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J Neurosci Methods. Author manuscript; available in PMC 2011 January 10.

Published in final edited form as:

Published online 2007 November 1. doi: 10.1016/j.jneumeth.2007.10.014

PMCID: PMC3017968

EMSID: UKMS33820

School of Biosciences, Cardiff University, Museum Avenue, Cardiff CF10 3US, UK

Correspondence: S. W. Hughes, School of Biosciences, Cardiff University, Museum Avenue, Cardiff CF10 3US, UK. Tel.: +44 (0)29 20879113, Fax.: +44 (0)29 20874986, Email: ku.ca.ffidraC@WSsehguH

The publisher's final edited version of this article is available at J Neurosci Methods

See other articles in PMC that cite the published article.

The dynamic clamp is a technique which allows the introduction of artificial conductances into living cells. Up to now, this technique has been mainly used to add small numbers of ‘virtual’ ion channels to real cells or to construct small hybrid neuronal circuits. In this paper we describe a prototype computer system, NeuReal, that extends the dynamic clamp technique to include i) the attachment of artificial dendritic structures consisting of multiple compartments and ii) the construction of large hybrid networks comprising several hundred biophysically realistic modelled neurons. NeuReal is a fully interactive system that runs on Windows XP, is written in a combination of C++ and assembler, and uses the Microsoft DirectX application programming interface (API) to achieve high-performance graphics. By using the sampling hardware-based representation of membrane potential at all stages of computation and by employing simple look-up tables, NeuReal can simulate over 1000 independent Hodgkin and Huxley type conductances in real-time on a modern personal computer (PC). In addition, whilst not being a hard real-time system, NeuReal still offers reliable performance and tolerable jitter levels up to an update rate of 50 kHz. A key feature of NeuReal is that rather than being a simple dedicated dynamic clamp, it operates as a fast simulation system within which neurons can be specified as either real or simulated. We demonstrate the power of NeuReal with several example experiments and argue that it provides an effective tool for examining various aspects of neuronal function.

The dynamic clamp is a technique which allows computer-simulated conductances to be introduced into living cells in real-time (Robinson and Kawai, 1993; Sharp et al., 1993a,b). The system operates by continuously sampling the membrane potential of an excitable cell at relatively high rates (typically 10-50 kHz) and then based on these samples and a set of differential equations stored in a computer which describe one or more voltage- and time-dependent conductances, calculating and injecting the membrane current that would result in the cell if these conductances were actually present (Fig. 1A). As such, the dynamic clamp creates ‘virtual’ conductances in real cells with the properties of these conductances being under the complete control of the experimenter. Whilst not being without its limitations, the most obvious being the introduction of current at a point source, this technique has proved to be a valuable tool for probing the function of excitable cells (Prinz et al., 2004). This is particularly true for neurons where the dynamic clamp has been extensively used to introduce both virtual intrinsic conductances, in order to examine the basic properties of single cells, as well as artificial synaptic conductances in order to construct and investigate small hybrid neuronal networks (Prinz et al., 2004).

To provide accessible dynamic clamping several research groups have constructed their own dynamic clamp systems (reviewed in Prinz, et al., 2004; but see also Nowotny, et al., 2006). Each of these systems has its own particular advantages and features with some emphasising ease-of-use and installation (Pinto et al., 2001; Nowotny et al., 2006) whilst others have focused on achieving hard real-time performance (Butera et al., 2001; Dorval et al., 2001; Kullmann et al., 2004; Raikov et al., 2004; Mũniz et al., 2005). However, in nearly all cases, these systems have been designed to allow the introduction of a relatively small number of conductances (typically <20) or to construct hybrid circuits comprising only a few cells. In this paper we describe a Windows XP-based prototype computer system, NeuReal, which extends the normal remit of the dynamic clamp system in two key ways. Firstly, this system allows the easy attachment of artificial, i.e. simulated, dendritic tree structures, comprising multiple compartments, to real neurons (Fig. 1B) (Hughes et al., 1998b,1999a; Dorval et al., 2001). Secondly, it facilitates the construction of hybrid neuronal networks that can contain several hundred biophysically realistic modelled cells (Fig. 1B). In delivering these two features, NeuReal provides a novel approach for investigating two technically demanding questions: i) How does dendritic structure affect the integrative properties of individual neurons? and ii) How are the properties of single neurons shaped by extensive network activity?

NeuReal currently employs the Axon Digidata 1200 to perform analogue to digital (ADC) and digital to analogue (DAC) conversions and can operate reliably at sampling/update rates of up to 50 kHz. The simulation speed of NeuReal is achieved by maintaining the sampling hardware-based representation of membrane potential at all stages of computation, using simple look-up tables to compute expensive functions and by utilising direct hardware access for performing all graphics operations during experiments. In tests run on a modern PC, at a step-size of 0.1 ms NeuReal was able to simulate 1380 Hodgkin and Huxley type conductances in real-time. However, even on a modestly-powered PC possessing a 700 MHz Pentium processor we were able to use NeuReal to attach an artificial dendritic tree structure comprising 155 compartments, each possessing up to 4 distinct active conductances, to a real thalamocortical (TC) neuron maintained *in vitro*. Importantly, rather than being simply a dedicated dynamic clamp system, NeuReal is essentially a simulation system within which individual neurons can be specified as either real or simulated. We believe that this represents a clear conceptual departure from more specialized dynamic clamp systems and one which provides a highly flexible experimental tool for studying neuronal function.

