Conclusion and discussion: This study demonstrated that the GMFM-66 has good psychometric properties. By providing a hierarchical structure and interval scaling, the GMFM-66 can provide a better understanding of motor development for children with CP than the 88 item GMFM and can improve the scoring and interpretation of data obtained with the GMFM.
Because of the impracticality of assessing individually thousands of synapses in even a small neuronal circuit, a mathematical procedure has been developed to permit determination of whether or not multiplicative scaling occurred following a global alteration in neuronal activity. The outcome of this procedure is then used to constrain the kinds of underlying biophysical mechanisms of synaptic regulation within the network. For example, a possible mechanism for multiplicative synaptic scaling after global changes in neuronal activity, would be insertion or removal of AMPA receptors into/from spines by the same factor across all synapses [3], [4]. Accordingly, the accurate estimation of the scaling procedure will affect any conclusions about its functional relevance (see Discussion).
Improved scaling
The concept of multiplicative scaling originally arose from a theoretical analysis of changes in the amplitudes of miniature excitatory postsynaptic currents (mEPSCs) following a period of global silencing or disinhibition of a network [6]. In this original study, the occurrence of multiplicative scaling was assessed by the degree of overlap between two distributions of mEPSC amplitudes when one distribution was scaled mathematically to match the other. If, after mathematical scaling, the distribution of mEPSC amplitudes obtained from activity-altered neurons overlapped with that of the control mEPSCs, it was concluded that all the excitatory synapses had been scaled multiplicatively [6].
Because the existence of true multiplicative scaling is critical for the conclusions that emerge from such studies, e.g., memory preservation, the validity of the test for scaling must be carefully examined. Inaccuracy in the determination of scaling patterns would challenge the suitability of the multiplicative scaling hypothesis to account for the data, and thereby potentially alter the biological interpretation of the synaptic scaling. We show here that limitations in the original scaling method can in fact lead to a distortion in the distributions of the mEPSCs, and accordingly could result in misleading conclusions. We now propose a new method that overcomes the problems, strengthens the test for multiplicative scaling, and thereby contributes to better interpretation of the empirical underpinnings of homeostatic synaptic plasticity and its functional significance.
Second, the rank-order plot method has limitations when non-detectable subthreshold values should be estimated from an extrapolation of suprathreshold data. In rank-order plots of experimental data, the smallest mEPSCs of control and TTX-treated cells are paired with each other, but the minimal TTX-treated mEPSCs may, again, be scaled up versions of subthreshold control mEPSCs, which would not have been detected experimentally (Figs. 2C,D). In an experimental rank-order plot, the smallest TTX mEPSC must be paired with the minimal control mEPSC, and therefore, the consequent rank-order plot of TTX-treated mEPSCs represents a shift of an ideal rank-order plot that includes subthreshold amplitudes (Fig. 2C). If the data points are evenly distributed across various amplitudes (Fig. 2C), the slope of the original linear fit will be preserved in the plot of suprathreshold data. In this case, the slope alone (without the y-intercept) might appear to be an accurate scaling factor [10]. Amplitudes of synaptic currents, however, typically distribute unevenly [11], [12], [13] (cf. Figs. 1A,D). If subthreshold points are excluded from unevenly distributed data, the remaining data points in a rank-order plot are shifted by heterogeneous distances (Fig. 2D). In this case, the calculated slope, i.e., the scaling factor, diverges from its true value. Consequently, a simple linear fit to the suprathreshold data will not reveal the information present in the original scaling function. In sum, the existence of a detection threshold for mE/IPSC amplitudes challenges the validity of conclusions based on the conventional test for multiplicative scaling.
In general, if one population is derived from another by multiplicative scaling up, then this should be a reversible operation; i.e., scaling the experimental distribution down by an appropriate factor should also produce overlap between experimental and control distributions. However, the existence of the detection threshold can create a problem here as well. For example, if an experimental population with a larger mean amplitude, e.g., mEPSCs of TTX-treated cells, is scaled down to determine its overlap with a control distribution, the low-end mEPSCs will fall below the actual experimental detection threshold (Fig. 3A). Because detectable mEPSCs of control cells cannot have such small amplitudes, the calculated, scaled- down TTX mEPSCs that fall below the threshold will not have control counterparts. This results in a non-overlapping portion of the down-scaled distribution (gray area in Fig. 3A).
