Effect of Applied Electrical Field on Asymptotic Propagation Speed

A Pinsky-Rinzel model of a neighbor-to-neighbor chain of 64 neurons is simulated. The asymptotic speed is computed by taking the spike times near the region of near constant slope.

A current pulse of duration 0.05 sec and magnitude 0.5 µA/cm² is injected into the soma initially for all neurons at 0.5 second. After a delay of τ, a second pulse is injected into neuron 1.

 

τ = 4 sec.  

Suppression of propagation occurs between E = -12.1 and -12.2 mV/cm. For E = 12.1 mV/cm, propagation stops at neuron number 28.

Propagation Suppression

Behavior at High Negative Fields

Behavior at Near-Zero Fields.

.

 
data files • propagation diagrams
  

 

 τ = 8sec.  

Suppression of propagation occurs between E = -12.1 and -12.2 mV/cm. For E = 12.1 mV/cm, propagation stops at neuron number 26.

Behavior at High Negative Fields

Behavior at Near-Zero Fields.
data files • propagation diagrams  

 
 Asymptotic Speed as a function of Applied Electric Field  
τ = 4 sec.
τ = 8sec.
Applied field, E
(mV/cm)

Propagation speed,c
(neurons/ sec)
Neurons
used for fit
Propagation speed,c
(neurons/ sec)
Neurons
used for fit
-1.0
 
 
172.6111 ± 0.0272
 21..64
-1.1
 
 
170.7623 ± 0.0387
 25..64
-1.2
 
 
133.5086 ± 0.0169
 30..64
-1.3
 11.8183 ± 0.0056
 11..64
 11.8280 ± 0.0011
 11..64
-1.4
 11.6874 ± 0.0029
 11..64
 11.7011 ± 0.0005
 11..64
-1.5
 11.5717 ± 0.0017
 11..64
 11.5883 ± 0.0002
 11..64
-1.6
 11.4725 ± 0.0012
 11..64
 11.4739 ± 0.0001
 11..64
-2.0
 11.0569 ± 0.0004
 11..64
 11.0543 ± 0.0001
 11..64
-3.0
 10.0901 ± 0.0002
 10..64
 10.0724 ± 0.0001
 10..64
-4.0
  9.2346 ± 0.0002
  9..64
  9.2353 ± 0.0001
  9..64
-5.0
  8.4283 ± 0.0002
  8..64
  8.4710 ± 0.0001
  8..64
-6.0
  7.6877 ± 0.0001
  7..64
  7.6873 ± 0.0001
  7..64
-7.0
  6.9624 ± 0.0002
  6..64
  6.9661 ± 0.0001
  6..64
-8.0
  6.2908 ± 0.0002
  5..64
  6.2908 ± 0.0001
  5..64
-9.0
  5.5677 ± 0.0001
  4..64
  5.6472 ± 0.0001
  4..64
-10.0
  4.8801 ± 0.0002
  4..64
  4.8813 ± 0.0001
  4..64
-11.0
  4.0681 ± 0.0003
  4..64
  4.0748 ± 0.0002
  4..64
-11.2
  3.8847 ± 0.0004
  4..64
  3.9036 ± 0.0004
  4..64
-11.4
  3.6792 ± 0.0002
  4..64
  3.7028 ± 0.0004
  4..64
-11.6
  3.4929 ± 0.0004
  4..64
  3.4802 ± 0.0002
  4..64
-11.8
  3.2303 ± 0.0006
  4..64
  3.2356 ± 0.0003
  4..64
-12.0
  2.9171 ± 0.0006
  4..64
  2.8955 ± 0.0005
  4..64
-12.1
  2.7204 ± 0.0011
  4..64
  2.7311 ± 0.0012
  4..64
-12.2
  2.4332 ± 0.0014
  4..28
  2.4613 ± 0.0016
  4..26
results

 

Behavior at High Negative Electrical Fields

At E = 12.2 mV/cm, propagation terminates at neuron 28 for τ = 4 sec and neuron 26 for τ = 4 sec. In order to determine if the partial propagation is caused by ephatic interactions, extracellular resistance in the neuron-chain (horizontal) direction is raise to a high level.

 

τ = 4 sec.  

At E = 12.2 mV/cm, propagation occurs but reduces to 11 neurons from the 28 neurons in the ephatic interactive chain.

At E = 12.1 mV/cm, propagation occur but reduces to 12 neurons from at least 64 neurons in the ephatic interactive chain.

 
data files • propagation diagrams  

 

 τ = 8sec.  

At E = 12.2 mV/cm, propagation occurs but reduces to 4 neurons from the 28 neurons in the ephatic interactive chain.

At E = 12.1 mV/cm, propagation occur buts reduces to 11 neurons from at least 64 neurons in the ephatic interactive chain.
data files • propagation diagrams  

 
 Asymptotic Speed as a function of Applied Electric Field, No Ephatic Interaction  
τ = 4 sec.
τ = 8sec.
Applied field, E
(mV/cm)

Propagation speed,c
(neurons/ sec)
Neurons
used for fit
Propagation speed,c
(neurons/ sec)
Neurons
used for fit
-2.0
 11.5422 ± 0.0011
 11..64
 11.5603 ± 0.0008
 11..64
-6.0
  7.6691 ± 0.0006
  7..64
  7.6706 ± 0.0004
  7..64
-10.0
  4.8968 ± 0.0002
  4..64
  4.8811 ± 0.0003
  4..64
-12.0
  2.9798 ± 0.0016
  4..64
  2.9822 ± 0.0009
  4..64
-12.1
  2.8203 ± 0.0035
  4..12
  2.8202 ± 0.0033
  4..11
-12.2
  2.6339 ± 0.0056
  4..11
  2.7130 ± ------
  3.. 4
results

 

Behavior at Near-Zero Electrical Fields

At near zero electric field, the initial propagation is induced by the current pulse. Eventually the down-chain neurons are dominated by natural spiking instead of propagation.

 τ = 4 sec.  
 
data files • propagation diagrams  

 

 τ = 8 sec.  
 
data files • propagation diagrams  

 

 Initial Speed as a function of Applied Near-Zero Electric Field  

 
τ = 4 sec.
τ = 8sec.
Applied field, E
(mV/cm)

Propagation speed,c
(neurons/ sec)
Neurons
used for fit
Propagation speed,c
(neurons/ sec)
Neurons
used for fit
-0.0
 13.7949 ± 0.0169
  3..11
 
 
-1.0
 12.7895 ± 0.0191
  3..17
 15.9875 ± 0.0046
  3..10
-1.1
    
 14.8199 ± 0.0067
  3..14
-1.2
    
 13.5067 ± 0.0091
  3..18
results  

 

Anomalies at Near-Zero Electrical Fields

At low negative and plosive applied field, natural spiking, without initiation by injected current pulses, occurs. As a result, some neurons do not respond to the current pulse when it is sufficiently close to the previous spike to be within it refractory period; that is, induced spiking is disabled by the hyperpolarization of the previous action potential.

 τ = 4 sec.  
 
data files • propagation diagrams  

 

 τ = 8 sec.  
 
data files • propagation diagrams