Dynamic clamp analyses of

Page 1

Jean-Marc Goaillard and Eve Marder Physiology 21:197-207, 2006. doi:10.1152/physiol.00063.2005 You might find this additional information useful... This article cites 84 articles, 55 of which you can access free at: http://physiologyonline.physiology.org/cgi/content/full/21/3/197#BIBL This article has been cited by 5 other HighWire hosted articles: Membrane Resonance in Bursting Pacemaker Neurons of an Oscillatory Network Is Correlated with Network Frequency V. Tohidi and F. Nadim J. Neurosci., May 20, 2009; 29 (20): 6427-6435. [Abstract] [Full Text] [PDF]

A novel approach to physiology education for biomedical engineering students J. DiCecco, J. Wu, K. Kuwasawa and Y. Sun Advan Physiol Educ, March 1, 2007; 31 (1): 45-50. [Abstract] [Full Text] [PDF] Hybrid Systems Analysis of the Control of Burst Duration by Low-Voltage-Activated Calcium Current in Leech Heart Interneurons A. Olypher, G. Cymbalyuk and R. L. Calabrese J Neurophysiol, December 1, 2006; 96 (6): 2857-2867. [Abstract] [Full Text] [PDF] Dynamic clamp: a powerful tool in cardiac electrophysiology R. Wilders J. Physiol., October 15, 2006; 576 (2): 349-359. [Abstract] [Full Text] [PDF] Medline items on this article's topics can be found at http://highwire.stanford.edu/lists/artbytopic.dtl on the following topics: Physiology .. Synaptic Conductance Updated information and services including high-resolution figures, can be found at: http://physiologyonline.physiology.org/cgi/content/full/21/3/197 Additional material and information about Physiology can be found at: http://www.the-aps.org/publications/physiol

This information is current as of December 13, 2009 .

Physiology (formerly published as News in Physiological Science) publishes brief review articles on major physiological developments. It is published bimonthly in February, April, June, August, October, and December by the American Physiological Society, 9650 Rockville Pike, Bethesda MD 20814-3991. Copyright Š 2005 by the American Physiological Society. ISSN: 1548-9213, ESSN: 1548-9221. Visit our website at http://www.the-aps.org/.

Downloaded from physiologyonline.physiology.org on December 13, 2009

Electrical Synapses Between AII Amacrine Cells: Dynamic Range and Functional Consequences of Variation in Junctional Conductance M. L. Veruki, L. Oltedal and E. Hartveit J Neurophysiol, December 1, 2008; 100 (6): 3305-3322. [Abstract] [Full Text] [PDF]


REVIEWS

PHYSIOLOGY 21: 197–207, 2006; 10.1152/physiol.00063.2005

Dynamic Clamp Analyses of Cardiac, Endocrine, and Neural Function The dynamic clamp introduces artificial conductances into cells to simulate elec-

Jean-Marc Goaillard and Eve Marder Volen Center and Biology Department, Brandeis University, Waltham, Massachusetts

trical coupling, votage-dependent, leak, and synaptic conductances. This review describes how the dynamic clamp has been used to address various questions in the cardiac, endocrine, and nervous systems.

Electrical Coupling Creating artificial electrical connections between two cells is the easiest task that can be performed using

dynamic clamp. Since electrical coupling is one of the most critical features involved in the proper function of the cardiac syncytium, it is no surprise that the first artificial electrical junction was developed in 1979 to study the synchronization of clusters of beating ventricular cells in chicken (57). Soon thereafter, analog and digital systems were being used extensively in studies of cardiac function to artificially couple biological cells (25, 26, 32, 35, 63, 69) or to couple biological cells to model cells (27, 74, 76, 77, 79) (see Hybrid Networks). The artificial electrical coupling of cardiac muscle cells has been used to address questions such as 1) the occurrence of unidirectional block of action potential conduction between ventricular cells of different sizes (32, 69), 2) the conduction of the action potential at the junction between Purkinje and ventricular cells, 3) the basis of arrhythmogenesis (26), and 4) the involvement of voltage-dependent conductances in action potential conduction (25, 35, 63). FIGURE 2A shows an example of the use of an artificial electrical junction and voltage clamp to determine the behavior of the calcium current during discontinuous conduction of the action potential between two ventricular cells of same size (35). After recording successes and failures of conduction for a high coupling resistance, the authors used the recorded waveforms as a voltage clamp command to define the precise magnitude and time course of the calcium current in both cells during the conduction of an action potential. Using this approach, they determined that the calcium current is strongly affected by the direction and the success or failure of conduction; the density of this current is always larger in the leader than in the follower cell. This asymmetry in the calcium current could be particularly significant when cells undergo high rates of stimulation and could lead to arrhythmogenesis. Electrical coupling is also important in many regions of the nervous system, such as in populations of cortical interneurons in mammals. Merriam et al. (45) used the dynamic clamp to demonstrate that the interplay between electrical and chemical synapses can control the extent to which interneurons fire synchronously or asynchronously. A similar problem was studied using the oscillating neuronal networks in the stomatogastric ganglion (STG) of crustaceans (58, 68, 73). Varona et al. (73) used the dynamic clamp to modify the strength of coupling between the two electrical-

1548-9213/05 8.00 ©2006 Int. Union Physiol. Sci./Am. Physiol. Soc.

Downloaded from physiologyonline.physiology.org on December 13, 2009

A common goal of many studies in physiological systems is to explain system behavior in terms of the behavior of their underlying components. In electrically excitable tissues such as those of the nervous, cardiac, and endocrine system, a classic problem is to understand how the properties of an individual cell depend on the interactions among its ion channels. In multi-cellular systems, it is also crucial to understand how the behavior of an organ or tissue depends on the properties of an individual cell and its interactions with its neighbors. The dynamic clamp is a set of related methods that allow investigators to address both the roles of individual membrane currents in cellular excitability and how the behavior of groups of cells depends on the properties of the cells and their interactions (50, 54, 59, 60). In this review, we use examples from cardiac, endocrine, and neuronal systems to illustrate the variety of configurations used in dynamic clamp experiments to illuminate important problems in physiology. In a dynamic clamp experiment, the investigator records the membrane potential and then uses either a digital computer or an analog circuit to inject current into the cell in such a way as to construct an artificial conductance that is effectively in parallel with the other conductances in the cell (FIGURE 1). To construct an artificial voltage-dependent conductance, the conductance is first modeled as a set of differential equations, allowing the investigator to set the maximal conductance (g) (number of ion channels), the reversal potential (E), and the activation and inactivation properties of the channel so that the injected current fluctuates as the cell’s membrane potential changes. To construct an artificial electrical junction, the injected current depends on the artificial junctional conductance and the voltage difference between the two cells. To create an artificial chemical synapse, the presynaptic cell’s membrane potential is used to gate a modeled conductance in the postsynaptic cell (FIGURE 1). In all cases, the dynamic clamp allows the investigator to do “biological simulations” to assess the functional role of a given biophysical parameter on the system’s behavior.

