Abstract
In this paper, we introduce a novel simplification method for dealing with physical systems that can be thought to consist of two subsystems connected in series, such as a neuron and a synapse. The aim of our method is to help find a simple, yet convincing model of the full cascade-connected system, assuming that a satisfactory model of one of the subsystems, e.g., the neuron, is already given. Our method allows us to validate a candidate model of the full cascade against data at a finer scale. In our main example, we apply our method to part of the squid’s giant fiber system. We first postulate a simple, hypothetical model of cell-to-cell signaling based on the squid’s escape response. Then, given a FitzHugh-type neuron model, we derive the verifiable model of the squid giant synapse that this hypothesis implies. We show that the derived synapse model accurately reproduces synaptic recordings, hence lending support to the postulated, simple model of cell-to-cell signaling, which thus, in turn, can be used as a basic building block for network models.
Highlights
In theoretical neuroscience, when modeling neurobiological systems, scientists are faced with a structural problem: “What details should be included, and what details should be left out?” nervous systems are studied at many levels of abstraction, there is no general agreement on which details matter, at a particular level, and which do not
Since our goal is to reach a functional network level of abstraction that allows for network models with feedback connections, we will start by considering complete signal paths, that is, paths from conductance to conductance, from potential to potential, or from transmitter concentration to transmitter concentration (Fig. 1)
We extend the example on signal representation to include more general signal transformations by complete signal paths and apply the method to the squid giant fiber system, where we use it to derive the synapse model required to complete the signal path indicated in Fig. 4. (The more general case is treated in the appendix, along with a network example)
Summary
1.1 The need for (network) simplificationsIn theoretical neuroscience, when modeling neurobiological systems, scientists are faced with a structural problem: “What details should be included, and what details should be left out?” nervous systems are studied at many levels of abstraction, there is no general agreement on which details matter, at a particular level, and which do not. Detailed models are not necessarily better (Dayan and Abbott 2001; Herz et al 2006) They need to be compared with data, and models with too many variables and parameters can often be made to fit almost any data. Even when composed of such simplified models, the analysis of networks (which from the neuron-level form the level up) remains daunting, and many simplifying assumptions are usually made in theoretical neuroscience (Dayan and Abbott 2001). These considerations lead us to the following questions.
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