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Kenneth Stewart Cole
Born	(1900-07-10)July 10, 1900 Ithaca, New York
Died	April 18, 1984(1984-04-18) (aged 83) La Jolla, California
Alma mater	Oberlin College Cornell University
Known for	Cole–Cole equation Voltage clamp
Spouse	Elizabeth Evans Roberts
Children	2
Awards	ForMemRS (1972) National Medal of Science (1967) Guggenheim Fellowship (1941)
Scientific career
Fields	Biophysics

Kenneth Stewart Cole (July 10, 1900 – April 18, 1984) was an Americanbiophysicist described by his peers as "a pioneer in the application of physical science to biology".^[1] He was awarded theNational Medal of Science in 1967.^[2][3]

He was born on July 10, 1900, inIthaca, New York, to Charles Nelson Cole, an instructor in Latin atCornell University and Mabel Stewart. Kenneth had a younger brother,Robert H. Cole [Wikidata], with whom he remained very close throughout his life despite a large difference in age; they were joint authors of four papers published between 1936 and 1942.^[4]

In 1902 the family moved toOberlin, Ohio, when his father took a post atOberlin College. His father would later become the Dean. Kenneth's mother was, and Cole graduated fromOberlin College in 1922 and received aPh.D. in physics withFloyd K. Richtmyer fromCornell University in 1926. He spent summers working at theGeneral Electric laboratory inSchenectady, New York.

In 1932, Cole married Elizabeth Evans Roberts, an attorney. Later, her work was mostly concerned with civil rights and in 1957 she joined the staff of theUnited States Commission on Civil Rights^[4]

Kenneth joined the staff ofColumbia University in 1937 and remained there until 1946. He had also been associated with thePresbyterian Hospital, and theGuggenheim Foundation for Advanced Study atPrinceton University and theUniversity of Chicago.

From 1949 to 1954 he was the technical director of theNaval Medicine Research Institute inBethesda, Maryland. In 1954 he became chief of the laboratory of biophysics of theNational Institute of Neurological Diseases and Blindness.

He achieved advances that led to the "sodium theory" of nerve transmission that later wonNobel Prizes forAlan L. Hodgkin andAndrew F. Huxley in 1963. Cole was elected a Fellow of theAmerican Physical Society in 1931,^[5] a member of theNational Academy of Sciences in 1956,^[6] and a Fellow of theAmerican Academy of Arts and Sciences in 1964.^[7] He was awarded theNational Medal of Science in 1967, the award citation, read: "As a result, we know far more about how the nervous system functions." In 1972 he was made a member of theRoyal Society of London. TheBiophysical Society awards the Kenneth S. Cole medal to a scientist studying cell membranes.

In 1980 he became an adjunct professor of the Department of Neurosciences at theScripps Institute of Oceanography inSan Diego. He had a son, Roger Braley Cole, and a daughter, Sarah Roberts Cole.

He died on April 18, 1984, inLa Jolla, California.^[2]

Tissue can be modeled as an electrical circuit with resistive and capacitive properties:

Its dispersion and absorption are represented by the empirical formula:

${\displaystyle {ϵ}^{\ast }-{ϵ}_{\mathrm{\infty }}={\displaystyle \frac{{ϵ}_0-{ϵ}_{\mathrm{\infty }}}{1+(i\omega {\tau }_0{)}^{1-\alpha }}}}$

In this equation${\displaystyle {ϵ}^{\ast }}$ is the complex dielectric constant,${\displaystyle {ϵ}_0}$ and${\displaystyle {ϵ}_{\mathrm{\infty }}}$ are the "static" and "infinite frequency" dielectric constants,${\displaystyle \omega =2\pi }$ times the frequency, and${\displaystyle {\tau }_0}$ is a generalized relaxation time. The parameter${\displaystyle \alpha }$ can assume values between 0 and 1, the former value giving the result of Debye for polar dielectrics. This expression requires that the locus of the dielectric constant in the complex plane be a circular arc with end points on the axis of reals and center below the axis.

It is worth emphasizing that the Cole–Cole model is an empirical model of the measured data. It has been successfully applied to a wide variety of tissues over the past 60 years, but it does not give any information about the underlying causes of the phenomena being measured.

Several references in the literature use a form of the Cole equation written in terms of impedance instead of a complex permittivity.^[8] The impedance${\displaystyle Z}$ is given by:

${\displaystyle Z=R_{\mathrm{\infty }}+\frac{R_0-R_{\mathrm{\infty }}}{1+(\frac{jf}{f_c}{)}^{1-\alpha }}}$

Where${\displaystyle R_0}$ and${\displaystyle R_{\mathrm{\infty }}}$ are the resistances at zero frequency (i.e. DC) and infinity, respectively.${\displaystyle f_c}$ is often referred to as the characteristic frequency. The characteristic frequency is not the same when the analysis is carried out in terms of the complex permittivity.A simple interpretation of the above equation is in terms of a circuit where a resistance${\displaystyle S}$ is in series with a capacitor${\displaystyle C}$ and this combination is placed in parallel with a resistance${\displaystyle R}$. In this case${\displaystyle R_0=R}$ and${\displaystyle R_{\mathrm{\infty }}=\frac{RS}{R+S}}$. It can be shown that${\displaystyle f_c}$ is given by${\displaystyle f_c=\frac{1}{2\pi C(R+S)}}$.

In a series of papers in 1930s—1940s, he experimentally studied the electric properties of living tissues, such as Nitella,^[9] frog eggs,^[10] and most famously, thesquid giant axon.^[11][12]

Figure 4 of^[11] is sometimes used as artistic representations of biophysics. It also appeared, rotated 90 degrees, in Swedish apartments as modern art.^[13]

• Action potential
• Cable theory
• Dendrite

• Cole, K.S. (1928)."Electrical Impedance of Suspensions of Spheres".Journal of General Physiology.12:29–36.doi:10.1085/jgp.12.1.29.PMC 2323685.PMID 19872446.
• Cole, K.S. (1979). "Mostly membranes".Annual Review of Physiology.41:1–23.doi:10.1146/annurev.ph.41.030179.000245.PMID 373584.
• Cole, K. S.; Cole, R. H. (1941)."Dispersion and absorption in dielectrics".J. Chem. Phys.9:341–351.
• Cole, K.S.; Baker, R.F. (1941). "Longitudinal Impedance of the Squid Giant Axon".J. Gen. Physiol.24:771–788. (Inductance of membrane)

• National Academy of Sciences Biographical Memoir

• 1900 births
• 1984 deaths
• American biophysicists
• 20th-century American physicists
• Columbia University staff
• Cornell University alumni
• Fellows of the American Academy of Arts and Sciences
• Fellows of the American Physical Society
• Foreign members of the Royal Society
• Manhattan Project people
• Members of the United States National Academy of Sciences
• National Medal of Science laureates
• Oberlin College alumni
• Scientists from Ithaca, New York
• Scripps Institution of Oceanography faculty
• Presidents of the Biophysical Society

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