197


REVIEWS Electrical coupling

Voltage-dependent conductance

when isolated or part of an islet (5, 34, 83). When part of an islet, ␤-cells Synaptic coupling Synapse are electrically coupled and produce bursts of I1 = g(V2)*(V1 – E) I2 = g(V1)*(V2 – E) I = g*(V – E) electrical activity at a cycle period of 10–60 s. When isolated, ␤-cells usually burst at faster (period of a few seconds) or slower frequency (period of a few minutes) but rarely at the intermeor or diate islet-like frequency. These differences are I 1 V1 I2 V2 I V associated with different patterns of calcium dynamics that track the electrical activity (FIGURE 3A). To determine Electrode whether these differCell ences are related to a change in ionic channel FIGURE 1. Uses of dynamic clamp Dynamic clamp can be used to either couple two cells with an artificial conductance (left) composition or are the or inject an artificial conductance into a single cell (right). When simulating electrical cou- consequence of the loss pling, the injected current is a function of the value of the artificial conductance (g) and of electrical coupling, the voltage-difference between the two cells (V1 – V2). For synaptic coupling, the conductance is also dependent on presynaptic voltage [g(Vx)]. In the case of synaptic or voltage- Bertram et al. (5) used dependent conductance simulation, the driving force (V – E) of the simulated conductance the dynamic clamp to determines the magnitude of the injected current. For voltage-dependent conductance show that isolated ␤-cells simulation, the conductance is also dependent on the membrane potential [g(V)]. could be converted from fast spikers to slow bursters (similar to the islet cells) ly coupled PD neurons. These neurons show synchroby injecting a small voltage-dependent inward current nized bursts without spike synchrony in control condiinto the cell, resulting in a calcium signal similar to the tions, synchronized spikes when the electrical couislet cell calcium signal (FIGURE 3A). The very small pling conductance is increased further, and burst in conductance necessary for the conversion of the pheanti-phase when it is decreased below control values notype of the ␤-cells led the authors to suggest that the (FIGURE 2B). This also shows that the dynamic clamp isolated cells have a stochastic behavior related to the can be used not only to add but to subtract conducsmall number of channels involved in producing their tances. electrical activity. When electrically coupled, the stochastic differences between the cells are averaged to Voltage-Dependent Conductances produce the typical slow bursting of islet cells. The injected conductance decreases the stochastic aspect The dynamic clamp has been used to create artificial of the electrical activity of isolated ␤-cells, thus rescuconductances that mimic the action of voltageing the expected islet-like electrical behavior. dependent or voltage-independent ion channels. The In the nervous system, the dynamic clamp has been injection of voltage-independent conductances has used to mimic the effects of many currents, including been used to study the effect of impalement-induced hyperpolarization-activated inward current (Ih) (23, 28, and physiological leak conductances in leech heart neurons (12, 20, 40), stretch-activated conductances 30, 33, 36, 72, 84), potassium currents (19, 36, 39, 41, 43, in atrial cells (75), and the impact of shunting synaptic 56, 66, 70), calcium currents (19, 29), and voltageinhibition on the activity of cerebellar granule cells dependent modulator-activated currents (3, 59, 67). (46) and lumbar motoneurons (8). The intrinsic diffiSimulating these ionic channels has led to better culty of understanding the role of voltage-dependent understanding of the bursting and oscillatory properconductances on cell function has led many investigaties of neurons (23, 28, 29, 33, 36), bistability (29), subtors to exploit the dynamic clamp in a variety of systhreshold resonance (30), regulation of excitability (19, tems. 72, 84), action potential and high-frequency firing The dynamic clamp has been used effectively to mechanisms (39, 41, 43, 56), integrative and short-term understand the origin of the differences between the dynamic properties of neurons (66, 70), and the effect bursting properties displayed by pancreatic ␤-cells of neuromodulators on neuronal activity (3, 23, 60, 67). I1 = g*(V2 – V1)

PHYSIOLOGY • Volume 21 • June 2006 • www.physiologyonline.org

I = g(V)*(V – E)

Downloaded from physiologyonline.physiology.org on December 13, 2009

198

I2 = g*(V1 – V2)


REVIEWS A Membrane potential (mV)

20 0 –20 –40 –60 –80 –100

Calcium current (pA/pF)

4 2 0 –2 –4 –6 –8 –10

Myocyte 2

Leader

Follower

Follower

Leader

Membrane potential (mV)

20 0 –20 –40 –60 –80 –100

Calcium current (pA/pF)

40

4 2 0 –2 –4 –6 –8 –10

0

40 80 120 160 200

0

40 80 120 160 200

Time (ms)

Vm (mV)

–32 –36 –40 –44 –48 –52

Vm (mV)

B

–30 –35 –40 –45 –50 –55

FIGURE 2. Artificial electrical coupling

–30 Vm (mV)

A: two myocytes were coupled with an analog-based dynamic clamp system. First and third panels show voltage waveforms recorded in myocytes 1 and 2 after stimulation of myocyte 1 or myocyte 2, respectively. Second and fourth panels show pharmacologically isolated calcium currents elicited in response to these waveforms. The calcium current is larger in the stimulated cell (leader: myocyte 1 in first and second panels, myocyte 2 in third and fourth panels). Figure was modified from Ref. 35. B: PD cells electrically coupled using a digital dynamic clamp system. When the electrical coupling conductance was not modified (top; g = 0.0 nS), the PD cells produced bursts synchronously and spikes asynchronously. When the electrical coupling conductance was decreased (middle; g = –250 nS), the two cells produced bursts in anti-phase. When the electrical coupling conductance was increased (bottom; g = +190 nS), both the bursts and the spikes were synchronized. Modified from Ref. 73.