Fundamental to the construction of NeuReal is the ability to rapidly simulate realistic neurons and networks. The following section briefly outlines how such computations are carried out. Some of these details have already been published in descriptions of an earlier version of NeuReal in preliminary form (Hughes et al., 1998b,1999a). All neurons were modelled according to the discretized cable equation:

$${\mathrm{C}}_{\mathrm{m}}\mathrm{d}{\mathrm{V}}_{\mathrm{k}}/\mathrm{d}\mathrm{t}={\mathrm{I}}_{\text{parent}}+\Sigma {\mathrm{I}}_{\text{child}}-(\Sigma {\mathrm{I}}_{\text{intrinsic}}+\Sigma {\mathrm{I}}_{\text{synaptic}}+{\mathrm{I}}_{\mathrm{inj}})$$

[1]

where C_{m} is the membrane capacitance, V_{k} is the membrane potential of compartment k, ∑ I_{intrinsic} and ∑ I_{synaptic} are the sum of intrinsic ionic currents and synaptic currents respectively, I_{inj} is the injected current and I_{parent} and I_{child} represents the current contributions of the parent compartment and a child compartment respectively and are given by:

$${\mathrm{I}}_{\text{parent}}={\gamma}_{\mathrm{k}}({\mathrm{V}}_{\text{parent}}-{\mathrm{V}}_{\mathrm{k}})$$

[2]

$${\mathrm{I}}_{\text{child}}={\gamma}_{\text{child}}({\mathrm{V}}_{\text{child}}-{\mathrm{V}}_{\mathrm{k}})$$

[3]

where γ_{k} is the coupling conductance between the parent compartment and compartment k, γ_{child} is the coupling conductance between compartment k and a child compartment, and V_{parent} and V_{child} are the respective membrane potentials of the parent and child compartments. Both γ_{k} and γ_{child} are of the form γ_{k}=(π.d_{k}^{2})/(4R_{a}.l_{k}) where d_{k} and l_{k} are the diameter and length of compartment k and R_{a} is the axial resistivity.

Each voltage-dependent intrinsic ionic current, I_{intrinsic}, was modelled using standard Hodgkin and Huxley formalism (Hodgkin and Huxley, 1952) as follows:

$${\mathrm{I}}_{\text{intrinsic}}={\mathrm{g}}_{\mathrm{max}}{\mathrm{m}}^{\mathrm{p}}{\mathrm{h}}^{\mathrm{q}}.({\mathrm{V}}_{\mathrm{m}}-{\mathrm{E}}_{\mathrm{r}})$$

[4]

Where g_{max} is the maximal conductance, m and h are the activation and inactivation variables respectively (with p and q their respective indices), and V_{r} is the reversal potential. Both m and h are governed by the first order equation:

$$\mathrm{d}\mathrm{x}/\mathrm{d}\mathrm{t}=({\mathrm{x}}_{\infty}-\mathrm{x})/{\tau}_{\mathrm{x}}\phantom{\rule{1em}{0ex}}(\mathrm{x}=\mathrm{m}\phantom{\rule{thinmathspace}{0ex}}\text{or}\phantom{\rule{thinmathspace}{0ex}}\mathrm{h})$$

[5]

where x_{∞} = *f*(V_{m}) gives the steady-state value of x and τ_{x} = *f*(V_{m}) gives the time constant of activation or inactivation.

Synaptic currents are modelled in NeuReal according to the methods described by Destexhe et al. (1994). Briefly, the relationship between the concentration of neurotransmitter in the synaptic cleft, [T], and presynaptic voltage, V_{pre}, is approximated by:

$$\left[\mathrm{T}\right]={\mathrm{T}}_{\mathrm{max}}/[1+\mathrm{exp}(-({\mathrm{V}}_{\mathrm{pre}}-2)/5\left)\right]$$

[6]

where T_{max} is the maximal concentration of transmitter and is usually taken as 1mM. The kinetics of the synaptic current are then modelled according to the scheme:

$$\mathrm{C}+\mathrm{T}\begin{array}{c}\hfill \alpha \hfill \\ \hfill \leftrightarrow \hfill \\ \hfill \beta \hfill \end{array}\mathrm{O}$$

[7]

where C and O represent channels in closed and open states respectively, and α and β are voltage-independent forward and backward rate constants. If r is defined as the fraction of receptors in the open state, then it can be described by:

$$\mathrm{d}\mathrm{r}/\mathrm{d}\mathrm{t}=\alpha \left[\mathrm{T}\right](1-\mathrm{r})-\beta \mathrm{r}$$

