**4. Equilibrium** *vs***. kinetic vitrifcation; Evolution of the "Fahy's" phase diagram**

This sub-chapter discusses in detail the phase diagram ("*Fahy-Rall*" vitrification diagram). We will also discuss using this diagram the two basic and reciprocal ways of achieving VF, which can be done: i) by cooling and warming at relatively moderate rates but very high concentrations of exogenous (and often toxic) vitrification agents/enhancers (VFAs), which is defined as *equilibrium* VF and ii) by increasing the rate of cooling with a few or not at all exogenous VFAs present, which we refer as *kinetic* VF. We will also emphasize that the border of "*non-achievable*" and "*achievable*" VF that was once set up by Fahy is arbitrary and largely depends on the currently achievable rates of cooling and warming.

**Fig. 5A** depicts the *original* diagram published by *Fahy* et al in **1984** [Fahy *et al.*, 1984]. The diagram is divided in 4 distinctive zones. **Zone IV** is the *equilibrium VF*, when it occurs at any practical rates of cooling and warming as it lies to the right of the junction of *Tm* ( i.e., no ice forming during cooling) and *Td* (no de-vitrifcation during warming). It is basically the zone where the line **E-F** on **Fig. 1** is drawn but with the notion that *Tg* in the Fahy's diagrams (apparently, for glycerol) lies substantially lower than in Devireddy's diagram (*Tg* of a fully dehydrated sample is well above 0 OC while *Tg* of glycerol is in range of -90OC and below [Pouplin *et al.*, 1999]. For *Tg*'s of some popular vitrificants see Table 1 in [Katkov & Levine, 2004]. **Zone III** is the zone when vitrification occurs. The left border is the junction of *Th* (showed in dotted line as it is hardly to estimate *Th* of very viscous samples) and glass transition curve *Tg* and it occurs at concentrated *Cv*'s, the minimal concentrations where *equilibrium* vitrification during cooling occurs at practically any speed. However, such concentration still may produce de-vitrification during re-warming as the devitrification curve *Td* crosses the melting (equilibrium warming) curve at the critical concentration of devitrification *Cdv*. Thus, this Zone III is the zone where warming must be done fast.

**Zone II**, called by Fahy and colleagues at that time (!) *"doubly unstable"* lies at concentration below *Cv*. At those concentrations, both cooling and warming must be done fast to avoid ice formatting and devitrification respectively. That is what we call kinetic vitrification as it deals with the speed of cooling and re-warming rather than with the equilibrium values. It means that the border between that Zone II, where vitrification is achievable with the **Zone I**, where successfully vitrification is impossible at any "reasonable speed" of cooling and warming largely depends on the rate of that cooling and warming: it is reciprocal to the *Cv* and *Cdv* so they move to the left into the area of the lower concentrations.

Thus, **there are 2 basic and reciprocal ways of achieving VF**: i) by raising the concentration, and as result, the viscosity of the intra- and extracellular milieu at relatively moderate and even slow rates of cooling but very high concentrations VFAs,

Kinetic Vitrification of Spermatozoa of Vertebrates: What Can We Learn from Nature? 21

Secondly, the authors of the chapter shifted the border between *"achievable"* and *"nonachievable"* vitrification (Zones I and II) to the left. It was a small concession to the reality, people have been successfully vitrifying oocytes and other "watery' cells with substantially less concentrations than40%, but yet it reflects the general *"drift to the left"*, so to speak.

Most importantly in our opinion is that the notorious *"killing darts"*, which marked the "unsuccessful vitrification" in the Zone I on the original Fahy's diagram in 1984… suddenly disappeared in a newer version. It means that the authors allowed (at least theoretically) the

C

Fig. 5. **A (top):** original diagram published *Fahy* et al. in **1984** [Fahy *et al.*, 1984]. The diagram

is divided in 4 distinctive zones. **Zone IV** is the *equilibrium VF*, when it occurs at any practical rates of cooling and warming as it lies to the right of the junction of *Tm* (i.e., no ice forming during cooling) and *Td* (no de-vitrifcation during warming) it is basically the zone

A B

which is defined as *equilibrium VF* and ii) by increasing the rate of cooling with a few or not at all exogenous VFAs present so deleterious intracellular ice formation is not achieved due to lack of time for growing ice crystal nuclei (*kinetic* VF). Note that the border between "*non-achievable*" and "*achievable*" VF (Zones I and II) that was once set up by Fahy is arbitrary and as we said, largely depends on the currently achievable rates of cooling and warming.

