Simulation of alcohol action upon a detailed Purkinje neuron model and a simpler surrogate model that runs >400 times faster
© Forrest; licensee BioMed Central. 2015
Received: 19 July 2014
Accepted: 10 April 2015
Published: 26 April 2015
An approach to investigate brain function/dysfunction is to simulate neuron circuits on a computer. A problem, however, is that detailed neuron descriptions are computationally expensive and this handicaps the pursuit of realistic network investigations, where many neurons need to be simulated.
We confront this issue; we employ a novel reduction algorithm to produce a 2 compartment model of the cerebellar Purkinje neuron from a previously published, 1089 compartment model. It runs more than 400 times faster and retains the electrical behavior of the full model. So, it is more suitable for inclusion in large network models, where computational power is a limiting issue. We show the utility of this reduced model by demonstrating that it can replicate the full model’s response to alcohol, which can in turn reproduce experimental recordings from Purkinje neurons following alcohol application.
We show that alcohol may modulate Purkinje neuron firing by an inhibition of their sodium-potassium pumps. We suggest that this action, upon cerebellar Purkinje neurons, is how alcohol ingestion can corrupt motor co-ordination. In this way, we relate events on the molecular scale to the level of behavior.
At present, there are two minimally interacting levels of investigation in computational neuroscience. In the first, researchers use Hodgkin-Huxley models of currents  and compartmental/cable modeling of dendrites [2,3] to assemble detailed single neuron descriptions. In the second, researchers study neural circuits and find it useful to represent each neuron and synapse as simply as possible, ignoring much of the biological detail. This demarcation is principally because the computational complexity of the former is not conducive to the scaling of the latter. This issue is unfortunate as there is some evidence that the richness of biophysical properties on the single neuron scale can supply mechanisms that serve as the building blocks for network dynamics . There is a great potential for bridging the gap between these two levels of enquiry, using network models with neurons of intermediate biological fidelity and moderate computational complexity. These studies can unify cellular and networks studies and identify how distinctive single neuron behaviors are important to network and system function.
In vitro, within cerebellar slices, Purkinje neurons can spontaneously fire action potentials in a repeating trimodal pattern that consists of tonic spiking, bursting and quiescence [5-10]. Our biophysically detailed Purkinje neuron model of  can replicate this activity. It has a faithfully reconstructed morphology and it is computationally intensive. It has 1089 compartments and requires ~8 minutes of CPU time for 1 second of simulation (Intel core PC, i5). So, whilst it is appropriate for studying properties of the individual Purkinje cell, it is unfavorable for incorporation into cerebellar network simulations. In this paper, we introduce and employ a novel mathematical transform to produce a simpler, surrogate version of this model that has the same electrical properties, but a much lower computational overhead. It has just 2 compartments – a somatic compartment and a dendrite compartment. It runs >400 times faster than the full model. We demonstrate its expediency by showing that it can replicate the full model’s simulated response to alcohol (ethanol). Both models are available to researchers in the ModelDB [12; RRID: nif-0000-00004].
Seo and Suh  studied, in vitro, alcohol’s effect upon the firing pattern of Purkinje neurons in rat cerebellar slices. Prior to the application of alcohol some Purkinje cells were quiescent and others fired spikes spontaneously - some continuously and others in an oscillatory pattern of firing and quiescence. The application of alcohol shifted some quiescent cells into continuous spiking, it shifted some simple and oscillatory firing cells into quiescence and it shifted some oscillatory cells into simple, continuous spiking. These results are hard to reconcile. Seo and Suh  observe and describe this behaviour; they do not provide an explanation for it. Here, we use our Purkinje neuron model – with its detailed and reduced versions - to deliver a hypothesis that can accommodate these observations. We suggest that these results can be understood if alcohol action upon Purkinje cells is via an inhibition of its Na+/K+ pumps. There is some precedent to this as alcohol has been reported to inhibit Na+/K+ pumping in a number of other contexts [14-19].