[8]

and the postsynaptic current is given by:

$${\mathrm{I}}_{\text{synaptic}}={\mathrm{g}}_{\mathrm{max}}\mathrm{r}({\mathrm{V}}_{\mathrm{m}}-{\mathrm{V}}_{\mathrm{r}})$$

[9]

As indicated above, the calculation of an intrinsic ionic current I_{intrinsic} at some point in time, t, and for some membrane potential, V_{m}, is performed according to equations [4] and [5]. If it is further assumed that V_{m} remains constant for some integration interval Δt then we can solve [5] analytically which gives:

$${\mathrm{x}}_{\mathrm{t}+\Delta \mathrm{t}}={\mathrm{x}}_{\infty}-({\mathrm{x}}_{\infty}-{\mathrm{x}}_{\mathrm{t}})\mathrm{exp}(-\Delta \mathrm{t}/{\tau}_{\mathrm{x}})$$

[10]

In NeuReal, both x_{∞} and τ_{x} need to be calculated in real-time on the basis of the most recently acquired (for dynamic clamp experiments) or calculated (for pure simulations) V_{m} value. However, because this usually involves the costly computation of exponential functions, and since V_{m} is represented by the Digidata board as a 12 bit signed integer value which can only take on 4096 different values, it is more efficient if x_{∞} and τ_{x} are represented in look-up tables which are indexed directly by the value obtained from the Digidata board or calculated by the system. Although the range of x is usually from 0-1, it is profitable (see below) to map these values onto the interval (0,255) before tabulation. Also, because equation [10] still contains an exponential term, it is advantageous to assume a constant sampling interval, Δt, and tabulate exp(-Δt/τ_{x}) instead of merely τ_{x} (Hughes et al., 1998b,1999a; see also Butera et al., 2001). Two disadvantages of this approach are: i) if Δt changes, then the table has to rebuilt, although this is not a problem unless there is a need for a constantly changing sampling rate, and ii) it is difficult to incorporate interactive acceleration and deceleration into the control of kinetics, i.e. including an on-the-fly alterable scaling factor λ, which is incorporated as follows:

$$\mathrm{exp}(-\Delta \mathrm{t}/(\lambda {\tau}_{\mathrm{x}}\left)\right)$$

[11]

If, however, it is assumed that λ can only take on a finite set of 16 values, say for example 0.01, 0.1, 0.2, 0.3 ,0.4, 0.5, 0.6, 0.7, 0.8, 0.9. 1.0, 1.2, 1.4, 1.6, 1.8 & 2.0, then using a two-dimensional array of floating point numbers for exp(-Δt/( λ.τ_{x})), which is indexed by V_{m} and l_{idx} (i.e. a cross reference index ranging from 0 to 15 and which corresponds to 0.1 to 2.0 as listed above). With this approach, calculation of an activation or inactivation variable requires one look-up, one floating point multiplication, two floating point subtractions, one integer addition and a 4 bit shift operation. To compute the proportion of open channels, i.e. m^{p}.h^{q}, another table which gives m^{p}.h^{q} based on two indices, m & h which have been mapped onto the interval (0,255) (see above) can be used. To obtain a value from this table, we simply need one look-up and one bytewise shift operation. If we wish to keep the maximal conductance and reversal potential as interactively alterable variables then in order to calculate the final intrinsic ionic current value, two additional floating multiplications and a subtraction are required (see equation [4]). Synaptic currents can be considered as a special case of an intrinsic current where r m, p=1, q=0, r_{∞} = α/(α + β) and τ_{r} = 1/(α + β). Although the kinetics are now simplified due to a lack of voltage-dependence, it is also now necessary to build a 4096 entry table for the function described in equation [6]. Electrical synapses were considered as a special case whereby r=1 and V_{r} is replaced by V_{pre} in equation [9].

If it is intended to incorporate currents calculated in the above manner to a compartment of a neuronal model (i.e. equation [1]) then as long as the membrane capacitance is specified in the correct units (pF), no further scaling needs to be performed (since the same number representing 1pA for I, represents 1mV for V_{m}). The resulting V_{m} value can then be used to index the activation, inactivation and time constant tables and facilitate further current computation. If, on the other hand, the calculated currents are to be injected into a real neuron via the Digidata 1200 and Axoclamp then hardware scaling issues must be taken into account.

