Dynamic Modulation of Neurons and Networks 
Eve Marder 
Center for Complex Systems 
Brandeis University 
Waltham, MA 02254 USA 
Abstract 
Biological neurons have a variety of intrinsic properties because of the 
large number of voltage dependent currents that control their activity. 
Neuromodulatory substances modify both the balance of conductances 
that determine intrinsic properties and the strength of synapses. These 
mechanisms alter circuit dynamics, and suggest that functional circuits 
exist only in the modulatory environment in which they operate. 
1 INTRODUCTION 
Many studies of artificial neural networks employ model neurons and synapses that are 
considerably simpler than their biological counterparts. A variety of motivations underly 
the use of simple models for neurons and synapses in artificial neural networks. Here, 
I discuss some of the properties of biological neurons and networks that are lost in overly 
simplified models of neurons and synapses. A fundamental principle in biological nervous 
systems is that neurons and networks operate over a wide range of time scales, and that 
these are modified by neuromodulatory substances. The flexible, multiple time scales in 
the nervous system allow smooth transitions between different modes of circuit operation. 
2 NEURONS HAVE DIFFERENT INTRINSIC PROPERTIES 
Each neuron has complex dynamical properties that depend on the number and kind of 
ion channels in its membrane. Ion channels have characteristic kinetics and voltage 
511 
512 Marder 
dependencies that depend on the sequence of amino acids of the protein. Ion channels 
may open and close in several milliseconds; others may stay open for hundreds of 
milliseconds or several seconds. 
Some neurons are silent unless they receive synaptic inputs. Silent neurons can be 
activated by depolarizing synaptic inputs, and many will fire on rebound from a 
hyperpolarizing input (postinhibitory rebound). Some neurons are tonically active in the 
absence of synaptic inputs, and synaptic inputs will increase or decrease their firing rate. 
Some neurons display rhythmic bursts of action potentials. These bursting neurons can 
display stable patterns of oscillatory activity, that respond to perturbing stimuli with 
behavior characteristic of oscillators, in that their period can be stably reset and 
entrained. Bursting neurons display a number of different voltage and time dependent 
conductances that interact to produce slow membrane potential oscillations with rapid 
action potentials riding on the depolarized phase. In a neuron such as R15 of Aplysia 
(Adams and Levitan 1985) or the AB neuron of the stomatogastric ganglion (STG) 
(Harris-Warrick and Flarnm 1987), the time scale of the burst is in the second range, but 
the individual action potentials are produced in the 5-10mc time scale. 
Neurons can generate bursts by combining a variety of different conductances. The 
particular balance of these conductantes can have significant impact on the oscillator's 
behavior (Epstein and Marder 1990; Kepler et al 1990; Skinner et al 1993), and therefore 
the choice of oscillator model to use must be made with care (Somers and Kopell 1993). 
Some neurons have a balance of conductances that give them bistable membrane 
potentials, allowing to produce plateau potentials. Typically, such neurons have two 
relatively stable states, a hyperpolarized silent state, and a sustained depolarized state in 
which they fire action potentials. The transition between these two modes of activity can 
be made with a short depolarizing or hyperpolarizing pulse (Fig. 1). Plateau potentials, 
like fiip-fiops" in electronics, are a "short-term memory" mechanism for neural circuits. 
The intrinsic properties of neurons can be modified by sustained changes in membrane 
potential. Because the intrinsic properties of neurons depend on the balance of 
conductantes that activate and inactivate in different membrane potential ranges and over 
a variety of time scales, hyperpolarization or depolarization can switch a neuron between 
modes of intrinsic activity (Llin,'is 1988; McCormick 1991; Leresche et al 1991). 
An interesting "memory-like"effect is produced by the slow inactivation properties of 
some K + currents (McCormick 1991; Storm 1987). In cells with such currents a 
sustained depolarization can "mplify"a synaptic input from subthreshold to 
suprathreshold, as the sustained depolarization causes the K + current to inactivate 
(Marom and Abbott 1994; Turrigiano, Marder and Abbott in preparation). This is another 
"hort-term memory"mechanism that does not depend on changes in synaptic efficacy. 