The Na+/K+ pump uses the energy of one ATP molecule to exchange three intracellular Na+ ions for two extracellular K+ ions . Thus the pump is electrogenic, extruding one net charge per cycle to hyperpolarize the membrane potential. We hypothesise, as we did in , that quiescent Purkinje cells are silent because the hyperpolarising action of the Na+/K+ pump clamps their intrinsic excitability and prevents spontaneous spike generation. Furthermore, in this manuscript we suggest that alcohol application inhibits the Na+/K+ pump, reduces its clamping action and permits spontaneous spiking. So, we suggest that spontaneously firing Purkinje cells are distinct from intrinsically quiescent Purkinje cells because of a lower Na+/K+ activity.
The Na+/Ca2+ exchanger current is net depolarizing (-1), inwardly passing 3 singly positive Na+ ions (3*[+1]) for the extrusion of every doubly positive Ca2+ ion (1*[+2]) . The Na+/K+ pump current, by contrast, is net hyperpolarizing (+1). Our model incorporates our hypothesis (which is partially founded in the experimental work of Genet and Kado ) that, in Purkinje neurons, the hyperpolarizing Na+/K+ pump current electrically balances a depolarizing Na+/Ca2+ exchanger current. We suggest that alcohol inhibits the Na+/K+ pump and that this results in membrane depolarisation, because there is no longer this counterbalance to the depolarising Na+/Ca2+ exchanger current. This depolarisation can cause quiescence through a depolarisation block.
We suggest that the quiescent periods in oscillatory patterns of spontaneous Purkinje cell firing are produced by the electrogenic action of Na+/K+ pumping. This hypothesis is incorporated in the model. Relevantly, in rat cerebellar slices, an ouabain block of Na+/K+ pumps eradicates the quiescent mode in the trimodal and bimodal patterns of Purkinje cell activity, which might suggest that Na+/K+ pumping is their generative mechanism . So, we suggest that alcohol inhibits the Na+/K+ pump and that this inhibition can switch a Purkinje cell from an oscillatory to a continuous firing mode. This is because there is no longer the requisite Na+/K+ pump activity to generate the quiescent periods.
This work aligns with our previous research [11,23-27] and suggests that the Na+/K+ pump controls the intrinsic activity mode of cerebellar Purkinje neurons. We previously modelled the Purkinje neuron in the context of its inputs and showed how the Na+/K+ pump may be directly involved in cerebellar information processing . The cerebellum is responsible for motor co-ordination  and alcohol consumption corrupts motor control. We speculate that ingested alcohol disrupts cerebellar computation, and motor control, by inhibiting the Na+/K+ pump in cerebellar Purkinje neurons.
Our reduced Purkinje neuron model is useful for inclusion in network models. This is its first application. The second is that it can be used to advance the future development of the full, detailed Purkinje neuron model. In single neuron modelling, most parameters can be established by experimental recordings. However, there is a problematic exception. Maximal conductance (gmax) values for ion currents are not well defined by present experimental techniques. In model construction, these are typically set as free parameters and tuned - often manually  (e.g. ) - by iteratively running the model with different values and observing which combination of these give the best fit between real and model cell output. Typically, a great number of model runs is required and with the computational expense of a detailed, morphologically faithful neuron model: each run takes a significant period of time. In the case of manual tuning, which can be the only route to an optimised model in some cases, it can be a very frustrating, time consuming and laborious process. Model tuning of two compartment models, with their faster run time, is an easier task. And with our two compartment Purkinje cell model, with its relation and concordance to the full Purkinje cell model: tuning gains in the two compartment model translates to equivalent gains in the full Purkinje cell model. Hence, the two compartment model can be used profitably as a proxy for tuning the full model. So, in this manuscript we present a reduced Purkinje neuron model. However, we anticipate that its principal legacy may be to facilitate the further development of more detailed, morphologically realistic Purkinje neuron models. We demonstrate this utility by using our reduced model to find parameter values that will permit our full model to replicate new behaviour; that observed experimentally for cerebellar Purkinje neurons in mice that have a BK channel genetic knockout [31,32]. These mice display cerebellar ataxia.