Although the above procedures are described for the 12 bit integer format of membrane potential provided by the Digidata 1200 board they can easily be adapted for higher resolution formats (e.g. 16 and 18 bit). Also, whilst the choice of 8 bit resolution for look- up tables for inactivation and activation variables is so that the system can function on modest computer hardware with limited memory, the accuracy can obviously be improved by increasing the resolution of the activation and inactivation variables when more memory is available, e.g. to 16 or 32 bits, with no loss in performance. Lastly, further performance improvements can be easily achieved at the expense of on-the-fly interactive control, e.g. by including the maximal conductance, driving force and, in the case of current injection, the hardware scaling as part of a look-up table (Butera et al., 2001)

The Digidata 1200 is an ADC/DAC device that is able to simultaneously sample and output 12 bit signals at up to 333 kHz. In NeuReal the Digidata is programmed in assembler such that voltage output signals are updated asynchronously by simply writing to the appropriate DAC data register whereas acquisition of input signals is timed by the on board clock. To ensure a fast access to acquired data the main simulation loop of NeuReal continuously polls the ADC FIFO (first in, first out) empty flag (-EF in the ADC/DAC control register) to check for the arrival of a new sample. As soon as this sample is available, the next action to take place is the writing of the most recently computed output current value. This ensures that the true time between outputted values is as close to the integration step-size as possible. To assess performance of the system we used the low level 64-bit RDTSC (read time stamp counter) Pentium assembler command which provides a precise readout of the number of CPU clock cycles that have elapsed since the last processor reset. Thus, by calling this instruction during every simulation cycle for a large number of consecutive cycles, storing it in a temporary array and then writing this array to a text file at the end of the experiment, we can obtain accurate statistics regarding the jitter of the system (see also Butera et al., 2001).

All other programming and user interface design and construction were done with Microsoft Visual C++. The organisation of the primary classes in NeuReal, which mainly comprise neurons, dendritic trees, conductances and synapses is shown in Fig. 2A. Templates of basic objects are constructed using easy-to-use editing windows and can then be stored in a NeuReal database file. Based on these templates a network is then constructed which is the primary object upon which an experiment or simulation is performed (see results). To provide high-performance graphics for visualizing experimental data we used the DirectX library. This library contains a collection of routines which allow direct access to the graphics memory space and which can take advantage of the onboard acceleration features that are present on different graphics cards. Fig. 2B shows the main interface and the basic oscilloscope display and interactive control panel components. NeuReal also provides a facility for recording up to 6 channels of data during an experiment which can then be replayed or exported to a text file. The source code for Neureal can be downloaded from www.thalamus.org.uk/html/software.html.

Procedures involving experimental animals were carried out in accordance with local ethical committee guidelines and the U.K. Animals (Scientific Procedure) Act, 1986. All efforts were made to minimize the suffering and number of animals used in each experiment. Young adult cats (1-1.5 kg) were deeply anaesthetized with a mixture of O_{2} and NO_{2} (2:1) and 2.5% isoflurane, a wide craniotomy performed and the brain removed. Sagittal slices (450-500 μm) of the thalamus containing the dorsal lateral geniculate nucleus (LGN) were prepared and maintained as described previously (Hughes et al., 2002a,b; Hughes et al., 2004). For recording, slices were perfused with a warmed (35±1 °C), continuously oxygenated (95% O_{2}, 5% CO_{2}), artificial cerebrospinal fluid (ACSF) containing (mM): NaCl (134); KCl (2); KH_{2}PO_{4} (1.25); MgSO_{4} (1); CaCl_{2} (2); NaHCO_{3} (16); glucose (10). Intracellular recordings, using the current clamp technique, were performed with standard-wall glass microelectrodes filled with 1M potassium acetate (resistance: 80-120 MΩ) and connected to an Axoclamp-2A amplifier (Axon Instruments, Foster City, USA) operating in bridge mode. Impaled cells were identified as TC neurons using established electrophysiological criteria (Hughes et al., 2002a,b; Hughes et al., 2004).

Any experiment in NeuReal is essentially a simulation of a network object which must consist of at least one neuron. Each neuron is based on a neuron type or template which in turn is built up from a variety of other objects such as intrinsic and synaptic conductances and dendritic tree structures (Fig. 2A). Up to 2 neurons in any one network can be specified as real meaning that their somatic membrane potential is obtained from a real neuron via a distinct recording electrode, amplifier and the ADC hardware, rather than being computed, and that all somatic currents calculated for that neuron are actually injected via the amplifier and recording electrode. Thus, to perform a basic dynamic clamp experiment involving the injection of one or more artificial conductances to a single cell, a network is created consisting of one neuron that possesses the required number and type of intrinsic conductances and which is specified as real. Additional neurons can then be added and modified within the network to produce increasingly complex types of hybrid or purely simulated cells and networks. Thus, NeuReal acts primarily as a real-time simulation system that is fully interactive, i.e. parameters can be modified on demand, and with which different types of dynamic clamp experiments can be performed yet represent merely a subset of possible experiments.

To test the capacity of NeuReal to simulate large numbers of conductances and neurons in real-time we first constructed a simple one compartment TC neuron template possessing a leak conductance, a fast inactivating Na^{+} current (I_{Na}), a delayed rectifier K^{+} (I_{Kdr}), an inactivating T-type Ca^{2+} current (I_{T}) and a hyperpolarization-activated mixed cation current (I_{h}) (see Appendix) (Toth and Crunelli, 1992; Hughes et al., 1998a,1999b; Emri et al., 2000). We then built a network object consisting of an ever increasing quantity of purely simulated instances of these neurons and assessed at which point the ability of NeuReal to simulate them at faster than real-time broke down (Fig. 3A). For an integration step-size of 0.1 ms, equivalent to a update/sampling rate of 10 kHz in a dynamic clamp experiment, on a PC possessing a 2.26GHz Intel Pentium processor and 2 GB of RAM, NeuReal could simulate 345 neurons at sub-real-time speeds (Fig. 3A). This equates to the parallel simulation of 690 inactivating and 690 non-inactivating conductances or, in other words, 2070 independent activation/inactivation variables.

