Role of gap junctions in a neuron-astrocyte network model David Terman Ohio State University IMA, 2018

Stroke - Ischemia Restriction in blood supply to tissues Shortage of oxygen and glucose Reduction in metabolism – ATP Failure of energy dependent processes (ionic pumps) Loss of ionic gradients, influx of calcium, release of glutamate Cell swelling, cell death (apoptosis) Lechleiter

Cytosol ATP K+ 2 Glucose Oxygen 1 Na+, H2O K+, VM 4 2K+ 3Na+ 3 5 Mitochondrion ATP 2 Glucose Oxygen 1 Na+, H2O K+, VM 4 2K+ 3Na+ ATPase Pump 3 K+ 5 Extracellular space

Failure of pumps leads to: -- Increases in extracellular K+ -- Depolarization of membrane potential Somjen 2001

Membrane depolarization may spread in a wave-like manner: - Spreading depression (migraines) - Spreading depolarization (stroke) Leo (1944) Grafstein (1956)

Goals of modeling studies: Develop biophysical model for spreading depolarizations (SD). Identify cellular processes responsible for initiation, propagation and recurrence of SD. Explore neuroprotective role of astrocytes in preventing SD.

Model for spreading depolarization (Neurons) ICl X = n, hp Na+/K+ ATPase pump Similar to many previous models: e.g. Miura, Kager, Somjen…

Solution of model Time (sec) Initiate wave by slowly increasing Cell Number Time (sec) 30 60 Initiate wave by slowly increasing Ke to middle 3 cells. Note: Wave propagates for wide range of pump strengths ρN.

How does the brain prevent spreading depolarizations? Glial cells, Astrocytes: Maintain homeostasis Support and protect neurons May play other important roles Not excitable – no action potentials Form syncytium through gap junctions

Are astrocytes “Good Samaritans” or “Executioners?” Do astrocytic gap junctions mediate protection or killing of neurons during or after hypoxic or ischemic insults? Farahani et al. 2005; Chew et al., 2010 Good Samaritan: Gap junctions allow astrocytes to more effectively buffer elevated levels of extracellular K+ and glutamate. Allow for passage of toxic molecules out of injured cell and neuroprotective molecules into cell. Executioner: Gap junctions allow for the spread of death messengers from injured cells to healthy neighboring cells – “gap junction-mediated bystander effect”. The strength of gap junctions may change in response to brain injury.

Full Model Neurons Extracellular Ke, Nae Space Astrocytes VN, Ki, Nai VA, Kia, Naia K+ Na+ Gap junctions

Model astrocyte

Electrical coupling (gap junctions) among astrocytes: For astrocyte j, : where the sum is over all astrocytes that are coupled with astrocyte j, and PK,gap = σgap PK N: Each astrocyte is connected to its N closest neighbors on each side.

Propagation failure if gaps are sufficiently strong ρN = ρA = 5, σgap = 0 40 Time (sec) 40 ρN = ρA = 20, σgap = 0 ρN = ρA = 5, σgap = .1, N=3 Cell # Time (sec) 40 350 Cell # ρN = ρA = 5, σgap = .1, N=5 Propagation failure if gaps are sufficiently strong If a wave does propagate then velocity increases with gap strength.

Why does gap junction coupling help prevent spreading depolarizations? Isopotentiality: An astrocyte’s associated syncytium provides powerful electrical coupling that equalizes the astrocyte’s VM with its neighbors. Spatial buffering: Gap junctions help to redistribute elevated extracellular K+ levels among the astrocytes.

Isopotentiality: Substitute K+ by Na+ in single astrocyte Ma, Buckalew, Du, Kiyoshi, Alford, Wang, McTigue, Enyeart, Terman, Zhou Glia 2016 Electrical coupling within a syncytium: VM can be maintained at a quasi-physiological level. Isolated astrocyte: Recorded cell depolarizes to ~ 0 mV

Isopotentiality depends on the number of astrocytes each astrocyte is electrically connected with. Note: Each hippocampal astrocytes is coupled directly with, on average, 11 of its nearest neighbors (Zhou)

Spatial buffering: Gap junctions help to redistribute elevated extracellular K+ levels among the astrocytes. Hi K+ Pump K+ channel 3Na+ 2K+ Gap junction Question: IK is usually an outward current. Why should K+ enter cell?

Why does K+ enter cell? Suppose: CM V’ = – INa – IK – IL – Ipump Without gap junctions Suppose: small CM V’ = – INa – IK – IL – Ipump ≈ − gNa (V − Ena) − gK (V − EK) Without gap junctions, we then expect: EK < V < ENa IK = gK (V − EK) > 0 K+ ions flow outward through channels

K+ With gap junctions: Membrane potentials of astrocytes within a ‘syncytium’ remain roughly constant Raise [K]e to one cell K+ However, V remains roughly constant IK = gK (V − EK) < 0 K+ ions flow inward through channels

Simulations: K+ Slowly raise [K]e to one astrocyte.

K+ t = 0: Increase Ke to middle 3 cells (subthreshold) Neurons Astrocytes Ke, Nae t = 0: Increase Ke to middle 3 cells (subthreshold) How does excitability of neurons depend on N?

As gap strength increases: Middle cells are less excitable t = 1 sec: Cell number Cell number Cell number As gap strength increases: Middle cells are less excitable Cells away from middle are more excitable. With gap junctions: It is more difficult to initiate a wave. If a wave is initiated, then its velocity increases.

Moderate gap junction strength: Delay in initiation of wave 40 Time (sec) σgap = .1, N=3 σgap = .1, N=5 Cell number Cell number Cell number Moderate gap junction strength: Delay in initiation of wave Increased wave velocity Strong gap junctions: No wave is initiated

Additions to the model: Further Questions: What is responsible for recurrent depolarizations? What about glutamate? What are the respective roles of K+ and glutamate in the initiation and propagation of RSDs ? Additions to the model: NMDA current (neurons) Na+/glutamate cotransporter (astrocytes) Glutamate and Ca2+ dynamics

NMDA current:

Na+/glutamate cotransporter (astrocyte) K+ H+ Normal conditions: Na+ and Glu- transported into the astrocyte. -- Powered by ion concentration differences Pathological conditions: Transporter can reverse. -- Na+ and Glu- transported out of cell - -- Glu- can then build up in extracellular space. -- Activated NMDA receptors -- Allows for Ca2+ to enter and build up in neurons (bad)

Full Model

Hours Solution of model: Start at rest with ‘normal’ pump strengths. Slowly decrease astrocytic pump strength, ρA. After ~ 1.2 hours, there are 6 recurrent depolarizations. Each depolarization lasts ~ 1.5 minutes. Duration between depolarizations ~ 10 minutes. Hours

Initiation of depolarizations

Recurrent spreading depolarizations

Discussion Collaborators: Min Zhou, Baofeng Ma Model suggests that gap junctions help prevent the initiation of SD (Good Samaritan), but enhance propagation once a wave is initiated (Executioner). The concept of K+ spatial buffering was first discussed by Orkland 60 years and there have been numerous experimental and modeling studies since then. These studies do not take into account isopotentiality and modeling studies have only considered slow, steady state, time scales. Collaborators: Min Zhou, Baofeng Ma Richard Buckalew, Gemma Huguet Anoushka Joglekar, Leopold Matamba Messi Sarah Wong , Ray Lee, Cameron Conte, Monica Sarkar Funded by NSF