Myocyte 1 40

Downloaded from physiologyonline.physiology.org on December 13, 2009

For example, Lien and Jonas (39) developed a fast dynamic clamp system (50-kHz sampling frequency) to define the role of Kv3 channels in the fastspiking phenotype of hippocampal GABAergic interneurons. Blocking this current induced spike broadening and a loss of their fast-spiking behavior. Replacing the biological current by the dynamic clamp-simulated current restored the fast-spiking behavior of the interneurons. Conversely, artificially subtracting the Kv3 current in a control cell mimicked the effect of pharmacological blockers in abolishing the fast-spiking behavior (FIGURE 3B). Even more convincing was the observation that the injection of this artificial conductance converted regular-spiking pyramidal cells to fast-spiking cells. By manipulating the activation and inactivation properties of the artificial Kv3 conductance, these authors demonstrated that the effects of Kv3 channels on spiking properties are strongly dependent on the gating properties of these channels. This study shows that the dynamic clamp is a perfect tool for determining the “tuning” of biophysical properties to a specific type of electrical activity. A few studies have used the dynamic clamp to simulate ion channels in cardiac cells (4, 64, 75). Sun and Wang (64) simulated the potassium current Ito in endocardial ventricular cells in an attempt to determine the biophysical differences between endocardial and epicardial cells, which could explain the transmural dispersion of the duration of the action potential. Subtracting Ito from epicardial cells or adding it to endocardial cells affected the early phase of repolarization of the action potential, whereas no change in duration of the action potential was observed, ruling out the possibility that the difference in expression of this channel could be responsible for the transmural dispersion of the action potential duration. In an elegant study, Berecki et al. (4) developed a new kind of dynamic clamp to study the consequence of long-QT syndrome-associated potassium human ether-a-go-go-related gene (hERG) channel

Time (ms)

g = 0.0 nS

g = –250 nS

g = 190 nS

–35 –40 –45 –50 0

2

4

6

Time (s)

PHYSIOLOGY • Volume 21 • June 2006 • www.physiologyonline.org

199


REVIEWS mutation (R56Q) on the action potential dynamics. In this technique, called dynamic action potential clamp, currents were recorded from a HEK-293 cell express-

C

Rescue

10

12

14

400 200

Fast + slow 0

4

8

12

16

20

24

28

Vm (mV)

50 mV 5 nA

80

Control Rescue Blocker

40 0

500

0

0.5 nA 0

1

2

3

4

5

6

Inst. AP freqency (Hz)

Voltage (mV)

–40 –60 0

800

1

2

3 4 5 Minutes

6

7

100

0

Subtraction

*

50

* *

0 60

–60

50 mV 5 nA 200 ms

7

–20

–60

80

Control

40 0

0

Subtraction Blocker

500 Time (ms)

1000

100

50

0

0

200 400 0 200 400 0 Time (ms)

200 400

0.008 nS

600 400 200

Voltage (mV)

0 –20 –40 –60

0

30

60

90 120 150 180 210 Time (s)

FIGURE 3. Artificial ionic conductances

A: simulation of inward conductances in isolated ␤-cells. The membrane potential and intracellular calcium signal were recorded in response to glucose application. Top pair shows isolated ␤-cell recordings showing the fast changes (top) or combined fast and slow changes (bottom) in calcium signal in response to glucose. Middle pair shows islet ␤-cell recordings showing the slow bursting profile in membrane potential (bottom) and calcium signal (top). Bottom pair shows that a dynamic-clamp injection of a small voltage-dependent conductance (g = 0.008 nS) into a fast-spiker isolated ␤-cell results in bursts of electrical activity and calcium signal. Modified from Ref. 5. B: hippocampal interneuron activity pattern obtained in response to a 0.5-nA current step injection. In control condition (black trace, 1st and 3rd panels), the cell fires at high frequency, and spike-frequency adaptation is observed (black line, 2nd and 4th panels). When the Kv3 channel is pharmacologically blocked (red trace, 1st and 3rd panels), the firing frequency and the spike-frequency adaptation decrease (red line, 2nd and 4th panels). Injecting an artificial Kv3 current (lower blue trace, 1st panel) using dynamic clamp rescues the original firing behavior of the cell (blue trace, 1st panel). The effect of pharmacological blockade of Kv3 channels can be mimicked by subtracting Kv3 artificial conductance (lower blue trace, 3rd panel) using dynamic clamp (blue trace, 3rd panel; blue line, 4th panel). C: voltage and current traces obtained in response to periodic stimulation of a myocyte at different frequencies (0.2, 2, and 5 Hz from left to right). The traces shown correspond to wild-type hERG channel (top 2 panels) or R56Q mutant hERG channel (bottom 2 panels). The action potentials and the corresponding currents last longer for the mutant than the wild-type current, and as a consequence only the wild-type current can follow high-frequency stimulation (5 Hz, traces on right). Modified from Ref. 4.

200

PHYSIOLOGY • Volume 21 • June 2006 • www.physiologyonline.org

Downloaded from physiologyonline.physiology.org on December 13, 2009

Blocker

1000

400

0

5 Hz

200 ms

Control

200

2 Hz

0

Wild type current (pA)

8

0.5 nA

0.2 Hz

60

Vm (mV)

0 2 4 6 10 mM glucose

Minutes [Ca2+Ii(nM)]

Blocker

Fast

200

0

[Ca2+Ii(nM)]

Control

400

0

[Ca2+Ii(nM)]

B

10 mM glucose

Inst. AP freqency (Hz)

[Ca2+Ii(nM)]

600

Mutant current (pA)

A

ing either a mutated channel or the wild-type channel. These currents were scaled and injected into an active ventricular cell where the IKr potassium current had


REVIEWS been previously pharmacologically blocked (FIGURE 3C). The mutated channel was associated with a delayed repolarization of the action potential in the

tested cell type (rabbit left-ventricular myocyte). Because of the differences in gating properties between the wild-type and the R56Q channel, the

A

B AMPA + NMDA

Current injection

50 mv

VTH

VTH

VTH

VTH

VTH

VTH

VTH

VTH

VTH

VTH

VTH

VTH

1

gNMDA 100 pA

4 nS

0

0

gAMPA

0

800

1600

2400 0

400

ms

800 1200 1600 2000 ms

AMPA + GABAA

AMPA alone

3

50 mV

0

2

6

4

8 10 20

0

2

4

s 14 12

20 gGABA

0

Period

gAMPA

10

15

3

0

1

8 6

10

20

40

60

3

2

1 0

2

4

2

5 AMPA alone

8 10 20

s

25

4 ns

6

80 100

Synaptic conductance (nS)

0

0

20

40

60

80 100

IH conductance (nS)