One of the main technical challenges when performing dynamic clamp experiments is limiting and controlling the amount of jitter, i.e. the variability in the update cycle interval (Butera et al., 2001; Dorval et al., 2001; Raikov et al., 2004). This is a particular problem when using operating systems that are not designed for real-time tasks such as Windows. Therefore, to test the amount of jitter present in NeuReal we collected data for 200000 samples over 20 trials from the Digidata board at sampling frequencies from 10 to 100 kHz. Because different scheduling priorities can be assigned to programs running on Windows we repeated this procedure for the priority classes NORMAL, ABOVE_NORMAL, HIGH and REALTIME. In doing so we found that jitter predictably increased with update frequency and became generally worse as program priority was lowered (Fig. 3B). However, despite obviously not matching the performance achieved with hard real-time systems, we deemed that up to 50 kHz the REALTIME priority class displayed a tolerable level of variability (Fig. 3B, filled black squares).

We next tested the ability of NeuReal to perform a basic dynamic clamp function. In particular, we compared the results of injecting an artificial T-type Ca^{2+} current (I_{T}) (g_{T}=60 nS) and hyperpolarization-activated mixed cation current (I_{h}) (g_{h}=40 nS) into a passive ‘model’ cell (Axon Instruments CLAMP-1U model cell) (Fig. 3C_{2}) with those from a pure simulation using the same currents in a neuron with identical passive properties (input resistance=50 MΩ and membrane capacitance=470 pF) (Fig. 3C_{1}). We also compared the results of these experiments with a pure simulation performed using conventional floating point operations (Fig. 3C_{3}). As shown in Fig. 3C, the output in each scenario was virtually indistinguishable (Fig. 3C_{4}). We also tested the ability of NeuReal to perform a basic dynamic clamp experiments on a real TC neuron. Specifically, we demonstrated the ability of NeuReal to recreate the I_{T}-mediated low-threshold Ca^{2+} potential (LTCP) following block of endogenous I_{T} with Ni^{2+} (Fig. 4) (Hughes et al., 1999b). This experiment also allowed us to highlight the value of providing the capacity to interactively alter key parameters such as the acceleration and deceleration of kinetics and maximal conductances because we often found that to achieve an accurate replication of the original LTCP required modifications in the kinetics (Fig. 4B).

To test the implementation of artificial dendrites we made additional intracellular recordings from TC neurons of the cat LGN and attached a 155 compartment dendritic tree structure possessing various types of ion channel distributions. This dendritic tree was based on the morphology of an X cell in the LGN (Fig. 5) (Bloomfield et al., 1987; Emri et al., 2000) (see Appendix) and possesses a simplified symmetrical branching pattern. To illustrate the ability of NeuReal to operate efficiently on a modestly powered computer, these experiments were run with a PC possessing a 700 MHz Pentium processor and 256 MB of RAM. In a first set of experiments we injected a simple positive current pulse at the soma whilst designating the dendritic tree as fully passive. In doing so we noted a minimal backpropagation of somatic action potential activity into the dendritic tree that was substantially attenuated beyond the first branch point (Fig. 5A). We then repeated this experiment with an active dendritic tree possessing a uniform distribution of I_{Na} and I_{Kdr} channels (25 and 12 mS/cm^{2}, respectively) (Fig. 5B). In this scenario, we noted that action potentials actively propagated into distal portions of the dendritic tree with minimal attenuation (Fig. 5B).

Previous modelling work has suggested that the ability of TC neurons to generate intrinsic δ oscillations at ~1-2 Hz (McCormick and Pape, 1990; Leresche et al., 1991) is not solely dependent on somatic T-type channels but is also influenced by dendritic T-type channels and the balance between the conductance of dendritic T-type channels and K^{+} channels (Emri et al., 2000). To test this we performed a second series of experiments where 8 identical artificial dendritic trees with a high uniform concentration of T-type channels (2 mS/cm^{2}) as in (Emri et al., 2000) were attached to a real LGN TC neuron that was otherwise not exhibiting spontaneous oscillatory activity (Fig. 6). In doing so, we found that characteristic oscillatory activity could be induced at the soma following artificial dendritic attachment as long as i) sufficient dendritic I_{h} was present (0.5 mS/cm^{2}) and ii) the dendritic leak conductance was reduced from 0.062 to 0.04 mS/cm^{2} (Fig. 6A and B). In these experiments, we also included a small amount of I_{Kdr} (2 mS/cm^{2}). Interestingly, because of the small amount of K^{+} conductance present on the dendrites in this scenario, introduction of a even moderate amount of dendritic Na^{+} conductance (6 mS/cm^{2}) led to oscillations taking on a more paroxysmal appearance in the dendrites that was clearly reflected at the soma (Fig. 6B).

