Models of Dopaminergic and Serotonergic Signaling

Abstract

Mathematical models of dopaminergic and serotonergic synapses have enabled the authors to study quantitative aspects of the synthesis, release and reuptake of dopamine and serotonin, to investigate the effects of autoreceptors, and to explore the influence of the neurochemistry on the firing patterns of cells known to be involved in the behavioral responses to dopaminergic and serotonergic signaling.

The models consist of coupled ordinary differential equations. Parameters are determined from biochemical and physiological measurements.

Three results from recent in silico experiments with the dopaminergic and serotonergic synapse models are described: (1) influence of substrate inhibition on the stability of dopamine and serotonin synthesis; (2) a predicted connection between serotonin reuptake transporter (SERT) density on terminals and tonic firing rates; (3) an explanation of data from autoreceptor knock-out experiments.

Mathematical models are useful for studying the biology of dopaminergic and serotonergic signaling because these systems are complex and involve interactions between neurochemistry and neurobiology.

References

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Appendix

In this appendix we describe the differential equations that constitute the model. The time-dependent variables in the model are the concentrations of the substrates in the pink boxes in [Fig. 1]; full names are given in the legend. The velocities of reactions (or net velocities in case of reversible reactions) or velocities of transport are always indicated by a capital V with subscripts and superscripts indicating which enzyme, transporter, or other process is involved. In each case, the variables that the process depends on are indicated. On the left sides we include square brackets around the variables as a reminder that the units of the variables are concentration (μM); on the right sides of the equations we omit the square brackets because they make the equations harder to read.

In order to indicate what is involved in the construction of such a model, we discuss a few of the terms. V _TPH (Trp, bh4, e5HT ) is the velocity of the reaction catalyzed by tryptophan hydroxylase that depends on the concentrations of cytosolic tryptophan and dihydrobiopterin, as well as the concentration of extracellular 5HT via the autoreceptors. The term release (e5HT ) · fire (t) · v5HT the rate of release of 5HT from the vesicles into the extracellular space per unit time at time t. v5HT is the concentration of 5HT in the vesicular compartment and fire (t) represents the firing rate of the neuron scaled so that it has value one in case of tonic firing. release (e5HT ) represents the effect on release of vesicular 5HT by the extracellular 5HT concentration via the autoreceptors. The term fluox (t) · VSERT (e5HT ) represents the rate of reuptake of 5HT from the extracellular space into the cytosol by the SERT transporters. fluox (t) is the fraction of transporters that are unblocked by fluoxetine at time t, so it equals one in the absence of fluoxetine. The term Vrem (e5HT ) represents the removal of 5HT from the extracellular space by uptake into capillaries and glial cells or diffusion out of the tissue. The most difficult part of the construction of the model is deciding on the functional form of the velocities (i. e., Michaelis-Menten or other forms) and determining appropriate values for the constants involved. This is described in [2] to which we refer the reader for details. It is worthwhile to point out that there is not a single “correct” model of a serotonergic synapse, nor are there single “correct” values for each parameter. As we remarked in the main body of the paper, the density of SERTs has been shown to vary by a factor of 5 in different terminal regions, which means the Vmax of the SERT will vary by the same factor depending on which terminals one is discussing. Similarly, it is known that TPH synthesis rates vary from brain region to brain region as do the types and densities of autoreceptors. It is very likely that these variations in parameters are not random but have functional significance. The purpose of a model, such as the one we have described here, is that it enables one to study how the overall behavior of the system depends on the properties of each of the parts (SERTs, autoreceptors, TPH), and how the system behavior changes when the parts change or are influenced by pharmacological agents.

Correspondence