AMPA + GABAA 0

800

1600 ms

2400 0

400

800 1200 1600 2000 ms

FIGURE 4. Artificial synapses A: simulation of synaptic background in rat cortical cells. Top left: when a simple current step is injected into the cell, the spike timing is highly variable between trials (bottom, raster plot). Bottom left: response to a fluctuating Poisson-like AMPA conductance. The number of spikes is decreased, but the spike timing is more reliable. Top right: response to combined Poisson-like AMPA and NMDA excitation. The spike-timing reliability is strong only when the NMDA conductance reaches steady state. Bottom right: response to combined fluctuating Poisson-like AMPA and GABA conductances. The spike-timing reliability is very strong independent of time during the stimulation. For all panels, top traces represent voltage responses (black is first trial, red is following trials), middle traces represent the conductance stimulus used to elicit firing of the cell, and bottom traces are raster plots of the spiking response of the cells. Modified from Ref. 24. B: synaptic coupling of two GM cells of the stomatogastric ganglion. Increasing the synaptic conductance increases the cycle period of the half-center oscillator (left column; synaptic conductance increases for traces from top to bottom). Increasing Ih conductance decreases the cycle period of the oscillator (right column; Ih conductance increases for traces from top to bottom). Modified from Ref. 61.

PHYSIOLOGY • Volume 21 • June 2006 • www.physiologyonline.org

201

Downloaded from physiologyonline.physiology.org on December 13, 2009

2


REVIEWS duration of the action potential and its dependence on the frequency stimulation were modified (FIGURE 3C). This creative implementation of the dynamic

A

clamp illustrates the evolution of dynamic clamp methodologies to address a variety of questions.

B Layers

Idig = gc*(Vreal – Vdig ) 1 Idig

Vreal

2

3

m

1 2

Confocal imaging system

Digital model cell

Digital model cell w AP1,1 PSC1,1 AP1,2

Myocyte

Membrane potential (mV)

60 40 20 0 –20 –40 –60 –80 –100

AP1,w PSC1,w

3.0

PSC2,1…w

Sum1,1

= I1,1

AP2,1…w

Sum1,2

= I1,2

V2,1…w

Sum1,w

= I1,3

F/FO

2.5 I1,1…w

2.0 1.5 1.0

0

50

100

150

200

1

250 1

Time (ms) Time (ms)

Uncoupled (GC = 0)

2

Coupled (GC = 8)

2

0.00 2.08

w

4.16

1 2

6.24

3 4

8.32

5 10.40

Layer 6 7

12.48

8 9

14.56

10 11

16.64

12 18.72

202

0

0.4

10 mm

PHYSIOLOGY • Volume 21 • June 2006 • www.physiologyonline.org

0.8 Time (s)

1.2

Downloaded from physiologyonline.physiology.org on December 13, 2009

PSC1,2


REVIEWS Chemical Synapses

Downloaded from physiologyonline.physiology.org on December 13, 2009

The number of synapses received by a single neuron can vary from a few to tens of thousands. The dynamic clamp has been used to simulate one synapse (2, 3, 9, 10, 15, 42, 51, 54, 68, 71), a small number of synapses (6, 9, 13, 18, 21, 22, 53, 81, 82), or thousands of synapses (1, 9, 11, 14, 16, 17, 24, 31, 44, 46, 55, 62, 65, 80, 85), and to determine their effect on neuronal activity. In some dynamic clamp experiments, an artificial synaptic conductance is injected into the neuron in response to a command given by the experimenter to mimic only the postsynaptic action of released neurotransmitter in an open-loop configuration. In a second type of experiment, the dynamic clamp is used to artificially couple two or three biological neurons by using the membrane potential waveform of the presynaptic neuron to control an artificial postsynaptic conductance. A large number of studies have employed the dynamic clamp to simulate “synaptic noise” or “background activity,” mimicking the thousands of inputs received by neurons in the mammalian brain (1, 9, 11, 14, 16, 17, 24, 31, 44, 46, 55, 62, 65, 80, 85). This approach consists of recording neurons in vitro while simulating the highly variable total synaptic input (excitatory and/or inhibitory) received by these neurons in vivo. This type of simulation has been used to address different questions about the integrative properties of neurons in vivo. Several studies have shown that increasing the variability of the synaptic signal, but not its mean, is sufficient to increase the gain of the response of the neuron to this input (1, 11, 46, 62). This is true not only for excitatory inputs but also for inhibitory inputs: for a constant excitatory input, increasing the variability of simulated GABAergic events decreases their average inhibitory influence on the firing of the neuron, demonstrating that the heterogeneity of the inhibitory synaptic inputs to a neuron could play a major role in setting the gain of the neuron’s response to excitatory synaptic inputs (1). Simulating synaptic background activity has also been very useful in analyzing the reliability and temporal precision of neuronal responses to different kinds of synaptic stimuli (24, 31, 65, 85). For example, Harsch and Robinson (24) used this approach to determine the influence of different components of the total synaptic input on the firing properties of rat cortical neurons. They separated the synaptic input into three components: the excitatory AMPA receptor-

mediated conductance, the excitatory conductance mediated by the NMDA receptor, and the GABAA receptor-mediated inhibitory conductance. The AMPA and NMDA components differ in their voltage dependence and in their kinetics; the NMDA component is slower than the AMPA component. When depolarized by a regular current injection, the neuron responds with little temporal precision (FIGURE 4A). When the neuron is stimulated with AMPA-like synaptic noise, spikes are produced with great temporal precision. The addition of the NMDA component reduces the temporal precision and confers a time dependence to this property: in the activating phase of the NMDA conductance, the temporal precision is poor and the spike production is unreliable, whereas the temporal precision becomes stronger and the spike production more reliable when the NMDA conductance reaches steady state (end of stimulation protocol). Adding an inhibitory component to the synaptic background decreases the firing frequency, but spikes are more precise and are produced with a delay. This suggests that excitatory inputs might be critical for establishing the firing rate of cortical neurons, whereas inhibitory inputs might define the temporal precision of response. In a recent study, Wolfart et al. (80) used the simulation of in vivo synaptic activity to demonstrate that the distinction between the canonical hyperpolarized “bursting” and depolarized “tonic” firing modes described for the relay thalamic neurons in vitro might not be as relevant when the neuron is given realistic synaptic inputs. When receiving synaptic noise, the neuron responds with a mix of single spikes and bursts of spikes independent of the membrane potential (80). In an elegant study (55), the same group developed a method for estimating the synaptic conductance changes occurring in cortical neurons when the network is activated. To perform this analysis, the authors recorded from cortical neurons during spontaneous activation of the network. The change in the voltage profile was then decomposed into an excitatory and inhibitory component, and the mean and variance of each component were determined. The validity of this analysis was tested by injecting the calculated component and reproducing the activity profile of the neuron observed during spontaneous activation of the network. Closed-loop studies in which artificial networks are created are less common. In one study, a closed-loop approach was used to study the phase relationships

