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Sun Z, Crompton D, Lankarany M, Skinner FK. Reduced oriens-lacunosum/moleculare cell model identifies biophysical current balances for in vivo theta frequency spiking resonance. Front Neural Circuits 2023; 17:1076761. [PMID: 36817648 PMCID: PMC9936813 DOI: 10.3389/fncir.2023.1076761] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2022] [Accepted: 01/16/2023] [Indexed: 02/05/2023] Open
Abstract
Conductance-based models have played an important role in the development of modern neuroscience. These mathematical models are powerful "tools" that enable theoretical explorations in experimentally untenable situations, and can lead to the development of novel hypotheses and predictions. With advances in cell imaging and computational power, multi-compartment models with morphological accuracy are becoming common practice. However, as more biological details are added, they make extensive explorations and analyses more challenging largely due to their huge computational expense. Here, we focus on oriens-lacunosum/moleculare (OLM) cell models. OLM cells can contribute to functionally relevant theta rhythms in the hippocampus by virtue of their ability to express spiking resonance at theta frequencies, but what characteristics underlie this is far from clear. We converted a previously developed detailed multi-compartment OLM cell model into a reduced single compartment model that retained biophysical fidelity with its underlying ion currents. We showed that the reduced OLM cell model can capture complex output that includes spiking resonance in in vivo-like scenarios as previously obtained with the multi-compartment model. Using the reduced model, we were able to greatly expand our in vivo-like scenarios. Applying spike-triggered average analyses, we were able to to determine that it is a combination of hyperpolarization-activated cation and muscarinic type potassium currents that specifically allow OLM cells to exhibit spiking resonance at theta frequencies. Further, we developed a robust Kalman Filtering (KF) method to estimate parameters of the reduced model in real-time. We showed that it may be possible to directly estimate conductance parameters from experiments since this KF method can reliably extract parameter values from model voltage recordings. Overall, our work showcases how the contribution of cellular biophysical current details could be determined and assessed for spiking resonance. As well, our work shows that it may be possible to directly extract these parameters from current clamp voltage recordings.
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Affiliation(s)
- Zhenyang Sun
- Krembil Brain Institute, University Health Network, Toronto, ON, Canada
| | - David Crompton
- Krembil Brain Institute, University Health Network, Toronto, ON, Canada
- Institute of Biomedical Engineering, University of Toronto, Toronto, ON, Canada
| | - Milad Lankarany
- Krembil Brain Institute, University Health Network, Toronto, ON, Canada
- Institute of Biomedical Engineering, University of Toronto, Toronto, ON, Canada
- Department of Physiology, University of Toronto, Toronto, ON, Canada
- KITE, Toronto Rehabilitation Institute, University Health Network, Toronto, ON, Canada
| | - Frances K. Skinner
- Krembil Brain Institute, University Health Network, Toronto, ON, Canada
- Departments of Medicine (Neurology) and Physiology, University of Toronto, Toronto, ON, Canada
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Armstrong E, Runge M, Gerardin J. Identifying the measurements required to estimate rates of COVID-19 transmission, infection, and detection, using variational data assimilation. Infect Dis Model 2020; 6:133-147. [PMID: 33163738 PMCID: PMC7605798 DOI: 10.1016/j.idm.2020.10.010] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2020] [Revised: 10/26/2020] [Accepted: 10/27/2020] [Indexed: 01/08/2023] Open
Abstract
We demonstrate the ability of statistical data assimilation (SDA) to identify the measurements required for accurate state and parameter estimation in an epidemiological model for the novel coronavirus disease COVID-19. Our context is an effort to inform policy regarding social behavior, to mitigate strain on hospital capacity. The model unknowns are taken to be: the time-varying transmission rate, the fraction of exposed cases that require hospitalization, and the time-varying detection probabilities of new asymptomatic and symptomatic cases. In simulations, we obtain estimates of undetected (that is, unmeasured) infectious populations, by measuring the detected cases together with the recovered and dead - and without assumed knowledge of the detection rates. Given a noiseless measurement of the recovered population, excellent estimates of all quantities are obtained using a temporal baseline of 101 days, with the exception of the time-varying transmission rate at times prior to the implementation of social distancing. With low noise added to the recovered population, accurate state estimates require a lengthening of the temporal baseline of measurements. Estimates of all parameters are sensitive to the contamination, highlighting the need for accurate and uniform methods of reporting. The aim of this paper is to exemplify the power of SDA to determine what properties of measurements will yield estimates of unknown parameters to a desired precision, in a model with the complexity required to capture important features of the COVID-19 pandemic.