Numerical simulations were performed with the NEURON 7.3 simulator [33; RRID: nif-0000-00081], using its backward Euler integration method and 25 μs time steps. Fixed time step integration was used throughout. Preliminary, feasibility testing with a variable time step method (CVODE in NEURON, ), even with a high error tolerance, did not produce significant speeding of simulations (data not shown).
Our reduction algorithm is a simple extension to an existing reduction algorithm [34,35]. Like the original formulation, it collapses the elaborate dendritic arbour into a smaller number of compartments whilst conserving axial resistance (Ra ). However, unlike prior formulations it collapses the dendritic tree to just a single compartment. Furthermore, it has an additional step whereby the length of the dendrite compartment is increased, with a compensatory change in radius to keep the compartment’s volume constant. This added step is required in order for the reduced Purkinje neuron model to replicate the behavior of the full Purkinje neuron model and express the trimodal activity pattern. The optimal dendrite length is found by manual tuning.
Recently an alternative extension to the algorithm of [34,35] has been published, in which the collapsing function incorporates a Strahler analysis of the dendritic tree [36,37]. However, this method typically produces reduced models of the cerebellar Purkinje cell that have tens of compartments and run, on average, ~20 times faster than the full model . Our reduction method produces a faithful 2 compartment model that runs >400 times faster.
This final manipulation is to confront the fact that the collapsing function does not conserve dendritic length. It gives the equivalent cylinder a short Length of 120.9 μm (and Diameter of 6.74 μm). This is a problem because Purkinje cell functioning requires a degree of uncoupling (distance) between somatic and dendritic events. With this length of dendritic compartment, the model cannot replicate the Purkinje cell’s trimodal firing pattern (data not shown). To address this, we set the equivalent cylinder with a Length of 529.29 μm and adjusted its Radius, to 1.61 μm, in order to keep the volume constant (Eq. 4). This optimal length was found by manual tuning and was with a specific axial resistivity (Ra) of 35.4 Ωcm (the default NEURON setting). If Ra is different, then the optimal dendrite compartment dimensions are different. For example, with a Ra value of 250 Ωcm, the dimensions are instead: Length = 240 μm; Radius = 4.78 μm.
We have previously published a 41 compartment and a 5 compartment model of the cerebellar Purkinje neuron . These models can replicate the Purkinje cell’s trimodal pattern of firing. However, the model of this current manuscript is superior to these because a model with just 2 compartments is the more elegant solution; not least because it runs faster. In addition, we describe the 2 compartment model here in immense detail to maximize its utility to other researchers. This level of detail is missing in .
The dendritic correction factor C d is the ratio of the total surface area of the dendritic segments to their equivalent cylinder (42,310/6,874 = 6.16). The model’s somatic compartment is not introduced into the collapsing algorithm and so in the reduced model it has the same dimensions as in the full model, and the C d correction factor is not applied to any of its parameters.
The Q parameter is a setting in the model’s description of extracellular K+ dynamics and in the full, 1089 compartment model it is 0.06. This parameter isn’t set or constrained by any feature of the reduction algorithm used and is not constrained by any experimental literature. It is a free parameter. We manually tuned this parameter to confer a best fit between reduced and full model output, ultimately assigning it a value of 0.0119. This is distinct from the value of 0.37 obtained by a C d manipulation (0.06 * C d = 0.37, where C d is 6.16) but this is of no consequence, as there is no directive in the literature for applying C d to such a parameter. If a different value of Ra is assigned, different dendrite dimensions are to be used (as aforementioned), and the Q parameter needs to be re-tuned. For example, if Ra = 250 Ωcm, Q = 0.0103 gives a best fit.
In the 1089 compartment model of Forrest et al. , spines were accounted for (implicitly) by setting the 1003 spiny dendrite compartments with a higher specific membrane capacitance (C m) value than the 84 smooth dendrite compartments (C m = 0.8 μF/cm2 for the smooth dendrites, C m = 1.5 μF/cm2 for the spiny dendrites). Our 2 compartment model makes no such account of spines; for its dendritic compartment: C m = 0.8 μF/cm2 (before the C d manipulation).