FIGURE 5. Hybrid networks A: digital system used to couple a digital model myocyte to a biological myocyte and record the calcium signal in the biological myocyte (top). Middle: voltage and calcium signal when the biological myocyte is either uncoupled (blue and green traces) or coupled to the digital model myocyte (red trace). The calcium signal rises faster and the peak amplitude is larger when the myocyte is electrically coupled to the digital model. Bottom: confocal images corresponding to traces a (left column) and b (right column). When electrically coupled (right column), the calcium signal rises faster and the amplitude of the signal is larger. Modified from Ref. 76. B: digital system used to create an artificial feedforward neuronal network (top). Top: network architecture and computational operations performed to simulate the network activity (see text). Bottom: raster plot showing that the activity synchronizes as it goes through an increasing number of layers in the feedforward network. Modified from Ref. 52.

PHYSIOLOGY • Volume 21 • June 2006 • www.physiologyonline.org

203


REVIEWS

Hybrid Networks The dynamic clamp has also been used to create “hybrid networks” consisting of one or more biological neurons coupled to one or more analog or digital model cells. In this way, large numbers of model neurons can be studied, over and above the relatively small number of biological cells that can be simultaneously recorded intracellularly (two to four). In theory, the size of a hybrid network is limited only by the computation rate, which is dependent on whether analog or digital models are used, on processing speed, and on model complexity. In the heart, two different types of hybrid networks have been developed: simple networks with one biological cell electrically coupled to one model cell (27, 74, 76, 78) and more complex networks in which one biological cell is connected to a two-dimensional sheet of electrically coupled model cells (77, 79). The twocell networks were used to determine the critical intercellular coupling for frequency entrainment in rabbit sinoatrial cells (78), to study the influence of injury cur204

PHYSIOLOGY • Volume 21 • June 2006 • www.physiologyonline.org

rent on Purkinje myocyte activity (27), and to study the appearance of an ectopic focus of activity by elevation of extracellular potassium (74). Wagner et al. (76) combined the dynamic clamp with calcium imaging to show that the intracellular calcium dynamics of a myocyte was altered by its coupling, here to a model (FIGURE 5A). The calcium signal was larger and faster when propagation was successful than when it was not. However, the modification in the calcium signal was smaller than expected based on the dynamics of the Ltype calcium current during successful propagation. The authors suggested that this discrepancy points to the involvement of the sarcoplasmic reticulum as a source of calcium during propagation of the action potential. In other studies, complex two-dimensional networks (square grids of cells) were developed that contained from 49 to 169 elements with only one central element being a biological cell (77, 79). By varying the coupling conductance within rows and within columns, the authors showed that anisotropy of the coupling within the network facilitates the development of ectopic foci and the spread of activity to the entire network. The authors suggested that the remodeling occurring in a peri-infarction zone could, by changing the anisotropy, facilitate or inhibit the development of arrhythmias. In the nervous system, hybrid networks have been used mostly to address two types of problems: 1) the problem of phase relationships and/or synchronization in small closed-loop networks of bursting or spiking cells (36, 47–49), and 2) to study signal propagation (37, 52). LeMasson et al. (37) created a three-neuron network consisting of an analog-based retinal cell projecting onto a real thalamocortical neuron, itself connected by reciprocal synapses to a computer-generated inhibitory interneuron from the nucleus reticularis. The study focused on the relationship between retinal spikes and thalamocortical firing output. The authors showed that neuromodulation of thalamocortical cells and a decrease of inhibition from the nucleus reticularis neuron induced a switch in the behavior of thalamocortical cells from bursting to spiking. The authors suggest that this change in behavior would lead thalamocortical cells to be most effective only during an aroused state. Reyes (52) developed an interesting strategy to study propagation of signals in a feedforward network (no recurrent connections) without having to record from more than one neuron in vitro (FIGURE 5B). The simulated network comprised m layers each composed of w neurons. All neurons in the first layer were modeled as firing repetitively and asynchronously at different frequencies. Each action potential resulted in a postsynaptic current (PSC). Ten percent of these trains of PSCs were randomly chosen and summed, and the sum was injected into the recorded neuron representing a neuron in layer 2. To simulate the response of the remaining (w ᎑1) neurons in layer 2,

Downloaded from physiologyonline.physiology.org on December 13, 2009

between cortical interneurons coupled with synaptic inputs of different kinetics (45). In the STG, closedloop approaches have been used extensively (2, 15, 42, 60, 61) to study the role of synaptic and intrinsic properties on network dynamics. Reciprocal inhibition is a common feature in many central pattern-generating networks, including those in the stomatogastric nervous system. Understanding this kind of symmetrical two-cell network was the subject of one of the early studies using dynamic clamp in the nervous system. Sharp et al. (61) coupled two gastric mill (GM) cells with synaptic conductances of different strengths and kinetics and studied the influence of these parameters on the behavior of the resulting half-center oscillators. Neurons in the STG release neurotransmitter as a graded function of membrane potential, and therefore the effect of changing the threshold of activation of the synapses was also tested. The simulation of an h-type conductance in the two GM cells was needed to induce stable oscillations of this half-center oscillator. FIGURE 4B summarizes the effects of changing the conductance of the reciprocal inhibitory synapses or the maximal conductance of the Ih current. Increasing the conductance of the synapses produced an increase in the cycle period of the half-center oscillator, whereas increasing the Ih maximal conductance decreased the cycle period of the oscillator (FIGURE 4B). Manipulation of other parameters, like the time constant of decay or the threshold of activation of the synaptic inputs, led to other network behaviors such as synchronous tonic spiking, synchronous bursting, or spontaneous switching between different states. This study was essentially a simulation study carried out with biological neurons, as extensive parameter searches were done.


REVIEWS the same sequence was repeated (w ᎑1) times. All the activity profiles generated by this operation were then used to create the PSC trains coming out of layer 2 neurons. Again, 10% of the PSCs generated by these neurons were injected into the recorded neuron, which now represented a layer 3 neuron. These different operations were repeated m times to simulate the propagation of signals through all of the layers. The interesting result from this study is that the activity of all neurons within a layer became more synchronized as the signal propagated through the layers, reaching almost perfect synchrony by the 11th layer, although the activity of the neurons in the first layer was completely unorganized.

