribution. Accordingly the question arises as to how this approach can be compared with previous studies which demonstrate a visible colocalization of AChRs and α-DG in muscle cells stimulated by nerve terminals [19
] or agrin [4
]. First we note that the present results do support a significant colocalization of the two molecules in agrin stimulated cells as compared to controls (Figure ), in general agreement with previous findings. That the correlation coefficient never approaches unity is also consistent with the previous work – in general it has been found that AChR aggregates contain α-DG, but visible concentrations of α-DG can be found in the absence of AChRs. Thus there appears to be a "one way correlation"; whether the stimulus is agrin or laminin AChR aggregation is an excellent predictor of α-DG aggregation, but the converse is not found (see particularly [4
]). This lack of reciprocity will of course reduce the label correlation as measured in the present study.
Nevertheless it is apparent from visual observations (e.g. Figure ) that there is less perfect colocalization of α-DG within AChR aggregates
in the present study than reported previously (see for example [4
] Figure 9 for a comparable study using Xenopus
muscle cell cultures). It seems likely that this is due to the more minimalist culture conditions used in the present study – younger cells, plated on clean glass coverslips, lacking in extensive adhesion plaques and presumably endowed with a less stratified cytoskeleton. This is supported by the finding that 48 hours of laminin stimulus is required for an increase in aggregate number, while in the 24-hour protocol reported at present only aggregate size is increased. It is to be expected that with greater stimulation time the colocalization would increase, which presents the prospect of studying the relative dynamics of AChR and α-DG colocalization.
Distribution of aggregates
The observation that receptor aggregates are distributed differently than would be expected at random deserves further comment. As a first approximation there are three ways that receptor aggregates on a given cell could be distributed: randomly, closer together, or further apart than random. A random distribution would imply that aggregate dynamics (initiation, development, and dispersal) are independent of that for neighboring aggregates. Aggregates distributed further apart than random would imply a local competition for the molecules required for aggregate formation or development or alternatively, regionally increased levels of components which cause aggregate dispersal. Conversely, a distribution of aggregates closer together than random could result from a local reduction in the rate of dispersal, or a regionally enhanced rate of initiation or development of new aggregates. Of course these effects need not be mutually exclusive – it could be that aggregate dynamics are cooperative in small regions of membrane while simultaneously competitive over larger scales.
We found that spontaneous receptor aggregates were distributed closer together than random (Figure ) although the deviation was small and only just significant statistically. However agrin and LN1 appear to have very different effects on aggregate distribution. Agrin dramatically increased the proximity of receptor aggregates, while laminin stimulation resulted in random distributions of aggregates. Interestingly, this latter effect was dominant, in the sense that agrin/LN1 combinations also resulted in random distributions. α-DG distributions were found to be closer together than random in all conditions examined.