1. Ion transport and electrochemical gradients under DC and AC signals
Alexander Walls, Qurat-ul-Ann Mirza, Merrell A. Johnson, Vannara Chhim
Horia I. Petrache, Bruce D. Ray, Elliott D. Rosen, Yogesh N. Joglekar
Indiana University-Purdue University Indianapolis, Indiana 46202
Abstract
The plasma membrane of a human cell remains much an enigma
as far as its behavior with the extracellular environment is
involved. The plasma membrane is a phospholipid bilayer
composed of molecules that are polar on one side and nonpolar
on other, thus they are amphipathic. The cell must be able to
exchange materials with its surrounding environment in order to
survive. Transport across the cell membrane can be
accomplished in two complementary ways: passive and active.
Active transport utilizes specialized membrane proteins such as
the Na+/K+ pump and requires the expenditure of energy in the
form of ATP or an applied potential like that of the proton gradient
established by a mitochondrion. Here we investigate passive
transport, which relies only on an electrochemical gradient
across a lipid membrane. The gradual change in the
concentration of a compound over a distance is its chemical
concentration gradient. Passive diffusion occurs naturally in the
direction of lower concentration. Charged molecules however,
also flow in the direction of electrical gradients. These two types
of gradients combine to form a net electrochemical gradient
dictating how charged molecules should move. In the lab, we
synthesize isolated lipid membranes in ionic solutions and insert
the antibiotic protein gramicidin which is permeable to positive
ions such as sodium and potassium. The energy required for ion
transport is supplied by an applied external potential (voltage).
The objective of our study is primarily centered on the electrical
properties of biological materials under DC and AC applied
signals.
Ion Channel Setup
Conclusions
Theory on Memristors
In 1976, Leon Chua stated that time-varying
conductances, whose variations are function of
first-order differential equations, are actually
memristive systems [1]. The proceeding table
compares the characteristics of the Hodgkin-
Huxley voltage gated ion channels and the
current driven memristor.
References
1. Justice, J. Matthew, Petrusca, N. Daniela, et al. (2009). “Effects of Lipid Interactions on Model Vesicle Engulfment By Alveolar
Macrophages.” 1-7.
2. Chua, L. O., & Kang, S. M. (1976). Memristive devices and systems. Proceedings of the IEEE, 64(2), 209-223.
3. Rostovtseva, K. Tatiana, Petrache, I. Horia, et al. (2007). “Interfacial Polar Interactions Affect Gramicidin Channel Kinetics.“L-23-L25.
• Potassium and chloride
ions are transported
across the membrane
using gramicidin ion
channels for a period of
time.
• Electrodes are used to
apply a potential across
the Teflon tape
containing the
membrane.
• Ions from the salt
solution move through
the membrane via
passive diffusion.
1M KCl diffuses toward 0.5M KCl (fig. A)
Current(pA)
• Figure A: Ions move toward areas that afford the highest entropy and lowest free energy.
• Ions will move down their concentration gradient toward areas of lower concentration.
• Current (pA) represents the flow of charged potassium and chloride ions as they diffuse toward equilibrium.
• As the current approaches zero, the two solutions become equal in concentration.
• Figure B: DOPC lipid membranes respond by alternating their direction of flow when an AC signal is applied.
• Figure C: Small amounts of LiCl destabilizes DOPC lipid membranes.
• Figure D: Gramicidin ion channels are indicated by a sharp rise in current for a period of time before it drops back
off.
AC Applied Signal DOPC Lipid (fig. B)
Current(pA)
Disrupted LiCl AC signal (fig. C)
10 mmol LiCl, 0.25M NaCl solution showing
an unstable DOPC lipid membrane.
Frequency of 0.1Hz
Procedure for Disrupted LiCl AC signal (fig. C)
Current(pA)
Time (s)
Figure B displays an AC signal being applied to a
stable DOPC lipid membrane in the absence of LiCl.
(DOPC in 1M NaCl)
AC Applied Signal DOPC Lipid (fig. B)
DC Applied Signaling
Hodgkin-Huxley
Voltage Gated Ion
Channels
Memristor
𝐼 𝜑 = 𝑔 𝜑(𝑥) 𝑉 − 𝑉𝜑
𝜑 = 𝐾, 𝑁𝑎, 𝑎𝑛𝑑 𝐿
𝐼 𝑀 = 𝑔 𝑀(𝑥) 𝑉 − 𝑉 𝑀
State Variable:
m, n, and h
State Variable:
x-doped fraction
𝑑𝑥
𝑑𝑡
= Ӻ(𝑥, 𝑉)
𝑑𝑥
𝑑𝑡
= Ԋ(𝑥, 𝐼)
Stimulus:
AC/DC Current
Stimulus :
AC/DC Voltage
Response:
AC Voltage Pattern with
Different Frequencies
Response:
AC Current with Different
Frequency
[2]
[3]
Raptorex
Research and data of ion channels were obtained to analyze the
various functions of the plasma membrane and its corresponding
membrane proteins (gramicidin). The current study helps to explain
anomalies, such as the 𝑳𝒊+ destabilizing the plasma membrane. The
flow of ions through the membrane via gramicidin ion channels can
be manipulated through the use of AC and DC applied signals.