The question of whether or not multiplicative scaling accurately describes homeostatic plasticity within a synaptic population has important consequences for understanding the nature of the plasticity. No test that examines a population of events can unambiguously identify the underlying cellular mechanisms involved at each synapse. Nevertheless, a truly multiplicative transformation would imply that: 1) every synapse in the population was affected and, 2) every synapse was affected to a degree proportional to its own original strength. Hence, whether or not a transformation of population responses is truly multiplicative may be useful in excluding certain potential candidate mechanisms. For example, if multiplicative scaling accurately describes enhancement of synaptic strengths across a population, then any form of plasticity that affected only a subset of synapses would be ruled out as being solely responsible. Well-established candidates such as: 1) the unsilencing of silent synapses, 2) the selective elimination of only weak synapses, 3) the emergence of new synapses, or 4) addition of a fixed number (rather than percentage) of receptors to each synapse, are incompatible with the observation of a multiplicative scaling of a population of events. Similarly, if the population showed a multiplicative down-scaling, then selective elimination of a subset of synapses, or the removal of a fixed number of receptors from each synapse, could be ruled out. In contrast, rejection of the multiplicative scaling hypothesis might mean that the population was not uniformly altered, and this could lead to a search for the relevant groups of synapses and investigation of the mechanism working at each subset. In this case, the kinds of mechanisms that are incompatible with multiplicative scaling would now be favored. This consideration underscores the importance of correctly determining whether or not multiplicative scaling actually occurs.
Despite its advantages, our new method does have some limitations. Because subthreshold values after arithmetic transformation are discarded, very small amplitudes are not subjected to the test. Therefore, the scaling pattern of very small events might not always be reliably determined. To investigate this possibility, we observed that the data generated by ax+b (Fig. 4) indeed had different scaling rules for small and large amplitude events, and that our method successfully detected the non-multiplicative scaling transformation. However, we cannot conclude from this single example that the new method will always succeed, and the caveat must be kept in mind. It would be interesting to examine multiplicative scaling in cells that have very large miniature synaptic currents. If all large mE/IPSCs could be accurately detected, a test for multiplicative scaling should not require the threshold-related correction that is introduced here.
It is of course possible to imagine more complicated forms of non-multiplicative scaling that would not be detected by our analytical procedure (or others). For example, if subsets of synapses within a population experienced opposite and off-setting changes (one group became stronger and another weaker in a precisely balanced way), this might erroneously appear to be a multiplicative scaling effect. An ideal way to remove such limitations would involve specifically tracking each of thousands of individual synapses over the time course of several days or more. Such an approach is presently beyond the reach of current experimental methods, and until it is, analytical methods for assessing population changes, as proposed here, should continue to be useful.
Despite the multiplicative synaptic scaling that was revealed by our new test, recent experimental findings conflict with the hypothesis that simple multiplicative scaling always occurs. Homeostatic plasticity onto a given neuron is afferent- or target-specific, resulting in heterogeneous changes [7], [8], [25], [26], [27], [28]. Non-uniform homeostatic plasticity also occurs even with purely excitatory synapses in neuronal cultures, where some subsets of synapses are affected more than others [29], [30]. These examples of heterogeneous plasticity are different from the aforementioned local synaptic scaling because these heterogeneities occur even when all the synapses experience the same manipulation, e.g., activity deprivation, whereas the local scaling postulates any synapses of which activity is perturbed would change its strength. However, multiplicative scaling and synapse-specific homeostatic plasticity are not necessarily mutually exclusive if multiplicative scaling occurs uniformly across one type of synapse. In addition, if homeostatic scaling (i.e., amplitude change) originates from a postsynaptic mechanism and other afferent-specific modifications are presynaptic, multiplicative scaling may be co-expressed with heterogeneous, synapses-specific changes. Indeed, this appears to be the case for inhibitory synapses in the hippocampus: mIPSCs in TTX-treated slice cultures display multiplicative scaling (Fig. 3D), whereas GABAergic synapses in the same preparation experience synapse-specific changes in presynaptic release probability [8]. 2ff7e9595c
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