So, to summarize the reduction methodology: the full morphology is collapsed into just a soma compartment and a single dendrite compartment. This is done using the algorithm/NEURON code of , but modified to collapse the dendrites to just one compartment instead of three (this modified code is included with our model entry in ModelDB ). The length of this single dendrite compartment is then manually tuned to confer the best fit between reduced and full model output. For an inputted change in dendrite length, coding is used to automatically update other linked variables such that the user only has to tune this single parameter. For a change in dendrite length, the dendrite radius is automatically, accordingly updated to keep the dendrite volume constant. Furthermore, the surface area of the updated dendrite compartment is measured and a new, appropriate C d value is automatically calculated and applied. This coding form is in the NEURON code of the model, available in ModelDB . So, to re-iterate, only a single variable needs be adjusted to tune the reduced model; such that it can best reproduce the behaviour of the full model. We adjusted it manually but with it being just a single parameter, it is likely tractable to automatic tuning methods. Thus described is the principal, crucial step to tuning. However, as aforementioned, after the optimal dendrite length has been found, an even closer fit between reduced and model output can then be reached by going on to tune the Q model parameter. This latter step is specific to this cerebellar Purkinje neuron model but we anticipate that the prior steps are more general and could be used to produce 2 compartment models for other neuron types.
C m is the membrane capacitance (0.8 μF/cm2), I is the current, V is the membrane potential in mV, t is time, T is temperature (36 ° C), Ra is the specific axial resistivity (35.4 Ωcm and gmax is the maximal conductance (“current density”).
Maximal current conductances (g max ; mS/cm 2 ) for the Full, 1089 Compartment model and the Simplified, Two Compartment model
Dendrite(1089 compartment model)
Dendrite (two compartment model)
Delayed rectifier K+
Highly TEA sensitive K+
Moderately TEA sensitive K+
TEA insenstitive K+
hyperpolarization activated cation, Ih
The soma is a cylinder (length = 22 μm, diameter = 22 μm). EK is the reversal potential for K+ (initiated at -88 mV), ENa is the reversal potential for Na+ (initiated at +70 mV), ECa is the reversal potential for Ca2+ (initiated by the NEURON default value; +132 mV), EL is the reversal potential for the Leak current (-70 mV), Eh is the reversal potential for the hyperpolarisation activated cation current (-30 mV), Intracellular Ca2+ concentration is initiated at the NEURON default of 5*10−5 mM; Extracellular Ca2+ concentration is initiated at the NEURON default of 2 mM. The somatic membrane voltage (V) is initiated at the NEURON default of -65 mV.
Dendrite – Soma electrotonic current 
VD is the membrane voltage at the centre of the dendrite compartment, VS is the membrane voltage at the centre of the soma compartment and RDS is the axial Resistance between the two. Ra is the specific axial Resistivity, LS and rS are the length and radius of the soma respectively; LD and rD are the length and radius of the dendrite respectively.
Highly TEA sensitive K+ current 
Moderately TEA sensitive K+ current 
TEA insensitive K+ current 
P-type Ca2+ current 
Hyperpolarisation activated cation current 
BK type K+ current 
Leak current 
Intracellular Ca2+ concentration 
SK type K+ current 
Na+/K+ pump 
Na+/Ca2+ exchanger current and an electrically counterbalancing Na+/K+ pump current 
Intracellular Na+ concentration 
The dendrite is a cylinder (length = 529.29 μm, diameter = 3.22 μm). EK is the reversal potential for K+ (initiated by the NEURON default value; -77 mV), ENa is the reversal potential for Na+ (initiated by the NEURON default value; +50 mV), ECa is the reversal potential for Ca2+ (initiated by the NEURON default value; +132 mV), EL is the reversal potential for the Leak current (-80 mV), Eh is the reversal potential for the hyperpolarisation activated cation current (-32.9 mV). Intracellular Ca2+ concentration is initiated at 4*10−5 mM; Extracellular Ca2+ concentration is initiated at 2.4 mM. Extracellular Na+ concentration is set by the NEURON default value; +140 mM.
