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  1. Evaluation Summary:

    The present MS describes an effort to create a general mathematical model of synaptic neurotransmission. The authors invested great efforts to create a complex model of the presynaptic mechanisms. This is an exceptionally challenging task and it falls short of a true general theory. Nonetheless, the model will be an important addition to an emerging field attempting to generate predictive models of complex neuronal biophysical processes, including synaptic transmission.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript.The reviewers remained anonymous to the authors.)

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  2. Reviewer #2 (Public Review):

    The present MS describes an effort to create a general mathematical model of synaptic neurotransmission. The authors invested great efforts to create a complex model of the presynaptic mechanisms, but their approach of the postsynaptic mechanisms is way oversimplified. The authors claim that their model is consistent with lots of in vivo and in vitro experimental data, but this night be true for a small subselection of experimental papers (they cite 7 experimental papers regularly in the MS!). The authors also indicate that their modeling has a realistic foundation, namely they can relate some parameters in their equations to molecules/molecular mechanisms. One example is the parameter N, which they claim indicate the number of SNARE complexes requires for fusion. The reviewer finds it rather misleading because it alludes that there is a parameter for complexin, Rim1, Rim-BP, Munc13-1 etc... The equations clearly cannot formulate and reflect diversity due to different isoforms of even the above mentioned key presynaptic molecules.

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  3. Reviewer #1 (Public Review):

    Wang and Dudko derive analytical equations for one special case of a model of Ca-dependent vesicle fusion, in the attempt to find a "general theory" of synaptic transmission. They use a model with 2 kinetically distinct fast and slow pools (equation 1).

    Critique

    1. Overall, the analytical approach applied here remains limited to the quite arbitrarily chosen 2-pool model. Thus, while the authors are able to re-capitulate the kinetics of transmitter release under a series of defined intracellular Ca-concentration steps, [Ca]i (see Fig. 2B; data from Woelfel et al. 2007 J. Neuroscience), this is nevertheless not surprising because the data by Woelfel et al. was originally also fit with a 2-pool model. More importantly, the 2-pool model is valid for describing release kinetics at high [Ca]i, but it cannot account for other important phenomena of synaptic transmission like e.g. spontaneous and asynchronous release which happen at lower [Ca]i, with different Ca cooperativity (Lou et al., 2005). Along the same lines, the derivations of the equations by Wang and Dudko are not valid in the range of low [Ca]i below about 1 micromolar (see "private recommendations" for details). This, however, limits the applicability of the model to AP-driven transmitter release, and it shows that based on one specific arbitrarily chosen model (here: the 2-pool model), one cannot claim to build a realistic and full "theory" for synaptic transmission.

    2. In their derivations, Wang and Dudko collapse the intracellular Ca-concentration [Ca]i, a parameter directly quantified in the several original experiments that went into Fig. 2A, into a dimensionless relative [Ca]i "c" (see equation 7). Similarly, the release rates are collapsed into a dimensionless quantity. With these normalizations, Ca-dependent transmitter release measured in several preparations seems to fall onto a single theoretical prediction (Fig. 2A). The deeper meaning behind the equalization of the data was unclear, except a demonstration that the data from these different experiments can in general be described with a two-pool model, which is at the core of the dimensionless equations. One issue might be that many of the original data sets used here derive from the same preparation (the calyx of Held), and therefore the previous data might not scatter strongly between studies. This could be clarified by the authors by also plotting the data from all studies on the non-normalized [Ca]i axis for comparison. Furthermore, it would be useful to include data from other preparations, like the inner hair cells (Beutner et al. 2001 Neuron; their Fig. 3) which likely have a lower Ca-sensitivity, i.e. are right-shifted as compared to the calyx (see discussion in Woelfel & Schneggenburger 2003 J. Neuroscience). Thus, it is unclear why normalization of [Ca]i to "c" should be an advantage, because differences in the intracellular Ca sensitivity of vesicle fusion exist between synapses (see above), and likely represent important physiological differences between secretory systems.

    3. Finally, the authors use their model to derive the number of SNARE proteins necessary for vesicle fusion, and they arrive at the quite strong conclusion that N = 2 SNAREs are required. Nevertheless, this estimate doesn't fit with the number of n = 4-5 Ca2+ ions which the original studies of Fig. 2A consistently found. The Ca-sensitivity at the calyx of Held, and the steepness of the release rate versus [Ca]i relation is determined by Ca-binding to Synatotagmin-2 (the specific Ca sensor isoform found at the calyx synapse), as has been determined in molecular studies at the calyx synapse (see Sun et al. 2007 Nature; Kochubey & Schneggenburger 2011 Neuron). Furthermore, in other secretory cells, the number of SNARE proteins has been estimated to be {greater than or equal to} 3 (Mohrmann et al., Science 2010).

    Taken together, the derivation of the analytical equations for the kinetic scheme of a 2-pool model is mathematically interesting, and the scholarly derived equations are trustworthy. Nevertheless, the derived analytical model in fact captures only a specific stage of synaptic transmission focusing on Ca-dependent fusion of vesicles from two pools at [Ca]i >1 microM. Other important processes and mechanistic components (e.g. spontaneous, asynchronous release, Ca-dependent pool replenishment, postsynaptic factors) are either over-simplified or remained out of the scope of the theory. Therefore, the paper is far from providing a general "theory for synaptic transmission", as the title promises.

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