kinetic analysis is performed for the overlapping temperature
range only (i.e., between À4.000 and À21.000
C). As a
result, the cell that was observed to freeze at À3.890
C in
the first video is omitted from the risk group. The cell that
experienced intracellular ice formation at À22.446
C in the
second video is also not included as an event in the table;
however, this cell is counted as part of the initial size of the
risk group (because it is unfrozen at the start of the kinetic
analysis, when the temperature is À4.000
C).
110. If all non-disqualified cells undergo intracellular crystallization, then the final value in the risk group column will be one.
If some cells do not experience intracellular ice formation
prior to the analysis end temperature, then the final value in
the risk group column will be equal to one plus the number of
unfrozen cells.
111. A conventional method to present intracellular ice formation
data is to plot the cumulative probability of intracellular
freezing as a function of descending temperature. Another
common metric used to quantify the experimental results is
the median intracellular ice formation temperature, which is
defined as the temperature at which P ¼ 0.5. Evaluation of
the median intracellular ice formation temperature does not
require computation of the cumulative probability, because it
is equivalent to the temperature at which the cumulative
hazard A ¼ ln(2).
Acknowledgments
The author gratefully acknowledges Peter Grocutt of Linkam Scientific Instruments for valuable discussions and technical support
during the development of the high-speed video cryomicroscopy
system and during the writing of this chapter. The original version
of this work was supported by National Science Foundation grant
CBET-1066619.
References
1. Mazur P, Leibo SP, Chu EHY (1972) A
two-factor hypothesis of freezing injury: evidence from Chinese hamster tissue-culture
cells. Exp Cell Res 71:345–355
2. Toner M (1993) Nucleation of ice crystals
inside biological cells. In: Steponkus P
(ed) Advances in low-temperature biology, vol
2. JAI Press, London, pp 1–51
3. Karlsson JOM, Cravalho EG, Toner M (1993)
Intracellular ice formation: causes and consequences. Cryo-Lett 14:323–336
4. Go ¨ppert HR (1830) Ueber die W€ armeEntwickelung in den Pflanzen, deren Gefrieren
und die Schutzmittel gegen dasselbe. Joseph
Max, Breslau
5. Molisch H (1897) Untersuchungen u ¨ber das
Erfrieren der Pflanzen. Gustav Fischer, Jena
6. Diller KR, Cravalho EG (1971) A cryomicroscope for the study of freezing and thawing
processes in biological cells. Cryobiology
7:191–199
268
Jens O. M. Karlsson
range only (i.e., between À4.000 and À21.000
C). As a
result, the cell that was observed to freeze at À3.890
C in
the first video is omitted from the risk group. The cell that
experienced intracellular ice formation at À22.446
C in the
second video is also not included as an event in the table;
however, this cell is counted as part of the initial size of the
risk group (because it is unfrozen at the start of the kinetic
analysis, when the temperature is À4.000
C).
110. If all non-disqualified cells undergo intracellular crystallization, then the final value in the risk group column will be one.
If some cells do not experience intracellular ice formation
prior to the analysis end temperature, then the final value in
the risk group column will be equal to one plus the number of
unfrozen cells.
111. A conventional method to present intracellular ice formation
data is to plot the cumulative probability of intracellular
freezing as a function of descending temperature. Another
common metric used to quantify the experimental results is
the median intracellular ice formation temperature, which is
defined as the temperature at which P ¼ 0.5. Evaluation of
the median intracellular ice formation temperature does not
require computation of the cumulative probability, because it
is equivalent to the temperature at which the cumulative
hazard A ¼ ln(2).
Acknowledgments
The author gratefully acknowledges Peter Grocutt of Linkam Scientific Instruments for valuable discussions and technical support
during the development of the high-speed video cryomicroscopy
system and during the writing of this chapter. The original version
of this work was supported by National Science Foundation grant
CBET-1066619.
References
1. Mazur P, Leibo SP, Chu EHY (1972) A
two-factor hypothesis of freezing injury: evidence from Chinese hamster tissue-culture
cells. Exp Cell Res 71:345–355
2. Toner M (1993) Nucleation of ice crystals
inside biological cells. In: Steponkus P
(ed) Advances in low-temperature biology, vol
2. JAI Press, London, pp 1–51
3. Karlsson JOM, Cravalho EG, Toner M (1993)
Intracellular ice formation: causes and consequences. Cryo-Lett 14:323–336
4. Go ¨ppert HR (1830) Ueber die W€ armeEntwickelung in den Pflanzen, deren Gefrieren
und die Schutzmittel gegen dasselbe. Joseph
Max, Breslau
5. Molisch H (1897) Untersuchungen u ¨ber das
Erfrieren der Pflanzen. Gustav Fischer, Jena
6. Diller KR, Cravalho EG (1971) A cryomicroscope for the study of freezing and thawing
processes in biological cells. Cryobiology
7:191–199
268
Jens O. M. Karlsson