Dynamic Modulation of Neurons and Networks 513 
A. CONTROL B 10'7M TNRNFLRFNH:, 
lse .Sse 
Figure 1: Intracellular recording from the DG neuron of the crab STG. A: control saline, 
a depolarizing current pulse elicits action potentials for its duration. B: In 
SDRNFLRFamide, a short depoIarization elicits a plateau potential that lasts until a short 
hyperpolarizing current pulse terminates it. Modified from Weimann et al 1993. 
2 INTRINSIC MEMBRANE PROPERTIES ARE MODULATED 
Biological nervous systems use many substances as neurotransmitters and 
neuromodulators. The effects of these substances include opening of rapid, relatively non- 
voltage dependent ion channels, such as those mediating conventional rapid synaptic 
potentials. Alternatively, modulatory substances can change the number or type of 
voltage-dependent conductances displayed by a neuron, and in so doing dramatically 
modify the intrinsic properties of a neuron. In Fig. 1, a peptide, SDRNFLRFamide 
transforms the DG neuron of the crab STG from a state in which it fires only during a 
alepolarizing pulse to one in which it displays long-lasting plateau properties (Weimann 
et al 1993). The salient feature here is that modulatory substances can elicit slow 
membrane properties not otherwise expressed. 
3 SYNAPTIC STRENGTH IS MODULATED 
In most neural network models synaptic weights are modified by learning rules, but are 
not dependent on the temporal pattern of presynaptic activity. In contrast, in many 
biological synapses the amount of transmitter released depends on the frequency of firing 
of the presynaptic neuron. Facilitation, the increase in the amplitude of the postsynaptic 
current when' the presynaptic neuron is activated several times in quick succession is quite 
common. Other synapses show depression. The same neuron may show facilitation at 
some of its terminals while showing depression at others (Katz et al 1993). The 
facilitation and depression properties of any given synapse can not be deduced on first 
principles, but must be determined empirically. 
Synaptic efficacy is often modified by modulatory substances. A dramatic example is seen 
in the Aplysia gill withdrawal reflex, where serotonin significantly enhances the amplitude 
of the monosynaptic connection from the sensory to motor neurons (Clark and Kandel 
1993; Emptage and Carew 1993). The effects of modulatory substances can occur on 
different branches on a neuron independently (Clark and Kandel 1993), and the same 
modulatory substance may have different actions at different sites of the same neuron. 
514 Marder 
Electrical synapses are also subject to neuromodulation (Dowling, 1989). For example, 
in the retina dopamine reversibly uncouples horizonal cells. 
Modulation of synaptic strength can be quite extreme; in some cases synaptic contacts 
may be virtually invisible in some modulatory environments, while strong in others. The 
implications of this for circuit operation will be discussed below. 
Hormones Neuromodulators 
[] DA [] ACh [] AST 
: 5-HT [] DA [] Buc 
[] Oct ;J GABA [] cCCK 
[] CC [] Oct  IornTK 
[] cCCK [] Momod 
[] IomTK  Pr 
[] RPCH [] RPCH 
[] SDRN 
 RN 
aln 
Sensory Transmitters 
I ACh 
AST [] 
Figure 2: Modulatory substances found in inputs to the STG. See Harris-Warrick et aL, 
1992 for details. Figure courtesy of P. Skiebe. 
4 TRANSMITTERS ARE COLOCALIZED IN NEURONS 
The time course of a synaptic potential evoked by a neurotransmitter or modulator is a 
characteristic property of the ion channels gated by the transmitter and/or the second 
messenger system activated by the signalling molecule. Synaptic currents can be relatively 
fast, such as the rapid action of ACh at the vertebrate skeletal neuromuscular junction 
where the synaptic currents decay in several milliseconds. Alternatively, second 
messenger activated synaptic events may have durations lasting hundreds of milliseconds, 
seconds, or even minutes. Many neurons contain several different neurotransmitters. 