The position of the borders between the zones also depends on the glass transition temperature of the solute (*Tg* curve). As we mentioned above, Fahy *et al.* had considered a permeable vitrificant with very low *Tg* in range of -90OC (glycerol). In the paper on vitrification of sperm that we published in 2003, we hypothesized that *Tg* of the intracellular milieu could *be much higher*, so the *Tg* of the intracellular exogenous solute would go much above of *Tg* of glycerol. We published a review in 2006 [Katkov *et al.*, 2006] (the abstract was presented much earlier in 2003 [Katkov *et al.*, 2003]) with that concept superimposed onto Fahy's diagram. This concept and an explanation as to why we could vitrify sperm at much less or no exogenous vitrificants at all is shown in **Fig 5B**. We emphasized that the *Tg* of a internal vitrificants can go very high, so the border between Zones I and II can be shifted substantially to the left so the successful vitrification (straight blue line) is achievable even the extracellular milieu has no glycerol.

This explanation (and at lesser extent the experimental data published at that time *per se*) had been dismissed both by Fahy and by other prominent cryobiologists, most notable of them would be Stan Leibo. They either called it *"quasi-vitrification"* or ignored that such work was published (due to the fact that it was not referred at PubMed, even though the leading author had distributed its copies among numerous scientists in the field). The striking example is the Fahy's chapter [Fahy & Rall, 2007] where he spent a great deal of time bashing kinetic vitrification, giving intricate details as to how its first scientists had failed lately to implement K-VF in practice. In regards to our work, he simply ignored that paper even existed, even though it had been sent it to him and we discussed it with him [Dr. Fahy] in meetings.

So, the *"contemporary vitrificators"* ignored mentioning the paper and notion of kinetic vitrification at very low concentration of the extracellular solute. That however, did not mean they had not learned or gained from it. Neither could they ignore the booming success of K-VF in the assisted reproduction field, which we mentioned above. The whole set of innovation was aimed to cool and warm cells faster, which allowed the ART practitioners to move away from the humongous concentrations of DMSO, EG, PG or glycerol, which would be necessary for equilibrium VF. So, that was actually reflected in the very same chapter published in **2007** [Fahy & Rall, 2007] as it presented a Fahy's diagram with some interesting and *key changes* in comparison to the publication in year **1984** (**Fig. 5C**). We deliberately superimposed those changes on the original Fahy's diagram [Fahy *et al.*, 1984].

First, the words *"doubly unstable"* have been eliminated and it made sense because 99% of publications on vitrification of oocytes and embryos have been done at concentrations that exactly represented the *"doubly unstable"* Zone. That would not make all people who have successfully and *stably* frozen their precious happy to realize that they actually worked in the *"double instability"* zone (and which *is not correct* anyway: the vitrified cells *are stable* at temperatures below of their glass transition, i.e., well below the LN2 temperature).

which is defined as *equilibrium VF* and ii) by increasing the rate of cooling with a few or not at all exogenous VFAs present so deleterious intracellular ice formation is not achieved due to lack of time for growing ice crystal nuclei (*kinetic* VF). Note that the border between "*non-achievable*" and "*achievable*" VF (Zones I and II) that was once set up by Fahy is arbitrary and as we said, largely depends on the currently achievable rates of

The position of the borders between the zones also depends on the glass transition temperature of the solute (*Tg* curve). As we mentioned above, Fahy *et al.* had considered a permeable vitrificant with very low *Tg* in range of -90OC (glycerol). In the paper on vitrification of sperm that we published in 2003, we hypothesized that *Tg* of the intracellular milieu could *be much higher*, so the *Tg* of the intracellular exogenous solute would go much above of *Tg* of glycerol. We published a review in 2006 [Katkov *et al.*, 2006] (the abstract was presented much earlier in 2003 [Katkov *et al.*, 2003]) with that concept superimposed onto Fahy's diagram. This concept and an explanation as to why we could vitrify sperm at much less or no exogenous vitrificants at all is shown in **Fig 5B**. We emphasized that the *Tg* of a internal vitrificants can go very high, so the border between Zones I and II can be shifted substantially to the left so the successful vitrification (straight blue line) is achievable even

