@MISC{Natschläger_findingthe, author = {Thomas Natschläger and Wolfgang Maass}, title = {Finding the Key to a Synapse}, year = {} }

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Abstract

Experimental data have shown that synapses are heterogeneous: different synapses respond with different sequences of amplitudes of postsynaptic responses to the same spike train. Neither the role of synaptic dynamics itself nor the role of the heterogeneity of synaptic dynamics for computations in neural circuits is well understood. We present in this article methods that make it feasible to compute for a given synapse with known synaptic parameters the spike train that is optimally fitted to the synapse, for example in the sense that it produces the largest sum of postsynaptic responses. To our surprise we find that most of these optimally fitted spike trains match common firing patterns of specific types of neurons that are discussed in the literature.

... 4 5 time [sec] Figure 1: Synaptic heterogeneity. A The parameters ¢ , § , and ¥ can be determined for biological synapses. Shown is the distribution of values for inhibitory synapses investigated =-=in [2]-=- which can be grouped into three mayor classes: facilitating (F1), depressing (F2) and recovering (F3). B Synapses produce quite different outputs for the same input for different values of the parame...

...o predict the response of a given synapse to a given spike train once proper values for these characteristic synaptic parameters have been found. The analysis of this article is based on the model of =-=[1], where three ¢¤-=-£¦¥¤£¦§ parameters control the dynamics of a synapse and a fourth ¨ parameter – which corresponds to the synaptic “weight” in static synapse models – scales the absolute sizes of the p...

...on algorithm known as “sequential quadratic programming” (SQP) 4 which is the state of the art approach for heuristically solving constrained optimization problems such as (2). We refer the reader=-= to [8]-=- for the mathematical background of this technique and to [4] for more details about the application of SQP for approximately computing optimal spike trains. Optimal Spike Trains for Different Firing ...

...mmon firing patterns (“accommodating”, “non-accommodating”, “stuttering”, “bursting” and “regular firing”) of neocortical interneurons reported under controlled conditions in vitro=-= [2, 5] and in vivo [7]. For � ex¤ � , , �-=-� and ample the temporal patterns of the “keys” to the synapses ¤ ¥ the discharge patterns of “accommodating” [2], “bursting” [5, 7], and “stuttering” [2] cells respectively. 100% 67...

...eurons (see Fig. 4). Note that there is experimental evidence that cortical neurons can switch their intrinsic firing behavior from “bursting” to “regular” depending on neuromodulator mediated=-= inputs [5, 6]-=-. This findings provide support for the idea of preferential addressing of postsynaptic targets implemented by the interplay of dynamic synapses and the intrinsic firing behavior of the presynaptic ne...

...as to replace the continuous state variable ��� by a discrete � variable � variable , and round ����� ��� ������� ��� � . For more details about the dis=-=cretization of the model we refer the reader to [4]. ����� � . 3 ���-=-��£��� to the nearest value of the corresponding discretesD [sec] 1 0.75 0.5 0.25 1 0.75 0.5 0.25 0 F [sec] F1−type F2−type F3−type PSfrag replacements U 0.75 1 0.25 0 0.5 PSfrag repl...

...response. ¥ If on the other hand the “key” to synapse ¤ � ( ¤ � ) is tested ¤ � on synapse ( ¤ � ) this synapse produces significantly less postsynaptic response. ¥ ¤ ¥ ¥ ¥ Fig. =-=4. Recent experiments [5, 6]-=- show that neuromodulators can control the firing mode of cortical neurons. In [5] it is shown that bursting neurons may switch to regular firing if norepinephine is applied. Together with the specifi...