Electrophys - Time integral of voltage

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SUMMARY

The discussion centers on the significance of the time integral of voltage in the context of electrophysiological measurements. The integration of voltage (V) over time (dt) is directly related to the total charge (in Coulombs) across a membrane, provided that resistance (R) and voltage (V) are known. The participants highlight that while the integral provides useful information about charge transfer, understanding the maximum voltage (Vmax) and the shape of the voltage curve is often more critical. Key equations discussed include the rise and fall of voltage over time, characterized by the time constant τ, which is defined as τ = r_m * c_m, where r is resistance and c is capacitance.

PREREQUISITES
  • Understanding of basic electrophysiology and voltage measurements
  • Familiarity with op-amp based voltage integrators
  • Knowledge of electrical concepts such as resistance (R) and capacitance (C)
  • Ability to interpret mathematical equations related to voltage and charge
NEXT STEPS
  • Research the principles of op-amp based voltage integrators in detail
  • Study the relationship between voltage, current, and charge in electrical circuits
  • Explore the mathematical modeling of voltage curves in electrophysiological contexts
  • Investigate the significance of time constants in biological systems
USEFUL FOR

Researchers in electrophysiology, electrical engineers, and anyone involved in measuring and interpreting voltage signals in biological systems will benefit from this discussion.

dom_stb
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Hello,

I have recorded voltage signals (in the time domain) using standard electrophys amplifiers. The voltage is that of an electrode inserted in a plant stem as charged objects are brought close to, then into contact with the flower.

I was wondering about the significance of the time integral of voltage: It is not clear to me what, if any physical significance this has.

Op-amp based voltage integraters in electronics measure the total electric flux through the amplifier - or so i understand it. Does this apply to the signals I measure?

I know if resistance is constant, voltage is proportional to current so the integration of V dt is proportional to charge, but without a reliable value for R this is useless to me.

I want to know exactly what quantity the integration of Vdt gives.
Any ideas?
Regards,
Dom.
 
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dom_stb said:
Hello,

I was wondering about the significance of the time integral of voltage: It is not clear to me what, if any physical significance this has.

I want to know exactly what quantity the integration of Vdt gives.
Any ideas?
Regards,
Dom.

It should give the total charge (in Coulombs) across a membrane in time t given R and V are known. I'm not sure you really need to know this.

In most cases, you want to know Vmax and the shape of the voltage curve.

So for a time constant \tau=r_{m}c_m where r is the resistance and c the capacitance of the membrane:

rise V(t)=Vmax(1-e^{-t/\tau})
fall V(t)=Vmax(e^{-t/\tau})
 
Last edited:
Thanks very much, that's helpful.

What I am measuring is really the transfer of charge (though i am measuring the voltage) between the object and the flower. It won't necessarily follow neuronal models, but it will be nice to see if te shape can be charactarised by any of these equations.

Thanks again.
 

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