This explanation (and at lesser extent the experimental data published at that time *per se*) had been dismissed both by Fahy and by other prominent cryobiologists, most notable of them would be Stan Leibo. They either called it *"quasi-vitrification"* or ignored that such work was published (due to the fact that it was not referred at PubMed, even though the leading author had distributed its copies among numerous scientists in the field). The striking example is the Fahy's chapter [Fahy & Rall, 2007] where he spent a great deal of time bashing kinetic vitrification, giving intricate details as to how its first scientists had failed lately to implement K-VF in practice. In regards to our work, he simply ignored that paper even existed, even though it had been sent it to him and we discussed it with him [Dr.

So, the *"contemporary vitrificators"* ignored mentioning the paper and notion of kinetic vitrification at very low concentration of the extracellular solute. That however, did not mean they had not learned or gained from it. Neither could they ignore the booming success of K-VF in the assisted reproduction field, which we mentioned above. The whole set of innovation was aimed to cool and warm cells faster, which allowed the ART practitioners to move away from the humongous concentrations of DMSO, EG, PG or glycerol, which would be necessary for equilibrium VF. So, that was actually reflected in the very same chapter published in **2007** [Fahy & Rall, 2007] as it presented a Fahy's diagram with some interesting and *key changes* in comparison to the publication in year **1984** (**Fig. 5C**). We deliberately superimposed those changes on the original Fahy's diagram [Fahy *et al.*, 1984]. First, the words *"doubly unstable"* have been eliminated and it made sense because 99% of publications on vitrification of oocytes and embryos have been done at concentrations that exactly represented the *"doubly unstable"* Zone. That would not make all people who have successfully and *stably* frozen their precious happy to realize that they actually worked in the *"double instability"* zone (and which *is not correct* anyway: the vitrified cells *are stable* at

temperatures below of their glass transition, i.e., well below the LN2 temperature).

cooling and warming.

Fahy] in meetings.

the extracellular milieu has no glycerol.

Secondly, the authors of the chapter shifted the border between *"achievable"* and *"nonachievable"* vitrification (Zones I and II) to the left. It was a small concession to the reality, people have been successfully vitrifying oocytes and other "watery' cells with substantially less concentrations than40%, but yet it reflects the general *"drift to the left"*, so to speak.

Most importantly in our opinion is that the notorious *"killing darts"*, which marked the "unsuccessful vitrification" in the Zone I on the original Fahy's diagram in 1984… suddenly disappeared in a newer version. It means that the authors allowed (at least theoretically) the

Fig. 5. **A (top):** original diagram published *Fahy* et al. in **1984** [Fahy *et al.*, 1984]. The diagram is divided in 4 distinctive zones. **Zone IV** is the *equilibrium VF*, when it occurs at any practical rates of cooling and warming as it lies to the right of the junction of *Tm* (i.e., no ice forming during cooling) and *Td* (no de-vitrifcation during warming) it is basically the zone

Kinetic Vitrification of Spermatozoa of Vertebrates: What Can We Learn from Nature? 23

There are other peculiar similarities between that chapter and some of our *earlier* papers, such as use of the equation for determination of the viscosity of the solute near *Tg* [Katkov & Levine, 2004] and storage below and above *Tg* of the sample [Katkov *et al.*, 2006]; we would encourage our readers to compare our work and the Fahy's review with the notion that WLF relationship for viscosity near *Tg* in our work is substituted by an equivalent VTF

**In conclusion**, of these sub-chapters, it is evident that the *kinetic* way dominates the present art of vitrification and all efforts are moving to the direction of increasing speeds and decreasing concentrations (see *"Race for The Pace"* below). On the other hand, the future of *equilibrium* vitrification even in the field where it cannot be substituted by K-VF such as organ CP (but can be done with precision SF as described in a Chapter by Butler and Pegg in

**7. Kinetic vitrification of sperm: why some species have while others have** 

turn of (relatively) recent events related to the *kinetic* VF of spermatozoa.