In a final set of experiments, we tested the ability of NeuReal to implement a large hybrid network simulation. Again, these experiments were performed with a modestly powered PC possessing a 700 MHz Pentium processor. Our previous work has indicated that the cat LGN contains a specialized subset of TC neurons which show intrinsic rhythmic bursting at ~10 Hz (high-threshold, HT, burst cells) and which are connected by electrical synapses (Hughes et al., 2004; Hughes and Crunelli, 2005). These properties lead to the generation of waxing and waning field oscillations at 10 Hz resembling *in vivo* alpha rhythms (Hughes et al., 2004; Hughes and Crunelli, 2007). To test the effect of these network oscillations on conventional tonic firing, i.e. relay mode, TC neurons which can also be linked to HT burst cells via electrical synapses (Hughes et al., 2002a), we constructed an artificial HT burst cell network and connected it via artificial electrical synapses to a real tonic firing TC neuron (Fig. 7).

The artificial network consisted of 49 HT bursting cells that were randomly interconnected by electrical synapses such that on average each cell was connected to 2.2 others (Fig. 7A). All HT bursting cells had equivalent properties (see Appendix) except that a random amount of steady current between 40 and 60 pA was applied to each cell. Under these conditions, the isolated network generated a waxing and waning population oscillation at ~8 Hz which closely resembled that observed in recent experiments (Fig. 7B) (Hughes et al., 2004; Hughes and Crunelli, 2007). Examination of individual cells showed that this waxing and waning was related to spontaneous and apparently random shifts in synchrony between individual cells (Fig. 7B). We then connected the network to a real tonic firing TC neuron by 3 additional electrical synapses originating from distinct HT burst cells (Fig. 7A and D). This led to the tonic firing TC neuron receiving a clear rhythmic modulation of membrane potential from the network (Fig. 7D, bottom left) with this modulation able to powerfully influence spike timing (Fig. 7D, bottom right).

We have described a Windows XP-based prototype computer system, NeuReal, which provides an easy-to-use fast simulation platform for facilitating the attachment of multi-compartmental artificial dendrites to real neurons and for implementing large hybrid neuronal networks. We demonstrate this system with a series of simple experiments in LGN TC neurons which highlight both the feasibility of the artificial dendrite concept as well as the benefits of examining large hybrid networks.

Until relatively recently, dendrites were considered to be passive structures that act to transmit distally-generated synaptic potentials to the site of action potential initiation. It is now well known though that such structures are endowed with a large variety of active ionic conductances which contribute greatly to determining the integrative properties of individual neurons (Hausser et al., 2000). However, the practical difficulties associated with directly investigating active dendritic structures are widely acknowledged and present considerable technical issues (Davie et al., 2006). This is especially true for distal or thin dendrites (Nevian et al., 2007) and for non-planar structures which can be easily compromised in brain slice preparations (Williams and Stuart, 2000). One solution to these problems is to use multicompartmental models which are constrained by a combination of available data and the requirement to realistically reproduce specific somatic activities (De Schutter and Bower, 1994; Traub et al., 1994; Mainen and Sejnowski, 1996; Emri et al., 2000). Despite the value of this approach an obvious drawback is that the results are to some extent always dependent on estimation and affected by incomplete data. The attachment of artificial dendrites to real neurons provides a compromise between direct electrical recording of dendrites and pure modelling. For example, whilst simulated dendrites are subject to the same issues that affect a pure simulation, the signals under investigation in these dendrites are at least partly dictated by the activity of a real neuron (e.g. Fig. 5). Similarly, it allows examination of how different types of dendritic morphology and ion channel distributions can influence the electrical behaviour of a real soma (e.g. Fig. 6).

Since we first introduced the concept of artificial dendrites (Hughes et al., 1998b,1999a) we are only aware of one other publication which has explored this idea (Dorval et al., 2001). However, to our knowledge, the current study is the first to demonstrate its application to real neurons. As such, we provide results which endorse the view that low frequency (~1-2 Hz) oscillatory activity in LGN TC neurons involves an active interaction of both somatic and dendritic T-type Ca^{2+} channels (Emri et al., 2000). Our results also indicate that a reduction of dendritic leak K^{+} conductance may be an important element in bringing about such oscillations. This is consistent with the known pro-oscillatory effects of activating metabotropic glutamate receptors (mGluRs) on TC neurons which are known to be located on distal dendrites and which are negatively coupled to leak K^{+} channels (Hughes et al. 2002b; Hughes et al., 2004).

We have also demonstrated the ability of NeuReal to implement a sizeable hybrid network. This enabled us to show how a specialized group of electrically coupled pacemaker cells might influence relay mode firing in conventional tonic firing TC neurons. More generally, and by employing more powerful computers, NeuReal offers the viable opportunity to examine how the activity of real neurons is shaped by being embedded in networks of several thousand biophysically realistic modelled cells which are entirely under the interactive control of the experimenter.