Soma - dendrite electrotonic current 
VS is the membrane voltage at the centre of the soma compartment, VD is the membrane voltage at the centre of the dendrite compartment and RSD is the axial Resistance between the two. Ra is the specific axial Resistivity, LS and rS are the length and radius of the soma respectively; LD and rD are the length and radius of the dendrite respectively.
T-type Ca2+ current 
E-type Ca2+ current 
P-type Ca2+ current 
Hyperpolarisation activated cation current 
Kv1.2 K+ current 
A-type K+ current 
M-type K+ current 
D-type K+ current 
These equations are based upon the NEURON code of , as opposed to the equations in their associated journal paper; there is some minor discrepancy between the two. This code was sourced from ModelDB .
Delayed Rectifier type K+ current 
BK type K+ current 
These equations are based upon the NEURON code of , as opposed to the equations in their associated journal paper; there is some minor discrepancy between the two. This code was sourced from ModelDB .
K2 type K+ current 
These equations are based upon the NEURON code of , as opposed to the equations in their associated journal paper; there is some minor discrepancy between the two. This code was sourced from ModelDB .
Leak current 
Intracellular Ca2+ dynamics 
Na+/K+ pump 
Na+/Ca2+ exchanger current and an electrically counterbalancing Na+/K+ pump current 
Extracellular K+ dynamics 
Eq. 141 is based upon the NEURON code of , as opposed to the relevant equation in their associated journal paper; there is a minor discrepancy between the two (the paper does not have the dimensionality factor (1000) in its equation).
On an Intel core PC (i5), the 2 compartment model took 1.11 seconds of CPU time for 1 second of simulation. So, simulations with this model run at real time (approximately). This is ~414* faster than the 1089 compartment model.
Alcohol action upon the Reduced Purkinje neuron model
Alcohol action upon the Detailed Purkinje neuron model
One will note that the reduced model’s response to alcohol is simulated for 120 seconds, whilst the full model’s response to alcohol is only simulated for 90 seconds. This is because of the computational expense of the full model. The reduced model could be run quickly on a laptop (Intel I5) and simulating it for 120 model seconds was not a problem. The full model, however, could not be simulated over this time frame, on these means, within a reasonable time span. We found that this is because the real time taken to simulate a given unit of model time increases to larger values with longer simulations. We simulated the full model for 20 seconds and using the real time taken for this simulation, we extrapolated that a simulation of 120 seconds would take at least 3 days; if not a lot more. The full model was uploaded to the Neuroscience Gateway Portal ; RRID: nlx_151553] and run on its Trestles high performance computing (HPC) system, hosted at the San Diego Supercomputer Centre (SDSC). The maximum run time permitted for a job submitted to this system is 15 hours. However, even 15 hours is not long enough for the full model to simulate 120 seconds; only ~90 seconds can be simulated before the 15 hour limit cuts out the simulation. The reduced model runs 560 times faster on a laptop than the detailed model runs on a supercomputer. Furthermore, the former is without the hassles of uploading, job cues, downtime and allocations/limits on use. Investigating the reduced model locally can prime investigations with the full model run on remote resources. Reasonably, we would not have been able to “find” the arbitrary functions of Na+/K+ pump density decline (Eq. 147) that produce the illustrative behavior in the full model (Figure 5), without going through the intermediary of the reduced model. This point is amplified upon, with another example, in the next section.
Our detailed Purkinje neuron model was run serially on the Trestles supercomputer but we anticipate that our source code could be changed in the future such that it could be run in a parallel fashion. Recently, a parallel computation method has been shown to be viable for single neuron models [47,48] and this method is available on the Neuroscience Gateway Portal .
The two compartment model as a resource for manual tuning of model parameters in a full model
Here we shall demonstrate that the 2 compartment, reduced model can be used as a proxy for tuning the detailed, morphologically faithful model. We show that the reduced model can be used to find parameter values that will permit the full model to replicate new behaviour; that observed experimentally for cerebellar Purkinje neurons in mice that have a BK channel genetic knockout [31,32].
