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Authors & Affiliations
Domas Linkevicius, Angus Chadwick, Melanie Stefan, David Sterratt
Abstract
Automated voltage-clamp recordings from 40 voltage-gated potassium (Kv) channels [1] revealed the inherent kinetic heterogeneity of some Kv types expressed in the brain (e.g. Kv1.3). A model capable of capturing the kinetic Kv heterogeneity requires both fixed model features shared between cells, and the ability to capture the variability present in individual cells. The classical Hodgkin Huxley (HH) formalism [2], by itself, does not possess these properties. We apply the Deep Non-Linear Mixed Effects (DeepNLME) framework [3] to model the kinetic Kv heterogeneity.
DeepNLME combines deep learning with non-linear mixed effects (NLME) modeling. NLME is a two level hierarchical modeling framework with fixed effects, parameters shared between cells, and random effects, cell-level parameters that permit deviations from the fixed effects [4]. These parameters can be used in an ordinary differential equation (ODE) system (e.g. channel gates in the HH model), whose numerical solution is fit to observed data (e.g. recorded channel current). We use the DeepNLME fitting algorithms implemented in Pumas.jl and DeepPumas.jl [3,4] to model the dependence of channel opening probabilities on voltage and temperature via neural networks instead of the functional forms used in HH models. Neural networks radically simplify the modeling process by removing the need for key assumptions about which parameters vary between cells, the functional form of temperature dependency, the nature and the number of the gates.
Our DeepNLME model of the Kv1.1 channel (channel with low kinetic heterogeneity presented) outperforms the model of the same channel from [1]. We then fitted a DeepNLME model for Kv1.3, the channel type with the highest levels of kinetic heterogeneity. Moreover, we explored the downstream consequences of channel heterogeneity in a compartmental neuron model by fixing the distributions of the same channel type but varying the distribution of kinetic properties. Our major contributions are: (1) state of the art Kv models capable of capturing kinetic Kv heterogeneity (2) introduction of the DeepNLME framework in a computational neuroscience context.
[1] Ranjan R et al. (2019). Front Cell Neurosci, 13. https://doi.org/10.3389/fncel.2019.00358
[2] Hodgkin AL & Huxley AF (1952). J Phhysiol, 117. doi:10.1113/jphysiol.1952.sp004764
[3] Rackauckas C & Ivaturi V (2019). ACoP 2019, Orlando, FL
[4] Rackauckas C et al. (2020). bioRxiv. https://doi.org/10.1101/2020.11.28.40