Compared to other systems which provide dynamic clamping the main advantage of NeuReal is the ability to rapidly construct and simulate a large number of intrinsic and synaptic conductances. The system is easy to use, possessing an intuitive Windows interface for object editing, rolling oscilloscope-like displays for visualizing data, a fully interactive experimental interface that allows all key parameters to be altered on demand and the ability to record, replay and export data. NeuReal offers a reasonable level of performance up to a sampling rate of 50 kHz. However, unlike other systems, NeuReal does not deliver so-called hard real-time performance, whereby the timing of the input and output of analogue voltage signals is precisely controlled and deterministic within a set of strict criteria, and because of the nature of the Windows operating system jitter is not normally distributed with occasionally long delays of a several milliseconds occurring. The accuracy of the system is also limited by the tabulation techniques and by the 12-bit integer representation of membrane potential provided by the ADC/DAC board. Whilst we fully acknowledge the importance of these issues our initial primary objective was solely to build a prototype system that could demonstrate the feasibility of implementing realistic artificial dendrites and large hybrid networks, and which could do so in an easy to use manner and on modest and readily available hardware. Having achieved this, our next aim is to address the more precise demands of hard real-time computing and enhance the accuracy of the numerical methods whist maintaining a high level of performance and usability. With respect to this, whilst other systems which deliver hard real-time performance have used extensions to the Linux operating system (Butera et al., 2001; Dorval et al., 2001; Raikov et al., 2004; Mũniz et al., 2005), the emergence of extensions to the Windows XP and Windows Vista operating systems that also offer hard real-time performance might provide a powerful combination of ease-of-use and high performance. Indeed, our preliminary tests using real-time extensions to Windows XP indicate that such a system is a viable prospect. We also plan to implement the use of more advanced ADC/DAC hardware interfaces and provide support for importing neuronal models built with other systems (e.g. Bower and Beeman, 1997; Hines and Carnevale, 1997; Gleeson et al., 2007) along similar, but ultimately more generic, lines to the RT-NEURON system (Debay et al., 2004). RT-NEURON is a real-time version of the NEURON simulation environment which operates under the linux operating system and which provides similar functionality to the system described here. It has been used extensively in a number of studies in recent years (Derjean et al., 2003; Rudolph et al., 2004; Wolfart et al., 2005; Pospischil et al., 2007).

Finally, an important aspect of NeuReal is that rather than being simply a dedicated dynamic clamp system, it is essentially a modelling system which allows the construction of hybrid real-artificial neuron simulations within which simple dynamic clamp experiments are just a small subset. As such, we believe that NeuReal represents a clear conceptual departure from more specialized dynamic clamp systems and has significant potential as a research tool which, if used appropriately taking into consideration the well known general limitations of dynamic clamp experiments (Prinz et al., 2004), greatly extends the range of experimental options that are immediately available to the investigative electrophysiologist.

This work was supported by the Wellcome Trust (grants 71436, 78403 to VC and 78311 to SWH). Additional information regarding this and our other published work is available at http://www.thalamus.org.uk.

In the following descriptions, g_{x} and E_{x} are the respective maximal conductances and reversal potentials.

Fast inactivating Na^{+} current, I_{Na}:

$${\mathrm{I}}_{\mathrm{Na}}={\mathrm{g}}_{\mathrm{Na}}{\mathrm{m}}^{3}\mathrm{h}(\mathrm{V}-{\mathrm{E}}_{\mathrm{Na}})$$

$$\begin{array}{c}\hfill {\tau}_{\mathrm{m}}=1/({\alpha}_{\mathrm{m}}+{\beta}_{\mathrm{m}})\phantom{\rule{thinmathspace}{0ex}}\text{and}\phantom{\rule{thinmathspace}{0ex}}{\mathrm{m}}_{\infty}={\alpha}_{\mathrm{m}}{\tau}_{\mathrm{m}}\hfill \\ \hfill {\tau}_{\mathrm{h}}=1/(\alpha \mathrm{h}+{\beta}_{\mathrm{h}})\phantom{\rule{thinmathspace}{0ex}}\text{and}\phantom{\rule{thinmathspace}{0ex}}{\mathrm{h}}_{\infty}={\alpha}_{\mathrm{h}}{\tau}_{\mathrm{h}}\hfill \end{array}$$

$$\begin{array}{c}\hfill {\alpha}_{\mathrm{m}}=032(\mathrm{V}+49.3)/[1-\mathrm{exp}(-(-\mathrm{V}+49.3)/4\left)\right]\hfill \\ \hfill {\beta}_{\mathrm{m}}=028(\mathrm{V}+22.3)/\left[\mathrm{exp}\right((\mathrm{V}+22.3)/5)-1]\hfill \\ \hfill {\alpha}_{\mathrm{h}}=0128\mathrm{exp}(-(\mathrm{V}+45.4)/18)\hfill \\ \hfill {\beta}_{\mathrm{h}}=4/\left[\mathrm{exp}\right(-(\mathrm{V}+22.4)/5+1]\hfill \end{array}$$