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Affiliation(s)
- Eve Armstrong
- Department of Physics, New York Institute of Technology, 1855 Broadway, New York, NY, 10023, USA
- Department of Astrophysics, American Museum of Natural History, New York, NY, 10024, USA
| | - Manuela Runge
- Department of Preventive Medicine, Northwestern University, 710 N Lake Shore Drive Suite 800, Chicago, IL, 60611, USA
| | - Jaline Gerardin
- Department of Preventive Medicine, Northwestern University, 710 N Lake Shore Drive Suite 800, Chicago, IL, 60611, USA
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Madi MK, Karameh FN. Hybrid Cubature Kalman filtering for identifying nonlinear models from sampled recording: Estimation of neuronal dynamics. PLoS One 2017; 12:e0181513. [PMID: 28727850 PMCID: PMC5519212 DOI: 10.1371/journal.pone.0181513] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2016] [Accepted: 07/03/2017] [Indexed: 11/18/2022] Open
Abstract
Kalman filtering methods have long been regarded as efficient adaptive Bayesian techniques for estimating hidden states in models of linear dynamical systems under Gaussian uncertainty. Recent advents of the Cubature Kalman filter (CKF) have extended this efficient estimation property to nonlinear systems, and also to hybrid nonlinear problems where by the processes are continuous and the observations are discrete (continuous-discrete CD-CKF). Employing CKF techniques, therefore, carries high promise for modeling many biological phenomena where the underlying processes exhibit inherently nonlinear, continuous, and noisy dynamics and the associated measurements are uncertain and time-sampled. This paper investigates the performance of cubature filtering (CKF and CD-CKF) in two flagship problems arising in the field of neuroscience upon relating brain functionality to aggregate neurophysiological recordings: (i) estimation of the firing dynamics and the neural circuit model parameters from electric potentials (EP) observations, and (ii) estimation of the hemodynamic model parameters and the underlying neural drive from BOLD (fMRI) signals. First, in simulated neural circuit models, estimation accuracy was investigated under varying levels of observation noise (SNR), process noise structures, and observation sampling intervals (dt). When compared to the CKF, the CD-CKF consistently exhibited better accuracy for a given SNR, sharp accuracy increase with higher SNR, and persistent error reduction with smaller dt. Remarkably, CD-CKF accuracy shows only a mild deterioration for non-Gaussian process noise, specifically with Poisson noise, a commonly assumed form of background fluctuations in neuronal systems. Second, in simulated hemodynamic models, parametric estimates were consistently improved under CD-CKF. Critically, time-localization of the underlying neural drive, a determinant factor in fMRI-based functional connectivity studies, was significantly more accurate under CD-CKF. In conclusion, and with the CKF recently benchmarked against other advanced Bayesian techniques, the CD-CKF framework could provide significant gains in robustness and accuracy when estimating a variety of biological phenomena models where the underlying process dynamics unfold at time scales faster than those seen in collected measurements.
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Affiliation(s)
- Mahmoud K. Madi
- Department of Electrical and Computer Engineering, American University of Beirut, Beirut, Lebanon
| | - Fadi N. Karameh
- Department of Electrical and Computer Engineering, American University of Beirut, Beirut, Lebanon
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Kameneva T, Abramian M, Zarelli D, Nĕsić D, Burkitt AN, Meffin H, Grayden DB. Spike history neural response model. J Comput Neurosci 2015; 38:463-81. [PMID: 25862472 DOI: 10.1007/s10827-015-0549-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2014] [Revised: 02/08/2015] [Accepted: 02/13/2015] [Indexed: 11/25/2022]
Abstract
There is a potential for improved efficacy of neural stimulation if stimulation levels can be modified dynamically based on the responses of neural tissue in real time. A neural model is developed that describes the response of neurons to electrical stimulation and that is suitable for feedback control neuroprosthetic stimulation. Experimental data from NZ white rabbit retinae is used with a data-driven technique to model neural dynamics. The linear-nonlinear approach is adapted to incorporate spike history and to predict the neural response of ganglion cells to electrical stimulation. To validate the fitness of the model, the penalty term is calculated based on the time difference between each simulated spike and the closest spike in time in the experimentally recorded train. The proposed model is able to robustly predict experimentally observed spike trains.
