# Simulation

Our models are routinely made available on ModelDB:

## Basal ganglia models:

### Spiking neuron model of the basal ganglia:

Humphries, Stewart & Gurney (2006) A physiologically plausible model of action selection and oscillatory activity in the basal ganglia. Journal of Neuroscience, 26: 12921-12942.

Model DB entry: http://senselab.med.yale.edu/modeldb/ShowModel.asp?model=83559

The purpose of this model was to test the “action selection” theory of basal ganglia operation: we set out to show that a basal ganglia model implementing action selection was consistent with a wide range of electrophysiological data on the dynamics of the basal ganglia nuclei.

In particular, this paper advanced the hypothesis that dopamine acts to de-couple the subthalamic nucleus (STN) – globus pallidus (GP) negative feedback loop in normal conditions, and that a reduction in tonic dopamine will re-couple the feedback loop. Consequently, we proposed that in parkinsonian states this loop will be permanently re-coupled, producing pathological rhythms that interfere with normal selection operation in the basal ganglia. Our hypothesis has been further tested by others (e.g. Holgado et al, 2010, J Neurosci; Hahn & McIntyre, 2010, J Comput Neurosci) who showed that such a re-coupling indeed produces pathological rhythmic dynamics.

### Population level models of basal ganglia circuitry

#### Basal ganglia circuit model

The basal ganglia model described in Gurney et al (2001a) and Gurney et al (2001b) is available in Simulink and MATLAB formats.

Model DB entry: http://senselab.med.yale.edu/modeldb/ShowModel.asp?model=83560

#### Thalamo-cortical basal ganglia model

The basal ganglia-thalamocortical loop model described in Humphries & Gurney (2002) is available in Simulink and MATLAB formats.

Model DB entry: http://senselab.med.yale.edu/modeldb/ShowModel.asp?model=83562

### Large-scale models of the striatum

#### First complete model (Model v1):

Humphries, Wood & Gurney (2009) Neural Networks

Model DB entry: http://senselab.med.yale.edu/modeldb/ShowModel.asp?model=128874

To begin identifying potential dynamically-defined computational elements within the striatum, we constructed a new three-dimensional model of the striatal microcircuit's connectivity, and instantiated this with our dopamine-modulated neuron models of the MSNs and FSIs. A new model of gap junctions between the FSIs was introduced and tuned to experimental data. We introduced a novel multiple spike-train analysis method, and apply this to the outputs of the model to find groups of synchronised neurons at multiple time-scales. We found that, with realistic in vivo background input, small assemblies of synchronised MSNs spontaneously appeared, consistent with experimental observations, and that the number of assemblies and the time-scale of synchronisation was strongly dependent on the simulated concentration of dopamine. We also showed that feed-forward inhibition from the FSIs counter-intuitively increases the firing rate of the MSNs.

The code archive contains all of the MATLAB scripts, functions and MEX files that produced the results from that paper; the source C++ code for the MEX files is also included so they can be recompiled for other systems. The code includes the full set of analysis routines for detecting cell assemblies in spike train data-sets.

The results archive contains all of the spike-trains data-sets from the simulations that were analysed in the paper. See the README file for further details.

#### Spatial scales of the striatal network (Model v1.5):

Humphries, Wood & Gurney (2010) PLoS Computational Biology

Model DB entry: http://senselab.med.yale.edu/modeldb/ShowModel.asp?model=137502

The main thrust of this paper was the development of the 3D anatomical network of the striatum's GABAergic microcircuit. We grew dendrite and axon models for the MSNs and FSIs and extracted probabilities for the presence of these neurites as a function of distance from the soma. From these, we found the probabilities of intersection between the neurites of two neurons given their inter-somatic distance, and used these to construct three-dimensional striatal networks. These networks were examined for their predictions for the distributions of the numbers and distances of connections for all the connections in the microcircuit. We then combined the neuron models from model v1 (see above) with the new anatomical model, forming v1.5. We used this model to examine the impact of the anatomical network on the firing properties of the MSN and FSI populations, and to study the influence of all the inputs to one MSN within the network.

The code archive contains all of the MATLAB scripts, functions and MEX files that produced the dynamical model results from that paper. The source C++ code for the MEX files is also included so they can be recompiled for other systems. The code includes the full set of analysis routines for finding the firing rate distributions (Fig. 9 in the paper) and for assessing the impact of the inputs to a single MSN in the network (Fig. 10 in the paper). We also make available a complete connectivity matrix (129MB) describing all the connections in a 1mm3 model with 1% FSIs. This can be loaded by the StriatumNetworkParameters.m function - see that function for instructions.

Notes: both the above models contain our first reduced models of the dopamine-modulated MSN. These have subsequently been updated and published separately (see below).

### Reduced Models of the Striatal Medium Spiny Neuron and its Modulation By Dopamine

Humphries, Lepora, Wood & Gurney (2009) Front. Comp. Neurosci.

Model DB entry: http://senselab.med.yale.edu/modeldb/ShowModel.asp?model=128818

We extended a reduced model of the striatal medium spiny neuron (MSN) to account for dopaminergic modulation of its intrinsic ion channels and synaptic inputs. We tuned our D1 and D2 receptor MSN models using data from a recent large-scale compartmental model. The new models capture the input-output relationships for both current injection and spiking input with remarkable accuracy, despite the order of magnitude decrease in system size. They also capture the paired pulse facilitation shown by MSNs. Finally, they show how the MSN membrane potential can be bimodal, even if the neuron is not bistable.

The code archive contains all of the MATLAB scripts and functions that produced the results from that paper. This includes the full code for the parameter search routines, so that they can be re-run if the model is changed and/or extended.

## Brainstem reticular formation models:

Model DB entry: http://senselab.med.yale.edu/modeldb/ShowModel.asp?model=128816

A set of models to study the medial reticular formation (mRF) of the brainstem. We developed a collection of algorithms to derive the adult-state wiring of the model: one set a stochastic model; the other set mimicking the developmental process. We found that the anatomical models had small-world properties, irrespective of the choice of algorithm; and that the cluster-like organisation of the mRF may have arisen to minimise wiring costs. (The model code includes options to be run as dynamic models; papers examining these dynamics are included in the .zip file).

The anatomical models are detailed in Humphries, Prescott & Gurney (2006) Proc Roy Soc B.

A review of the functions of the mRF, and study of a simple population-level dynamic model are in Humphries, Prescott & Gurney (2007) Phil Trans Roy Soc B. An extended review and study of a simple network-level dynamic model are in Humphries, Prescott & Gurney (2011) The medial reticular formation: a brainstem substrate for simple action selection?. In “Modelling Natural Action Selection”. CUP: Cambridge.