Delayed rectifier K^{+} current, I_{Kdr}:

$${\mathrm{I}}_{\mathrm{K}\mathrm{dr}}={\mathrm{g}}_{\mathrm{K}\mathrm{dr}}{\mathrm{m}}^{4}.(\mathrm{V}-{\mathrm{E}}_{\mathrm{K}})$$

$${\tau}_{\mathrm{m}}=1/({\alpha}_{\mathrm{m}}+{\beta}_{\mathrm{m}})\phantom{\rule{thinmathspace}{0ex}}\text{and}\phantom{\rule{thinmathspace}{0ex}}{\mathrm{m}}_{\infty}={\alpha}_{\mathrm{m}}.{\tau}_{\mathrm{m}}$$

$${\alpha}_{\mathrm{m}}=0.159(\mathrm{V}+53.7)/[1-\mathrm{exp}(-(\mathrm{V}+53.7)/5\left)\right]$$

$${\beta}_{\mathrm{m}}=2.48.\mathrm{exp}(-(\mathrm{V}+55.2)/40)$$

Low-threshold Ca^{2+} current, I_{T}:

$${\mathrm{I}}_{\mathrm{T}}={\mathrm{g}}_{\mathrm{T}}{\mathrm{m}}^{3}\mathrm{h}(\mathrm{V}-{\mathrm{E}}_{\mathrm{Ca}})$$

$$\begin{array}{c}\hfill {\mathrm{m}}_{\infty}=1/\{1+\mathrm{exp}[-(\mathrm{V}+63)/7.8\left]\right\}\hfill \\ \hfill {\mathrm{h}}_{\infty}=1/\{1+\mathrm{exp}[(\mathrm{V}+83.5)/6.3\left]\right\}\hfill \end{array}$$

$$\begin{array}{c}\hfill {\tau}_{\mathrm{m}}={\lambda}_{\mathrm{m}}[2.44+0.0250\mathrm{exp}(-0.0984.\mathrm{V}\left)\right]\hfill \\ \hfill {\tau}_{\mathrm{h}}={\lambda}_{\mathrm{h}}[19.15+0.07171\mathrm{exp}(-0.1054.\mathrm{V}\left)\right]\hfill \end{array}$$

Where λ_{m}=λ_{h}=1.0, unless otherwise stated, and λ_{m}=0.1 and λ_{h}=0.3 for the HT burst cell model (Hughes et al., 2004).

Hyperpolarization-activated mixed cation current, I_{h}:

$${\mathrm{I}}_{\mathrm{h}}={\mathrm{g}}_{\mathrm{h}}{\mathrm{m}}^{3}\mathrm{h}(\mathrm{V}-{\mathrm{E}}_{\mathrm{h}})$$

$$\begin{array}{c}\hfill {\mathrm{m}}_{\infty}=1/\{1+\mathrm{exp}[(\mathrm{V}+75)/5.5\left]\right\}\hfill \\ \hfill {\tau}_{\mathrm{m}}=20820\mathrm{exp}\left(0.0614\mathrm{V}\right)\phantom{\rule{thinmathspace}{0ex}}\text{if}\phantom{\rule{thinmathspace}{0ex}}\mathrm{V}\le -77.58\hfill \\ \hfill {\tau}_{\mathrm{m}}=29.54\mathrm{exp}(-0.0458\mathrm{V})\phantom{\rule{thinmathspace}{0ex}}\text{if}\phantom{\rule{thinmathspace}{0ex}}\mathrm{V}>-77.58\hfill \end{array}$$

For all simulations we also included a leak K^{+} current with a reversal potential of -95 mV.

The dendritic tree structure used in this study was identical to that used in the recent modelling study by Emri et al. (2000). Briefly, it has a somato-dendritic path of symmetrical geometry with 5 levels of hierarchy and bifurcations at each level. The respective lengths of each level, starting from the most proximal, are 20, 17.5, 4, 55 and 75 μm and their respective diameters are 3.7, 2.3, 1.5, 0.9 and 0.6 μm. Each dendritic branch is subdivided into 5 independent compartments of less than 0.05 electrotonic length (L). The axial resistivity, R_{a}=0.33 Ωcm and the membrane capacitance, C_{m}=1μF/cm^{2}. The membrane resistivity, R_{m}=15 kΩcm^{2} m and was adjusted to yield a total electrotonic length of L=0.53.

HT burst cells were modelled as a single compartment with a surface area of 5000 μm^{2} giving a total membrane capacitance of 50 pF. Each cell possessed I_{Na}, I_{Kdr}, I_{T}, I_{h} and I_{Leak} with maximal conductances of 1677 nS, 400 nS, 50 nS, 40 nS and 3 nS respectively. All electrical synapses had a conductance of 500 pS.

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