General Conclusion

References

Boyden ES, Zhang F, Bamberg E, Nagel G, and Deisseroth K. Millisecond-timescale, genetically targeted optical control of neural activity. Nat Neurosci 8: 1263—1268, 2005.

8.

Brizzi L, Meunier C, Zytnicki D, Donnet M, Hansel D, D’Incamps BL, and Van Vreeswijk C. How shunting inhibition affects the discharge of lumbar motoneurones: a dynamic clamp study in anaesthetized cats. J Physiol 558: 671—683, 2004.

9.

Carter AG and Regehr WG. Quantal events shape cerebellar interneuron firing. Nat Neurosci 5: 1309—1318, 2002.

10. Cathala L, Brickley S, Cull-Candy S, and Farrant M. Maturation of EPSCs and intrinsic membrane properties enhances precision at a cerebellar synapse. J Neurosci 23: 6074—6085, 2003. 11. Chance FS, Abbott LF, and Reyes AD. Gain modulation from background synaptic input. Neuron 35: 773—782, 2002. 12. Cymbalyuk GS, Gaudry Q, Masino MA, and Calabrese RL. Bursting in leech heart interneurons: cell-autonomous and network-based mechanisms. J Neurosci 22: 10580—10592, 2002. 13. Derjean D, Bertrand S, Le Masson G, Landry M, Morisset V, and Nagy F. Dynamic balance of metabotropic inputs causes dorsal horn neurons to switch functional states. Nat Neurosci 6: 274—281, 2003.

Downloaded from physiologyonline.physiology.org on December 13, 2009

The dynamic clamp technique has been used in a variety of different systems to answer a plethora of questions. We anticipate that the future will bring more innovative and creative uses of the dynamic clamp and hybrid circuits to understand the consequences of the nonlinearities central to most physiological processes. Because the dynamic clamp allows one to simulate networks of biological cells, the dynamic clamp theorist can allow the biological tissue itself to take care of many of the parameters that are still unknown or difficult to compute. It is a tremendous advantage to be able to do simulations in which the only parameters to be studied are under tight experimental control and the remaining parameters are by definition correct, because cells are themselves “computing” them in real time and space. As genetic manipulations provide tools to optically stimulate tissues (7, 38), one can imagine that hybrid optical devices will extend dynamic clamp-like methodologies to a larger number of neurons, allowing new and exciting ways to do network simulations with biological tissues.

7.

14. Destexhe A, Rudolph M, Fellous JM, and Sejnowski TJ. Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons. Neuroscience 107: 13—24, 2001. 15. Elson RC, Selverston AI, Abarbanel HD, and Rabinovich MI. Inhibitory synchronization of bursting in biological neurons: dependence on synaptic time constant. J Neurophysiol 88: 1166—1176, 2002. 16. Fellous JM, Rudolph M, Destexhe A, and Sejnowski TJ. Synaptic background noise controls the input/output characteristics of single cells in an in vitro model of in vivo activity. Neuroscience 122: 811—829, 2003. 17. Fellous JM and Sejnowski TJ. Regulation of persistent activity by background inhibition in an in vitro model of a cortical microcircuit. Cereb Cortex 13: 1232—1241, 2003. 18. Foldy C, Aradi I, Howard A, and Soltesz I. Diversity beyond variance: modulation of firing rates and network coherence by GABAergic subpopulations. Eur J Neurosci 19: 119—130, 2004. 19. Goldman MS, Golowasch J, Marder E, and Abbott LF. Global structure, robustness, and modulation of neuronal models. J Neurosci 21: 5229—5238, 2001. 20. Gramoll S, Schmidt J, and Calabrese RL. Switching in the activity state of an interneuron that controls coordination of the hearts in the medicinal leech (Hirudo medicinalis). J Exp Biol 186: 157—171, 1994. 21. Grande LA, Kinney GA, Miracle GL, and Spain WJ. Dynamic influences on coincidence detection in neocortical pyramidal neurons. J Neurosci 24: 1839—1851, 2004. 22. Hanson JE and Jaeger D. Short-term plasticity shapes the response to simulated normal and parkinsonian input patterns in the globus pallidus. J Neurosci 22: 5164—5172, 2002.

1.

Aradi I, Santhakumar V, and Soltesz I. Impact of heterogeneous perisomatic IPSC populations on pyramidal cell firing rates. J Neurophysiol 91: 2849—2858, 2004.

2.

Bartos M, Manor Y, Nadim F, Marder E, and Nusbaum MP. Coordination of fast and slow rhythmic neuronal circuits. J Neurosci 19: 6650—6660, 1999.

23. Harris-Warrick RM, Coniglio LM, Levini RM, Gueron S, and Guckenheimer J. Dopamine modulation of two subthreshold currents produces phase shifts in activity of an identified motoneuron. J Neurophysiol 74: 1404—1420, 1995.

3.

Beenhakker MP, DeLong ND, Saideman SR, Nadim F, and Nusbaum MP. Proprioceptor regulation of motor circuit activity by presynaptic inhibition of a modulatory projection neuron. J Neurosci 25: 8794—8806, 2005.

24. Harsch A and Robinson HP. Postsynaptic variability of firing in rat cortical neurons: the roles of input synchronization and synaptic NMDA receptor conductance. J Neurosci 20: 6181— 6192, 2000.

4.

Berecki G, Zegers JG, Verkerk AO, Bhuiyan ZA, de Jonge B, Veldkamp MW, Wilders R, and van Ginneken AC. HERG channel (dys)function revealed by dynamic action potential clamp technique. Biophys J 88: 566—578, 2005.

25. Huelsing DJ, Pollard AE, and Spitzer KW. Transient outward current modulates discontinuous conduction in rabbit ventricular cell pairs. Cardiovasc Res 49: 779—789, 2001.

5.

Bertram R, Previte J, Sherman A, Kinard TA, and Satin LS. The phantom burster model for pancreatic beta-cells. Biophys J 79: 2880—2892, 2000.

26. Huelsing DJ, Spitzer KW, Cordeiro JM, and Pollard AE. Modulation of repolarization in rabbit Purkinje and ventricular myocytes coupled by a variable resistance. Am J Physiol Heart Circ Physiol 276: H572—H581, 1999.

6.

Blitz DM and Regehr WG. Retinogeniculate synaptic properties controlling spike number and timing in relay neurons. J Neurophysiol 90: 2438—2450, 2003.

27. Huelsing DJ, Spitzer KW, and Pollard AE. Spontaneous activity induced in rabbit Purkinje myocytes during coupling to a depolarized model cell. Cardiovasc Res 59: 620—627, 2003.