Now, as we are fully equipped to discuss the core topic of the Chapter, let us refresh the

**7.1 A turn of the helix: The Isachenkos' experiments on vitrification of human sperm**  As we mentioned in the Introductory sub-chapter, 1, after earlier attempts to vitrify sperm with contradictory results, the findings of the cryoprotective role of glycerol and other CPAs at slow freezing moved the field of cryopreservation of spermatozoa from early attempts of K-VF toward E-SF. It has been successfully applied to many types of sperm, yet somewhere in 1990s, the data started accumulating that suggested that glycerol, DMSO and other permeable CPAs might adversely affect the genetic and especially epigenetic fabric of spermatozoa. At the same time, several Japanese groups had successful CP of very sensitive mouse spermatozoa without any permeable CPA but with 18% of impermeable raffinose (a 3-ring sugar) and a mixture of proteins (skim milk) [Okuyama *et al.*, 1990; Tada *et al.*, 1990; Yokoyama *et al.*, 1990]. It worked so exceptionally well, that the Mazur's group, which had originally cryopreserved mouse sperm with glycerol [Mazur *et al.*, 2000] (though found that it can be indeed chemically toxic to the sperm [Katkov *et al.*, 1998]) finally also reported that fast immersion of mouse spermatozoa into liquid nitrogen without any CPA worked perfectly [Koshimoto *et al.*, 2000]. In any case, those data had inspired Evgenia and Vladimir Isachenko to freeze human sperm in tiny pellicles by plunging those "cryogenic loops" without any CPA whatsoever. They published their findings in 2002, and a year later, the explanation why it worked was followed [Isachenko *et al.*, 2003; Nawroth *et al.*, 2002]. That marked the *"second wind"* in the kinetic VF of spermatozoa. The history of the development is described in numerous papers [Isachenko *et al.*, 2004a; Isachenko *et al.*, 2008; Isachenko *et al.*, 2004b; Isachenko *et al.*, 2005] and several reviews by the authors [Isachenko *et al.*, 2007; Isachenko *et al.*, 2010; Katkov *et al.*, 2007] and briefly touched in this Book in Chapter 2 [Isachenko *et al.*, 2012]. The method has been involved from a cryo loop (pellicle) through droplets in LN2 to quite elaborated "aseptic technology". Some of the carriers used by the

equation in the Fahy's chapter (see **Appendix 1**).

**not been vitrified?** 

this Book [Butler & Pegg, 2012]), remains largely unclear.

Isachenkos at different stages are shown in **Fig. 6**.

when the line **E-F** on **Fig. 1** is drawn but with the notion that *Tg* in the Fahy's diagrams (apparently, for glycerol) lies substantially lower than in Devireddy's diagram (*Tg* of fully anhydrated sample is well above OC while for glycerol *Tg* depicted on this diagram is in range of -90OC and below [Pouplin *et al.*, 1999]. For *Tg*'s of other popular vitrificants see Table 1 in [Katkov & Levine, 2004]. **Zone I** is the zone of "non-achievable" VF, **Zone II** is *kinetic* VF marked as *"doubly unstable"*, and **Zone III** is an intermediate zone where devitrification must be avoided while VF is achievable at slow rates. Note two *"killing darts"* in Zone I that indicate ice crystallization (vitrification is not achieved).

**B** (**middle**): Fahy's diagram supplemented by us in **2006** [Katkov *et al.*, 2006] with the notion that the border between Zones I (unsuccessful VF) and II (successful *kinetic* VF) in diagram **A** is arbitrary and can be moved far left to the area of very low concentrations of external VFA's (or no VFA not at all as in case of human sperm). The blue line indicates successful *kinetic* VF, it is analogous with the **G-H** line on **Fig. 1**.

**C** (**bottom**): Fahy's diagram, version **2007** depicted in [Fahy & Rall, 2007] but superimposed by us on the original diagram **A**. Note the following notable changes: i) "disappearance of words "doubly instable"; ii) shifting the border between zones I and II to the left; iii) disappearance of the *"killing darts"* in Zone 1; in addition of **Zone V** (E-VF achievable even with a introduction of exogenous ice: propagation of the ice is stopped). See the major text for further explanation.

blasphemous idea that vitrification could occur at *any* concentration of the solute, however low it might be. And it is true, even the pure water can also be vitrified, though the rate of vitrification must be in range of tens to hundreds of millions OC/min [Angell, 2004]. We can only speculate where all those Zones would go in *that* case. Apparently, they would all disappear! Finally, Fahy and Rall made two crucial concessions in their text (probably, insisted by Bill Rall taking to the account his vast experience and knowledge of the ART field), which we cite below in full:


Those two citations exactly explain how *kinetic* vitrification works without even mentioning it! While we are quite accustomed to the that style of ignoring "inconvenient" publications from several prominent cryobilogists and pushing their explanation aside the facts that "adjusted" (with the reality) Fahy's curve together with the two statements above clearly indicate that even as the staunchest orthodox proponents of equilibrium ("right") vitrification as Dr. Fahy could not ignore the facts and explanation why and how the *kinetic* one is working and dominating the scene now. Apparently and evidently they learned from our publication, as well as from the publications of others.

devitrification must be avoided while VF is achievable at slow rates. Note two *"killing darts"*

**B** (**middle**): Fahy's diagram supplemented by us in **2006** [Katkov *et al.*, 2006] with the notion that the border between Zones I (unsuccessful VF) and II (successful *kinetic* VF) in diagram **A** is arbitrary and can be moved far left to the area of very low concentrations of external VFA's (or no VFA not at all as in case of human sperm). The blue line indicates successful

**C** (**bottom**): Fahy's diagram, version **2007** depicted in [Fahy & Rall, 2007] but superimposed by us on the original diagram **A**. Note the following notable changes: i) "disappearance of words "doubly instable"; ii) shifting the border between zones I and II to the left; iii) disappearance of the *"killing darts"* in Zone 1; in addition of **Zone V** (E-VF achievable even

blasphemous idea that vitrification could occur at *any* concentration of the solute, however low it might be. And it is true, even the pure water can also be vitrified, though the rate of vitrification must be in range of tens to hundreds of millions OC/min [Angell, 2004]. We can only speculate where all those Zones would go in *that* case. Apparently, they would all disappear! Finally, Fahy and Rall made two crucial concessions in their text (probably, insisted by Bill Rall taking to the account his vast experience and knowledge of the ART



Those two citations exactly explain how *kinetic* vitrification works without even mentioning it! While we are quite accustomed to the that style of ignoring "inconvenient" publications from several prominent cryobilogists and pushing their explanation aside the facts that "adjusted" (with the reality) Fahy's curve together with the two statements above clearly indicate that even as the staunchest orthodox proponents of equilibrium ("right") vitrification as Dr. Fahy could not ignore the facts and explanation why and how the *kinetic* one is working and dominating the scene now. Apparently and evidently they learned from

in Zone I that indicate ice crystallization (vitrification is not achieved).

with a introduction of exogenous ice: propagation of the ice is stopped).

*kinetic* VF, it is analogous with the **G-H** line on **Fig. 1**.

See the major text for further explanation.

field), which we cite below in full:

*mentioning of our work whatsoever!]* 

our publication, as well as from the publications of others.

*feasible."* 

when the line **E-F** on **Fig. 1** is drawn but with the notion that *Tg* in the Fahy's diagrams (apparently, for glycerol) lies substantially lower than in Devireddy's diagram (*Tg* of fully anhydrated sample is well above OC while for glycerol *Tg* depicted on this diagram is in range of -90OC and below [Pouplin *et al.*, 1999]. For *Tg*'s of other popular vitrificants see Table 1 in [Katkov & Levine, 2004]. **Zone I** is the zone of "non-achievable" VF, **Zone II** is *kinetic* VF marked as *"doubly unstable"*, and **Zone III** is an intermediate zone where

There are other peculiar similarities between that chapter and some of our *earlier* papers, such as use of the equation for determination of the viscosity of the solute near *Tg* [Katkov & Levine, 2004] and storage below and above *Tg* of the sample [Katkov *et al.*, 2006]; we would encourage our readers to compare our work and the Fahy's review with the notion that WLF relationship for viscosity near *Tg* in our work is substituted by an equivalent VTF equation in the Fahy's chapter (see **Appendix 1**).

**In conclusion**, of these sub-chapters, it is evident that the *kinetic* way dominates the present art of vitrification and all efforts are moving to the direction of increasing speeds and decreasing concentrations (see *"Race for The Pace"* below). On the other hand, the future of *equilibrium* vitrification even in the field where it cannot be substituted by K-VF such as organ CP (but can be done with precision SF as described in a Chapter by Butler and Pegg in this Book [Butler & Pegg, 2012]), remains largely unclear.