It is common to find a small molecule such as glutamate or GABA colocalized with an 
amine such as serotonin or histamine and one or more neuropeptides. To describe the 
synaptic actions of such neurons, it is necessary to determine for each' signalling molecule 
how its release depends on the frequency and pattern of activity in the presynaptic 
Dynamic Modulation of Neurons and Networks 515 
terminal, and characterize its postsynaptic actions. This is important, because different 
mixtures of cotransmitters, and consequently of postsynaptic action may occur with 
different presynaptic patterns of activity. 
5 NEURAL NETWORKS ARE MULTIPLY MODULATED 
Neural networks are controlled by many modulatory inputs and substances. Figure 2 
illustrates the patterns of modulatory control to the crustacean stomatogastric nervous 
system, where the motor patterns produced by the only 30 neurons of the stomatogastric 
ganglion are controlled by about 60 input fibers (Coleman et al 1992) that contain at least 
15 different substances, including a variety of amines, amino acids, and neuropeptides 
(Marder and Weimann 1992; Harris-Warrick et al 1992). Each of these 
modulatory substances produces characteristic and different effects on the motor patterns 
of the STG (Figs. 3,4). This can be understood if one remembers that the intrinsic 
membrane properties as well as the strengths of the synaptic connections within this 
group of neurons are all subject to modulation. Because each cell has many conductantes, 
many of which are subject to modulation, and because of the large number of synaptic 
connections, the modes of circuit operation are theoretically large. 
6 CIRCUIT RECONFIGURATION BY MODULATORY CONTROL 
Figure 3 illustrates that modulatory substances can tune the operation of a single 
functional circuit. However, neuromodulatory substances can also produce far more 
extensive changes in the functional organization of neuronal networks. Recent work on 
the STG demonstrates that sensory and modulatory neurons and substances can cause 
neurons to switch between different functional circuits, so that the same neuron is part 
of several different pattern generating circuits at different times (Hooper and Moulins 
1989; Dickinson et al 1990; Weimann et al 1991; Meyrand et al 1991; Heinzel et al 
1993). 
In the example shown in Fig. 4, in control saline the LG neuron is firing in time with the 
fast pyloric rhythm (the LP neuron is also firing in pyloric time), but there is no ongoing 
gastric rhythm. When the gastric rhythm was activated by application of the peptide 
SDRNFLRFNm, the LG neuron fired in time with the gastric rhythm (Weimann et al 
1993). These and other data lead us to conclude that it is the modulatory environment 
that constructs the functional circuit that produces a given behavior (Meyrand et al 
1991). Thus, by tuning intrinsic membrane properties and synaptic strengths, 
neuromodulatory agents can recombine the same neurons into a variety of circuits, 
capable of generating remarkably distinct outputs. 
Acknowledgements 
I thank Dr. Petra Skiebe for Fig 3 art work. Research was supported by NS17813. 
516 Marder 
CONTROL 
PD 
PILOCARPINE SEROTONIN 
'.g I,1 i,h l. hL, lu [,,I, .,., ![i 1!I;,111, ,.,,,,,.,, !. I, 
LP 
PD 
Ivn 
SDRNFLRFNH 2 
PROCTOLIN 
CCAP 
Figure 3: Different forms of the pyloric rhythm different modulators. Each panel, the top 
two traces: simulataneous intracellular recordings from LP and PD neurons of crab STG; 
bottom trace: extracellular recording, lvn nerve. Control, rhythmic pyloric activity 
absent. Substances were bath applied, the pyloric patterns produced were different. 
Modified from Marder and Weimann 1992. 
DG - - 
dgn 
LG 
VD 
Figure 4: Neurons switch between different pattern-genreating circuits. Left panel, the 
gastric rhythm not active (monitored by DG neuron), LG neuron in time with the pyloric 
rhythm (seen as activity in LP neuron). Right panel, gastric rhythm activated by 
SDRNFLRFamide, monitored by the DG neuron bursts recorded on the dgn. LG now 
fired in alternation with DG neuron. Pyloric time is seen as the interruptions in the 
activity of the VD neuron. Modified from Marder and Weimann 1992. 
Dynamic Modulation of Neurons and Networks 517 
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