PHYSIOLOGY • Volume 21 • June 2006 • www.physiologyonline.org

205


REVIEWS 28. Hughes SW, Cope DW, and Crunelli V. Dynamic clamp study of Ih modulation of burst firing and delta oscillations in thalamocortical neurons in vitro. Neuroscience 87: 541—550, 1998. 29. Hughes SW, Cope DW, Toth TI, Williams SR, and Crunelli V. All thalamocortical neurones possess a T-type Ca2+ ‘window’ current that enables the expression of bistability-mediated activities. J Physiol 517: 805—815, 1999. 30. Hutcheon B, Miura RM, and Puil E. Models of subthreshold membrane resonance in neocortical neurons. J Neurophysiol 76: 698—714, 1996. 31. Jaeger D and Bower JM. Synaptic control of spiking in cerebellar Purkinje cells: dynamic current clamp based on model conductances. J Neurosci 19: 6090—6101, 1999. 32. Joyner RW, Sugiura H, and Tan RC. Unidirectional block between isolated rabbit ventricular cells coupled by a variable resistance. Biophys J 60: 1038—1045, 1991.

34. Kinard TA, de Vries G, Sherman A, and Satin LS. Modulation of the bursting properties of single mouse pancreatic beta-cells by artificial conductances. Biophys J 76: 1423—1435, 1999. 35. Kumar R and Joyner RW. Calcium currents of ventricular cell pairs during action potential conduction. Am J Physiol Heart Circ Physiol 268: H2476—H2486, 1995.

46. Mitchell SJ and Silver RA. Shunting inhibition modulates neuronal gain during synaptic excitation. Neuron 38: 433—445, 2003. 47. Netoff TI, Banks MI, Dorval AD, Acker CD, Haas JS, Kopell N, and White JA. Synchronization in hybrid neuronal networks of the hippocampal formation. J Neurophysiol 93: 1197—1208, 2005. 48. Nowotny T, Zhigulin VP, Selverston AI, Abarbanel HD, and Rabinovich MI. Enhancement of synchronization in a hybrid neural circuit by spike-timing dependent plasticity. J Neurosci 23: 9776—9785, 2003. 49. Oprisan SA, Prinz AA, and Canavier CC. Phase resetting and phase locking in hybrid circuits of one model and one biological neuron. Biophys J 87: 2283—2298, 2004. 50. Prinz AA, Abbott LF, and Marder E. The dynamic clamp comes of age. Trends Neurosci 27: 218— 224, 2004. 51. Prinz AA, Thirumalai V, and Marder E. The functional consequences of changes in the strength and duration of synaptic inputs to oscillatory neurons. J Neurosci 23: 943—954, 2003. 52. Reyes AD. Synchrony-dependent propagation of firing rate in iteratively constructed networks in vitro. Nat Neurosci 6: 593—599, 2003. 53. Reyes AD, Rubel EW, and Spain WJ. In vitro analysis of optimal stimuli for phase-locking and timedelayed modulation of firing in avian nucleus laminaris neurons. J Neurosci 16: 993—1007, 1996.

36. Le Masson G, Le Masson S, and Moulins M. From conductances to neural network properties: analysis of simple circuits using the hybrid network method. Prog Biophys Mol Biol 64: 201—220, 1995.

54. Robinson HP and Kawai N. Injection of digitally synthesized synaptic conductance transients to measure the integrative properties of neurons. J Neurosci Methods 49: 157—165, 1993.

37. Le Masson G, Renaud-Le Masson S, Debay D, and Bal T. Feedback inhibition controls spike transfer in hybrid thalamic circuits. Nature 417: 854—858, 2002.

55. Rudolph M, Piwkowska Z, Badoual M, Bal T, and Destexhe A. A method to estimate synaptic conductances from membrane potential fluctuations. J Neurophysiol 91: 2884—2896, 2004.

38. Li X, Gutierrez DV, Hanson MG, Han J, Mark MD, Chiel H, Hegemann P, Landmesser LT, and Herlitze S. Fast noninvasive activation and inhibition of neural and network activity by vertebrate rhodopsin and green algae channelrhodopsin. Proc Natl Acad Sci USA 102: 17816—17821, 2005.

56. Schreiber S, Fellous JM, Tiesinga P, and Sejnowski TJ. Influence of ionic conductances on spike timing reliability of cortical neurons for suprathreshold rhythmic inputs. J Neurophysiol 91: 194—205, 2004.

39. Lien CC and Jonas P. Kv3 potassium conductance is necessary and kinetically optimized for high-frequency action potential generation in hippocampal interneurons. J Neurosci 23: 2058—2068, 2003. 40. Lu J, Gramoll S, Schmidt J, and Calabrese RL. Motor pattern switching in the heartbeat pattern generator of the medicinal leech: membrane properties and lack of synaptic interaction in switch interneurons. J Comp Physiol [A] 184: 311—324, 1999. K+

41. Ma M and Koester J. The role of currents in frequency-dependent spike broadening in Aplysia R20 neurons: a dynamic-clamp analysis. J Neurosci 16: 4089—4101, 1996. 42. Mamiya A and Nadim F. Dynamic interaction of oscillatory neurons coupled with reciprocally inhibitory synapses acts to stabilize the rhythm period. J Neurosci 24: 5140—5150, 2004. 43. Manuel M, Meunier C, Donnet M, and Zytnicki D. How much afterhyperpolarization conductance is recruited by an action potential? A dynamicclamp study in cat lumbar motoneurons. J Neurosci 25: 8917—8923, 2005. 44. McCormick DA, Shu Y, Hasenstaub A, SanchezVives M, Badoual M, and Bal T. Persistent cortical activity: mechanisms of generation and effects on neuronal excitability. Cereb Cortex 13: 1219— 1231, 2003.