In the cerebellum of a BK knockout mouse (BK-/-), where BK loss is certainly absolute, a large percentage (>50%) of Purkinje neurons are observed to be stuck in depolarisation block quiescence [31,32]. This is in contrast to the wild-type, where none of them are. This data supports our model. However, even in BK-/- mice, some Purkinje neurons are still observed to fire in tonic and/or burst forms. In this case there must be an alternative current acting to repolarise dendritic Ca2+ spikes. This may be due to a “homeostatic remodelling” process  – the increased expression of other K+ currents during development to compensate for the absence of BK channels. Or it could be that a certain percentage of Purkinje neurons, even in the wild-type, do not use BK to repolarise dendritic Ca2+ spikes; but instead use some alternative. So, in different Purkinje neurons, there may be different ionic solutions to producing a certain firing pattern. This may be a more general feature of neurons – there may not be a single, stereotypical set of conductances for a particular neuron type, but a family of different settings – possibly all producing very similar firing characteristics .
What alternative conductance could repolarise dendritic Ca2+ spikes in Purkinje neurons? Purkinje neurons express Kv3.3 and Kv3.4 in their soma and dendrites . McKay & Turner  concluded that these are the principal agents to the repolarisation of dendritic Ca2+ spikes. They came to this conclusion because TEA, which blocks Kv3 and BK, produced a much greater deleterious effect upon this repolarisation than CBTX, which blocks BK only. However, as aforementioned, BK in Purkinje neurons has a CBTX resistant fraction and this was not factored into their interpretation. Furthermore, in Kv3.3-/- knockout mice, there is a maintained repolarisation of dendritic Ca2+ spikes in Purkinje neurons . Albeit that they are larger (reflecting a diminished repolarisation capacity) and occur more readily (have a lower threshold). SK may be involved but its block by apamin or scyllatoxin does not block repolarisation of dendritic Ca2+ spikes and the expression of the trimodal firing motif [6,7]. Intermediate conductance Ca2+-activated K+ channels (KCa3) are present in Purkinje neurons  but this channel class is blocked by CBTX and CBTX application does not block dendritic repolarisation and the trimodal pattern of firing .
Having found that ERG can repolarise dendritic Ca2+ spikes in the reduced model, we then tested it with the full model. The BK maximal conductance is set to 0 in all compartments; ERG is introduced into the model’s 1088 dendrite compartments with a maximal conductance (gmax) of 0.5 mS/cm2. We found that ERG can repolarise dendritic Ca2+ spikes in the full model also, at an equivalent maximal conductance value (Figure 8). This is the important point to take away here, over and above our illustrative “ERG hypothesis”: That the reduced model can be used as a proxy for tuning of the detailed model.
This result with ERG is intriguing because ERG is not typically associated with roles in the nervous system. Transcripts encoding ERG potassium channels are expressed by most neurons of the CNS but few ERG currents have actually been recorded in these neurons . ERG is typically known for its role in cardiac repolarisation and its dysfunction is associated with a number of cardiac arrhythmias [61,62].
A number of seminal theories of cerebellar functioning [63,64] have considered its component neurons to be linear summing devices (“integrate and fire”), ignoring their complexity, nonlinearity and computations. This is likely too abstractive. We believe that to understand the cerebellar network, researchers should employ network simulations that incorporate more detailed neuron descriptions. The Purkinje cell model of  is an intricate in silico experimental preparation. It favors detail over abstraction but this makes it computationally intensive and unsuitable for use in network simulations, with the computational resources that most investigators have available. With this in mind, we have used mathematical transforms to produce a simpler, faithful surrogate. We hope that researchers will utilize this in future cerebellar network studies; and identify how distinctive Purkinje cell behaviors are important to network and system function.
Wider utility of the reduction algorithm
We anticipate that the algorithm used here, to arrive upon a 2 compartment model of the cerebellar Purkinje cell, can be used to generate 2 compartment models of other neuronal types. Some research groups are aiming to model large neuron circuits, and even the entire brain , with morphologically realistic neuron descriptions and physiological numbers of brain cells. They aim to address the computational intensiveness issues by utilizing a supercomputer or a massively parallel CPU cluster. However, even with these resources, computational power will remain a significant limiting step for a long time to come; especially for simulations of brain activity on the scale of seconds or minutes. An interim step could be to assemble brain simulations with two compartment descriptions of neurons; using the kind of description that we have produced here for the cerebellar Purkinje cell.
