For a cochlear hair cell bathed in the endolymph of the inner ear, the external K+ concentration is 100mMwhile the internal K+ concentration is 10mM.Recall: VK = 61.5mV/z x log10 Co/CiAssuming K+ channels are open, what movement of K+ will occur if the cell's membrane potential isexperimentally shifted briefly to 30.75 mV?O K+ will move into the cellO There will be no net movement of K+ across the membraneO K+ movement cannot be determined from the information given.O K+ will move out of the cell

Answered: For a cochlear hair cell bathed in the…

Biomedical Instrumentation Systems

1st Edition

ISBN:9781133478294

Author:Chatterjee

Publisher:Chatterjee

Chapter3: Biosignals And Noise

Section: Chapter Questions

Problem 3RT

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Question

For a cochlear hair cell bathed in the endolymph of the inner ear, the external K+ concentration is 100mM
while the internal K+ concentration is 10mM.
Recall: VK = 61.5mV/z x log10 Co/Ci
Assuming K+ channels are open, what movement of K+ will occur if the cell's membrane potential is
experimentally shifted briefly to 30.75 mV?
O K+ will move into the cell
O There will be no net movement of K+ across the membrane
O K+ movement cannot be determined from the information given.
O K+ will move out of the cell

Expert Solution

Voltage Gated Channels

Voltage gated Channels are a type of passive transport i.e. no energy is expended for this kind of transport and in-fact these kind of transport only happens if the Gibbs free energy of transport ( $∆ G_{t}$ ) is a negative value. The voltage gated potassium ion channel is an example for this kind of transport. Generally, the potassium concentration is greater inside of a cell compared to the outside but here in the cochlear hair cells its the opposite.

$∆ G_{t} = R T l n (\frac{C_{f i n a l p o i n t}}{C_{s t a r t i n g p o i n t}}) + Z F ∆ V h e r e R i s t h e u n i v e r s a l g a s c o n s \tan t = 8.314 J m o l^{- 1} K^{- 1} T i s t h e t e m p e r a t u r e i n k e l v i n; T = 310.15 K p h y s i o \log i c a l l y C_{f i n a l p o i n t} i s t h e c o n c e n t r a t i o n o f t h e t r a n s p o r t m o l e c u l e i n i t s e n d p o i n t C_{s t a r t i n g p o i n t} i s t h e c o n c e n t r a t i o n o f t h e t r a n s p o r t m o l e c u l e i n i t s s t a r t i n g p o i n t i . e . i f t h e t r a n s p o r t h a p p e n s f r o m i n s i d e t o o u t s i d e o f a c e l l; C_{f i n a l p o i n t} i s t h e c o n c e n t r a t i o n o u t s i d e t h e c e l l a n d C_{s t a r t i n g p o i n t} i s t h e c o n c e n t r a t i o n i n s i d e t h e c e l l Z i s c h a r g e o f t r a n s p o r t m o l e c u l e, p o t a s s i u m h a s a c h a g e o f + 1 F i s t h e F a r a d a y s c o n s \tan t = 96485 C / m o l ∆ V i s t h e m e m b r a n e p o t e n t i a l i n v o l t s (V)$