206

57. Scott S. Stimulation Simulations of Young Yet Cultured Beating Hearts (PhD thesis). Buffalo, NY: State University of New York, 1979. 58. Sharp AA, Abbott LF, and Marder E. Artificial electrical synapses in oscillatory networks. J Neurophysiol 67: 1691—1694, 1992. 59. Sharp AA, O’Neil MB, Abbott LF, and Marder E. The dynamic clamp: artificial conductances in biological neurons. Trends Neurosci 16: 389—394, 1993. 60. Sharp AA, O’Neil MB, Abbott LF, and Marder E. Dynamic clamp: computer-generated conductances in real neurons. J Neurophysiol 69: 992— 995, 1993. 61. Sharp AA, Skinner FK, and Marder E. Mechanisms of oscillation in dynamic clamp constructed twocell half-center circuits. J Neurophysiol 76: 867— 883, 1996. 62. Shu Y, Hasenstaub A, Badoual M, Bal T, and McCormick DA. Barrages of synaptic activity control the gain and sensitivity of cortical neurons. J Neurosci 23: 10388—10401, 2003. 63. Sugiura H and Joyner RW. Action potential conduction between guinea pig ventricular cells can be modulated by calcium current. Am J Physiol Heart Circ Physiol 263: H1591—H1604, 1992. 64. Sun X and Wang HS. Role of the transient outward current (Ito) in shaping canine ventricular action potential: a dynamic clamp study. J Physiol 564: 411—419, 2005.

PHYSIOLOGY • Volume 21 • June 2006 • www.physiologyonline.org

65. Suter KJ and Jaeger D. Reliable control of spike rate and spike timing by rapid input transients in cerebellar stellate cells. Neuroscience 124: 305— 317, 2004. 66. Svirskis G, Kotak V, Sanes DH, and Rinzel J. Enhancement of signal-to-noise ratio and phase locking for small inputs by a low-threshold outward current in auditory neurons. J Neurosci 22: 11019—11025, 2002. 67. Swensen AM and Marder E. Modulators with convergent cellular actions elicit distinct circuit outputs. J Neurosci 21: 4050—4058, 2001. 68. Szucs A, Varona P, Volkovskii AR, Abarbanel HD, Rabinovich MI, and Selverston AI. Interacting biological and electronic neurons generate realistic oscillatory rhythms. Neuroreport 11: 563—569, 2000. 69. Tan RC and Joyner RW. Electrotonic influences on action potentials from isolated ventricular cells. Circ Res 67: 1071—1081, 1990. 70. Turrigiano GG, Marder E, and Abbott LF. Cellular short-term memory from a slow potassium conductance. J Neurophysiol 75: 963—966, 1996. 71. Ulrich D and Huguenard JR. Gamma-aminobutyric acid type B receptor-dependent burst-firing in thalamic neurons: a dynamic clamp study. Proc Natl Acad Sci USA 93: 13245—13249, 1996. 72. van Welie I, van Hooft JA, and Wadman WJ. Homeostatic scaling of neuronal excitability by synaptic modulation of somatic hyperpolarizationactivated Ih channels. Proc Natl Acad Sci USA 101: 5123—5128, 2004. 73. Varona P, Torres JJ, Abarbanel HD, Rabinovich MI, and Elson RC. Dynamics of two electrically coupled chaotic neurons: experimental observations and model analysis. Biol Cybern 84: 91—101, 2001. 74. Wagner MB, Golod D, Wilders R, Verheijck EE, Joyner RW, Kumar R, Jongsma HJ, Van Ginneken AC, and Goolsby WN. Modulation of propagation from an ectopic focus by electrical load and by extracellular potassium. Am J Physiol Heart Circ Physiol 272: H1759—H1769, 1997. 75. Wagner MB, Kumar R, Joyner RW, and Wang Y. Induced automaticity in isolated rat atrial cells by incorporation of a stretch-activated conductance. Pflügers Arch 447: 819—829, 2004. 76. Wagner MB, Wang YG, Kumar R, Golod DA, Goolsby WN, and Joyner RW. Measurements of calcium transients in ventricular cells during discontinuous action potential conduction. Am J Physiol Heart Circ Physiol 278: H444—H451, 2000. 77. Wang YG, Kumar R, Wagner MB, Wilders R, Golod DA, Goolsby WN, and Joyner RW. Electrical interactions between a real ventricular cell and an anisotropic two-dimensional sheet of model cells. Am J Physiol Heart Circ Physiol 278: H452—H460, 2000. 78. Wilders R, Verheijck EE, Kumar R, Goolsby WN, van Ginneken AC, Joyner RW, and Jongsma HJ. Model clamp and its application to synchronization of rabbit sinoatrial node cells. Am J Physiol Heart Circ Physiol 271: H2168—H2182, 1996. 79. Wilders R, Wagner MB, Golod DA, Kumar R, Wang YG, Goolsby WN, Joyner RW, and Jongsma HJ. Effects of anisotropy on the development of cardiac arrhythmias associated with focal activity. Pflügers Arch 441: 301—312, 2000. 80. Wolfart J, Debay D, Le Masson G, Destexhe A, and Bal T. Synaptic background activity controls spike transfer from thalamus to cortex. Nat Neurosci 8: 1760—1767, 2005. 81. Xu-Friedman MA and Regehr WG. Dynamicclamp analysis of the effects of convergence on spike timing. I. Many synaptic inputs. J Neurophysiol 94: 2512—2525, 2005.

Downloaded from physiologyonline.physiology.org on December 13, 2009

33. Kiehn O, Kjaerulff O, Tresch MC, and HarrisWarrick RM. Contributions of intrinsic motor neuron properties to the production of rhythmic motor output in the mammalian spinal cord. Brain Res Bull 53: 649—659, 2000.

45. Merriam EB, Netoff TI, and Banks MI. Bistable network behavior of layer I interneurons in auditory cortex. J Neurosci 25: 6175—6186, 2005.


REVIEWS 82. Xu-Friedman MA and Regehr WG. Dynamicclamp analysis of the effects of convergence on spike timing. II. Few synaptic inputs. J Neurophysiol 94: 2526—2534, 2005.

83. Zhang M, Goforth P, Bertram R, Sherman A, and Satin L. The Ca2+ dynamics of isolated mouse beta-cells and islets: implications for mathematical models. Biophys J 84: 2852—2870, 2003.

85. Zsiros V and Hestrin S. Background synaptic conductance and precision of EPSP-spike coupling at pyramidal cells. J Neurophysiol 93: 3248—3256, 2005.

84. Zhang Y, Oliva R, Gisselmann G, Hatt H, Guckenheimer J, and Harris-Warrick RM. Overexpression of a hyperpolarization-activated cation current (Ih) channel gene modifies the firing activity of identified motor neurons in a small neural network. J Neurosci 23: 9059—9067, 2003.

Downloaded from physiologyonline.physiology.org on December 13, 2009

PHYSIOLOGY • Volume 21 • June 2006 • www.physiologyonline.org

207


Turn static files into dynamic content formats.

Create a flipbook
Issuu converts static files into: digital portfolios, online yearbooks, online catalogs, digital photo albums and more. Sign up and create your flipbook.