We believe that our method of producing a two compartment model is superior to other methods that rely on an abstractive, coupling parameter between the two compartments . Our method produces a reduced model with more concordance to the full model, and permits findings from the reduced model to be more readily related to the full model.
Democratising neuroscience research
Computational neuroscience can be expensive. Many computational approaches are costly, requiring infrastructure (clusters, grids, supercomputers etc.) that typical researchers in the developing world cannot afford. However, we show that it is still possible to compete at the bleeding edge of single neuron modelling with just a PC. Extremely detailed neuron models can be developed on very limited computational resources if a reduced model is used as a proxy for development. This approach hinges upon creating and using a reduced 2 compartment neuron model, with its quick run-time, to explore new hypothesises and parameter settings. Then once an achievement has been attained in this system, investigating if the settings found in the reduced model can produce the same behaviour in the full model. It should be the case. The second confirmatory step can be accelerated by uploading the full model to the Neuroscience Gateway Portal ; although it can be very protracted even on these resources. This two-step approach can democratise participation in neuroscience research. Anyone with a PC can successfully participate and progress in developing detailed neuron models. This is important because there are many individuals that don’t have access to expensive computational infrastructure and/or experimental laboratory facilities but seek to contribute to science research.
A biophysical basis to the operating diversity of the cerebellar Purkinje neuron
Our detailed Purkinje neuron model  is not an exact simulacrum of a cerebellar Purkinje neuron and our work is not the final word in Purkinje neuron modelling. We have described our full  and reduced models in as much detail as we can with the hope that others can build upon our work as we have built upon the work of others e.g. [40,43,65-69]. Through the research community’s co-operative and iterative building, testing and exploring of models – feeding into, and responding to, experimental investigation - we can assemble a formal, quantitative underpinning to neuroscience . Models are especially useful for making sense of disparate data and explaining why different behaviour is observed in different Purkinje cells and/or in different experiments. In this study, we have used modelling to show how Purkinje cells can exhibit different activity states and how alcohol can shift them between these activity states. This work aligns with our previous study  and suggests that at the foundation of the Purkinje cell’s intrinsic multimodality, there is the working of just a single molecular species – the Na+/K+ pump.
Alcohol and the cerebellar Purkinje neuron
Alcohol consumption corrupts motor function and this is a significant factor in a large number of accidental injuries and deaths every year. The cerebellum controls motor co-ordination . In previous publications we have suggested that the Na+/K+ pump controls the intrinsic activity of cerebellar Purkinje neurons  and that it might be directly involved in cerebellar information processing . Here we suggest that alcohol inhibits Na+/K+ pumping in cerebellar Purkinje neurons. This may be a factor in the motor dysfunction concordant with inebriation. It would be interesting to use animal models to explore if factors that potentiate Na+/K+ pumping can counter alcohol associated motor dysfunction. Alcohol may inhibit a proportion of Na+/K+ pumps but if the activity of the remaining, uninhibited cohort can be increased then this may compensate. This avenue of research could provide one dimension to a “sobriety pill”, taken to counteract the effects of ingested alcohol when they are no longer desired. It would likely not be the complete solution as alcohol probably actions against a number of molecular targets, across numerous brain regions, not simply the Na+/K+ pump in cerebellar Purkinje neurons [71-91]. However, it may well improve motor co-ordination and reaction times in individuals with alcohol in their system; this may confer some safety benefits. Indeed, more generally, alcohol’s corruptive effect to the motor system is widely considered an unwanted side-effect to alcohol’s coveted effects on mood and sociability. An alcoholic beverage ingredient that could counteract/block alcohol’s effect upon the motor system, and leave its other physiological effects intact, would likely have a commercial potential. However, this aim is complicated because the cerebellum may control some higher-order cognitive and emotional functions, in addition to its motor role [92,93], and may confer additional aspects to