Limits...
Assimilating seizure dynamics.

Ullah G, Schiff SJ - PLoS Comput. Biol. (2010)

Bottom Line: However, existing techniques are too limited to measure all but a small fraction of the physical variables and parameters of neuronal networks.We demonstrate that it is now possible to meaningfully estimate the dynamics of small neuronal networks using as few as a single measured variable.Data assimilation, the fusing of measurement with computational models, has significant potential to improve the way we observe and understand brain dynamics.

View Article: PubMed Central - PubMed

Affiliation: Center for Neural Engineering, Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, Pennsylvania, USA. ghanim@psu.edu

ABSTRACT
Observability of a dynamical system requires an understanding of its state-the collective values of its variables. However, existing techniques are too limited to measure all but a small fraction of the physical variables and parameters of neuronal networks. We constructed models of the biophysical properties of neuronal membrane, synaptic, and microenvironment dynamics, and incorporated them into a model-based predictor-controller framework from modern control theory. We demonstrate that it is now possible to meaningfully estimate the dynamics of small neuronal networks using as few as a single measured variable. Specifically, we assimilate noisy membrane potential measurements from individual hippocampal neurons to reconstruct the dynamics of networks of these cells, their extracellular microenvironment, and the activities of different neuronal types during seizures. We use reconstruction to account for unmeasured parts of the neuronal system, relating micro-domain metabolic processes to cellular excitability, and validate the reconstruction of cellular dynamical interactions against actual measurements. Data assimilation, the fusing of measurement with computational models, has significant potential to improve the way we observe and understand brain dynamics.

Show MeSH

Related in: MedlinePlus

Reconstructing network interaction.Measured (A, red) and estimated (B, black)  for pyramidal cell. (C) Estimated  for interneuron. We used the membrane potential recorded from the pyramidal cell (shown in A, red) to not only reconstruct the full dynamics of the same pyramidal cell (only membrane potential shown in B, black) but also reconstructed the dynamics of the interneuron (only membrane potential shown in C, black). Simultaneously recorded  from the IN is shown in (D, red) for comparison. Estimates for intracellular  concentration and gating variables ,  for PC are shown in Figure S2 and the synaptic variables, ,  are shown in Figure S3. Estimated  for IN (E) and PC (F) by assimilating measured  from IN (shown in (D)). (D–F) are converses of the simulations in (A–C). That is, In (D–F) we used membrane potential recorded from the interneuron (shown in D, red) to not only reconstruct the full dynamics of the same interneuron (only membrane potential shown in E, black) but also the coupled pyramidal cell (only membrane potential shown in F, black: compare with actual values shown in A, red). Simultaneous membrane potential measurements shown in (A,D) were from a pyramidal cell and OLM interneuron in the hippocampus using simultaneous dual whole cell patch clamp recordings demonstrating the firing interplay between these cells during in vitro seizures. Data provided by Jokubas Ziburkus. Panels (A,D) are modified from [23] with permission  American Physiological Society.
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2865517&req=5

pcbi-1000776-g008: Reconstructing network interaction.Measured (A, red) and estimated (B, black) for pyramidal cell. (C) Estimated for interneuron. We used the membrane potential recorded from the pyramidal cell (shown in A, red) to not only reconstruct the full dynamics of the same pyramidal cell (only membrane potential shown in B, black) but also reconstructed the dynamics of the interneuron (only membrane potential shown in C, black). Simultaneously recorded from the IN is shown in (D, red) for comparison. Estimates for intracellular concentration and gating variables , for PC are shown in Figure S2 and the synaptic variables, , are shown in Figure S3. Estimated for IN (E) and PC (F) by assimilating measured from IN (shown in (D)). (D–F) are converses of the simulations in (A–C). That is, In (D–F) we used membrane potential recorded from the interneuron (shown in D, red) to not only reconstruct the full dynamics of the same interneuron (only membrane potential shown in E, black) but also the coupled pyramidal cell (only membrane potential shown in F, black: compare with actual values shown in A, red). Simultaneous membrane potential measurements shown in (A,D) were from a pyramidal cell and OLM interneuron in the hippocampus using simultaneous dual whole cell patch clamp recordings demonstrating the firing interplay between these cells during in vitro seizures. Data provided by Jokubas Ziburkus. Panels (A,D) are modified from [23] with permission American Physiological Society.

Mentions: Since the interaction of neurons determines network patterns of activity, it is within such interactions that we seek unifying principles for epilepsy. To demonstrate that the UKF framework can be utilized to study cellular interactions, we reconstructed the dynamics of one cell type by assimilating the measured data from another cell type in the network. In Figure 8 we only show the estimated membrane potentials, but we also reconstructed the remaining variables and parameters of both cells (Figures S2 and S3). We first assimilated the membrane potential of the PC to estimate the dynamics of the same cell and also the dynamics of a coupled IN (Figure 8A–D). Conversely, we estimate the dynamics of PC from the simultaneously measured membrane potential measurements of the IN (Figure 8D–F). As is evident from Figure 8 the filter framework is successful at reciprocally reconstructing and tracking the dynamics of these different cells within this network. In Figure S2, we show intracellular concentration and gating variables of and channels in PCs for simulation in Figure 8A–D. The variables modeling the synaptic inputs for both INs and PCs in Figure 8A–D are shown in Figure S3. As clear from Figure S3 (D), the variable (equation 8) reaches very high values when the INs lock into depolarization block, shutting off the inhibitory inputs from INs to PCs.