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Affiliation(s)
- Tatiana Kameneva
- Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne, Australia,
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Rigatos GG. Estimation of wave-type dynamics in neurons' membrane with the use of the Derivative-free nonlinear Kalman Filter. Neurocomputing 2014. [DOI: 10.1016/j.neucom.2013.10.016] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Ching S, Ritt JT. Control strategies for underactuated neural ensembles driven by optogenetic stimulation. Front Neural Circuits 2013; 7:54. [PMID: 23576956 PMCID: PMC3620532 DOI: 10.3389/fncir.2013.00054] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2012] [Accepted: 03/11/2013] [Indexed: 02/01/2023] Open
Abstract
Motivated by experiments employing optogenetic stimulation of cortical regions, we consider spike control strategies for ensembles of uncoupled integrate and fire neurons with a common conductance input. We construct strategies for control of spike patterns, that is, multineuron trains of action potentials, up to some maximal spike rate determined by the neural biophysics. We emphasize a constructive role for parameter heterogeneity, and find a simple rule for controllability in pairs of neurons. In particular, we determine parameters for which common drive is not limited to inducing synchronous spiking. For large ensembles, we determine how the number of controllable neurons varies with the number of observed (recorded) neurons, and what collateral spiking occurs in the full ensemble during control of the subensemble. While complete control of spiking in every neuron is not possible with a single input, we find that a degree of subensemble control is made possible by exploiting dynamical heterogeneity. As most available technologies for neural stimulation are underactuated, in the sense that the number of target neurons far exceeds the number of independent channels of stimulation, these results suggest partial control strategies that may be important in the development of sensory neuroprosthetics and other neurocontrol applications.
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Affiliation(s)
- ShiNung Ching
- Department of Electrical and Systems Engineering, Washington University in St. Louis St. Louis, MO, USA
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Mitra A, Manitius A, Sauer T. Prediction of single neuron spiking activity using an optimized nonlinear dynamic model. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2012; 2012:2543-2546. [PMID: 23366443 DOI: 10.1109/embc.2012.6346482] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The increasing need of knowledge in the treatment of brain diseases has driven a huge interest in understanding the phenomenon of neural spiking. Researchers have successfully been able to create mathematical models which, with specific parameters, are able to reproduce the experimental neuronal responses. The spiking activity is characterized using spike trains and it is essential to develop methods for parameter estimation that rely solely on the spike times or interspike intervals (ISI). In this paper we describe a new technique for optimization of a single neuron model using an experimental spike train from a biological neuron. We are able to fit model parameters using the gradient descent method. The optimized model is then used to predict the activity of the biological neuron and the performance is quantified using a spike distance measure.
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Affiliation(s)
- Anish Mitra
- Department of Electrical and Computer Engineering, George Mason University, Fairfax, VA 22030, USA.
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Talathi SS, Carney PR, Khargonekar PP. Control of neural synchrony using channelrhodopsin-2: a computational study. J Comput Neurosci 2010; 31:87-103. [PMID: 21174227 DOI: 10.1007/s10827-010-0296-6] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2010] [Revised: 11/03/2010] [Accepted: 11/18/2010] [Indexed: 10/18/2022]
Abstract
In this paper, we present an optical stimulation based approach to induce 1:1 in-phase synchrony in a network of coupled interneurons wherein each interneuron expresses the light sensitive protein channelrhodopsin-2 (ChR2). We begin with a transition rate model for the channel kinetics of ChR2 in response to light stimulation. We then define "functional optical time response curve (fOTRC)" as a measure of the response of a periodically firing interneuron (transfected with ChR2 ion channel) to a periodic light pulse stimulation. We specifically consider the case of unidirectionally coupled (UCI) network and propose an open loop control architecture that uses light as an actuation signal to induce 1:1 in-phase synchrony in the UCI network. Using general properties of the spike time response curves (STRCs) for Type-1 neuron model (Ermentrout, Neural Comput 8:979-1001, 1996) and fOTRC, we estimate the (open loop) optimal actuation signal parameters required to induce 1:1 in-phase synchrony. We then propose a closed loop controller architecture and a controller algorithm to robustly sustain stable 1:1 in-phase synchrony in the presence of unknown deviations in the network parameters. Finally, we test the performance of this closed-loop controller in a network of mutually coupled (MCI) interneurons.
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Affiliation(s)
- Sachin S Talathi
- Department of Pediatrics, University of Florida, Gainesville, FL 32611, USA.
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