the alcohol response. Furthermore, alcohol may act upon other brain cells/regions by Na+/K+ pump inhibition. Alcohol has been shown to inhibit the Na+/K+ pump in cerebellar Golgi cells and this could be another locus by which alcohol disrupts cerebellar computation [92-96]. This locus might also be helped by the application of Na+/K+ pump potentiating agents. Dimethyl sulfoxide (DMSO) has been shown to directly promote Na+/K+ pump activity , is licensed by the FDA as a therapeutic for a number of disorders, is used widely as a dietary supplement but has also been associated with toxicity and side effects e.g. . Follistatin-like 1 is a protein produced by the FSTL1 gene and it can bind to, and increase pumping by, the α1 Na+/K+ pump isoform . The Allen Brain Atlas  shows that FSTL1 is expressed widely in the mouse brain but not in the cerebellar cortex (data not shown). If this gene is expressed in this part of the brain, through an experimental intervention, it may have effects upon the behavioural response to alcohol. Although, perhaps not: Purkinje neurons may not express the α1 isoform . Purkinje neurons are particularly rich in the α3 Na+/K+ pump isoform and Carbon Monoxide (CO) gas, which is likely an endogenous signalling molecule , has been shown to increase pumping by this isoform in this cell class . CO seems to promote Na+/K+ pumping through cGMP and Protein Kinase G (PKG); CO levels are regulated by glutamate binding to glutamate receptors . It might be that this system could be pharmacologically manipulated to counterbalance the effects of alcohol upon cerebellar Purkinje neurons. We now have a crystal structure of the Na+/K+ pump, and an increasing knowledge of how it functions as we gain atomic resolution views of it in different conformational states [102-107]. We envisage that in the future it will be possible to rationally design new drugs to bind/ interact with it and to directly promote its action. Although, there are already agents, some endogenous, that can fulfil this action e.g. phosphatidylcholine or phosphatidylethanolamine . Alcohol may act upon the Na+/K+ pump by altering the membrane lipid bilayer in which it floats, which is a factor in setting its structure (hence function), and/or it may interact with the Na+/K+ pump molecule directly. If the latter, in the future it may be possible to design a drug – using molecular dynamics (MD) simulations - that would interact with the Na+/K+ pump and block alcohol’s negative action upon it.
In this study, we have explored intrinsic electrical activities. The next step would be to simulate and explore the Purkinje cell models under conditions of synaptic input. The Purkinje neuron receives numerous inputs (e.g. ~200,000 parallel fiber (PF) inputs) and it is computationally expensive to simulate them all. Typically, Purkinje modellers only simulate a fraction of the total and can increase the frequency of those modelled, over and above the physiological rate, to compensate for this omission [109,110]. For example, the 200,000 asynchronous PF inputs – each with a firing frequency of ~0.01 Hz - could be approximated by a single PF input with a firing frequency of 2000 Hz; for computational brevity. Our reduced Purkinje cell model is unlikely to be the most minimal biophysical description that can reproduce the dynamical features of the full model. It can probably be further idealized. Although we have reduced the compartment number, we have not investigated if any currents can be omitted. It is likely that some can.
At present, neuroscience research is heavily reductionist. For example, cellular and system studies are not well integrated. To elucidate brain functioning we need to build bridges between the different levels of description: to relate genes to molecules, molecules to cells, cells to circuits, circuits to systems and systems to perception/behavior. We lay the framework for one such bridge in this study. We produce a reduced Purkinje neuron model with significant cellular fidelity, low computational overhead and suitability for inclusion in large circuit and network simulations. Furthermore, the research of this study reaffirms our previous studies [11,23-27], which assert that the Na+/K+ pump controls the activity mode of cerebellar Purkinje neurons and is a computational element in the cerebellum. In this paper, we go further and show that alcohol may inhibit the Na+/K+ pump in cerebellar Purkinje neurons and we propose that this may be the mechanism to alcohol’s corruption of motor control. We speculate that a pharmacological intervention at the Na+/K+ pump will modulate the body’s physiological response to alcohol.
Availability of supporting data
Our full (1089 compartment) and reduced (2 compartment) Purkinje neuron models are available in the ModelDB [12; RRID: nif-0000-00004] at http://modeldb.yale.edu/180789.
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