Assimilating seizure dynamics.

Ullah G, Schiff SJ - PLoS Comput. Biol. (2010)

Reconstructing network interaction.Measured (A, red) and estimated (B, black)  for pyramidal cell. (C) Estimated  for interneuron. We used the membrane potential recorded from the pyramidal cell (shown in A, red) to not only reconstruct the full dynamics of the same pyramidal cell (only membrane potential shown in B, black) but also reconstructed the dynamics of the interneuron (only membrane potential shown in C, black). Simultaneously recorded  from the IN is shown in (D, red) for comparison. Estimates for intracellular  concentration and gating variables ,  for PC are shown in Figure S2 and the synaptic variables, ,  are shown in Figure S3. Estimated  for IN (E) and PC (F) by assimilating measured  from IN (shown in (D)). (D–F) are converses of the simulations in (A–C). That is, In (D–F) we used membrane potential recorded from the interneuron (shown in D, red) to not only reconstruct the full dynamics of the same interneuron (only membrane potential shown in E, black) but also the coupled pyramidal cell (only membrane potential shown in F, black: compare with actual values shown in A, red). Simultaneous membrane potential measurements shown in (A,D) were from a pyramidal cell and OLM interneuron in the hippocampus using simultaneous dual whole cell patch clamp recordings demonstrating the firing interplay between these cells during in vitro seizures. Data provided by Jokubas Ziburkus. Panels (A,D) are modified from [23] with permission  American Physiological Society.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2865517&req=5

pcbi-1000776-g008: Reconstructing network interaction.Measured (A, red) and estimated (B, black) for pyramidal cell. (C) Estimated for interneuron. We used the membrane potential recorded from the pyramidal cell (shown in A, red) to not only reconstruct the full dynamics of the same pyramidal cell (only membrane potential shown in B, black) but also reconstructed the dynamics of the interneuron (only membrane potential shown in C, black). Simultaneously recorded from the IN is shown in (D, red) for comparison. Estimates for intracellular concentration and gating variables , for PC are shown in Figure S2 and the synaptic variables, , are shown in Figure S3. Estimated for IN (E) and PC (F) by assimilating measured from IN (shown in (D)). (D–F) are converses of the simulations in (A–C). That is, In (D–F) we used membrane potential recorded from the interneuron (shown in D, red) to not only reconstruct the full dynamics of the same interneuron (only membrane potential shown in E, black) but also the coupled pyramidal cell (only membrane potential shown in F, black: compare with actual values shown in A, red). Simultaneous membrane potential measurements shown in (A,D) were from a pyramidal cell and OLM interneuron in the hippocampus using simultaneous dual whole cell patch clamp recordings demonstrating the firing interplay between these cells during in vitro seizures. Data provided by Jokubas Ziburkus. Panels (A,D) are modified from [23] with permission American Physiological Society.
Mentions: Since the interaction of neurons determines network patterns of activity, it is within such interactions that we seek unifying principles for epilepsy. To demonstrate that the UKF framework can be utilized to study cellular interactions, we reconstructed the dynamics of one cell type by assimilating the measured data from another cell type in the network. In Figure 8 we only show the estimated membrane potentials, but we also reconstructed the remaining variables and parameters of both cells (Figures S2 and S3). We first assimilated the membrane potential of the PC to estimate the dynamics of the same cell and also the dynamics of a coupled IN (Figure 8A–D). Conversely, we estimate the dynamics of PC from the simultaneously measured membrane potential measurements of the IN (Figure 8D–F). As is evident from Figure 8 the filter framework is successful at reciprocally reconstructing and tracking the dynamics of these different cells within this network. In Figure S2, we show intracellular concentration and gating variables of and channels in PCs for simulation in Figure 8A–D. The variables modeling the synaptic inputs for both INs and PCs in Figure 8A–D are shown in Figure S3. As clear from Figure S3 (D), the variable (equation 8) reaches very high values when the INs lock into depolarization block, shutting off the inhibitory inputs from INs to PCs.

Bottom Line: However, existing techniques are too limited to measure all but a small fraction of the physical variables and parameters of neuronal networks.We demonstrate that it is now possible to meaningfully estimate the dynamics of small neuronal networks using as few as a single measured variable.Data assimilation, the fusing of measurement with computational models, has significant potential to improve the way we observe and understand brain dynamics.

View Article: PubMed Central - PubMed

Affiliation: Center for Neural Engineering, Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, Pennsylvania, USA. ghanim@psu.edu

ABSTRACT
Observability of a dynamical system requires an understanding of its state-the collective values of its variables. However, existing techniques are too limited to measure all but a small fraction of the physical variables and parameters of neuronal networks. We constructed models of the biophysical properties of neuronal membrane, synaptic, and microenvironment dynamics, and incorporated them into a model-based predictor-controller framework from modern control theory. We demonstrate that it is now possible to meaningfully estimate the dynamics of small neuronal networks using as few as a single measured variable. Specifically, we assimilate noisy membrane potential measurements from individual hippocampal neurons to reconstruct the dynamics of networks of these cells, their extracellular microenvironment, and the activities of different neuronal types during seizures. We use reconstruction to account for unmeasured parts of the neuronal system, relating micro-domain metabolic processes to cellular excitability, and validate the reconstruction of cellular dynamical interactions against actual measurements. Data assimilation, the fusing of measurement with computational models, has significant potential to improve the way we observe and understand brain dynamics.

Show MeSH
Related in: MedlinePlus