Editing Hysteresis (section)

==== Biochemical systems: regulating the cell cycle in yeast ====
Biochemical systems can also show hysteresis-like output when slowly varying states that are not directly monitored are involved, as in the case of the cell cycle arrest in yeast exposed to mating pheromone.<ref name="Doncic 2013">{{cite journal |author1=Doncic, Andreas |author2=Skotheim, Jan M |year=2013 |title=Feedforward regulation ensures stability and rapid reversibility of a cellular state |journal=Molecular Cell |volume=50 |issue=6 |pages=856–68 |doi=10.1016/j.molcel.2013.04.014 |pmc=3696412 |pmid=23685071}}</ref> The proposed model is that α-factor, a yeast mating pheromone binds to its analog receptor on another yeast cell promoting transcription of Fus3 and promoting mating. Fus3 further promotes Far1 which inhibits Cln1/2, activators of the cell cycle. This is representative of a coherent feedforward loop that can modeled as a hysteresis curve.

Far1 transcription is the primary mechanism responsible for the hysteresis observed in cell-cycle reentry.<ref>{{Cite journal |last1=Doncic |first1=Andreas |last2=Skotheim |first2=Jan M. |date=2013-06-27 |title=Feedforward Regulation Ensures Stability and Rapid Reversibility of a Cellular State |journal=Molecular Cell |volume=50 |issue=6 |pages=856–868 |doi=10.1016/j.molcel.2013.04.014 |pmid=23685071 |pmc=3696412 |issn=1097-2765}}</ref> The history of pheromone exposure influences the accumulation of Far1, which, in turn, determines the delay in cell-cycle reentry. Previous pulse experiments demonstrated that after exposure to high pheromone concentrations, cells enter a stabilized arrested state where reentry thresholds are elevated due to increased Far1-dependent inhibition of CDK activity. Even when pheromone levels drop to concentrations that would allow naive cells to reenter the cell cycle, pre-exposed cells take longer to resume proliferation. This delay reflects the history-dependent nature of hysteresis, where past exposure to high pheromone concentrations influences the current state. Hysteresis ensures that cells make robust and irreversible decisions about mating and proliferation in response to pheromone signals. It allows cells to "remember" high pheromone exposure, and this helps yeast cells adapt and stability their responses to environmental conditions, avoiding fast premature reentry into the cell cycle, the moment that pheromone signal dies down.

Additionally, the duration of cell cycle arrest depends not only on the final level of input Fus3, but also on the previously achieved Fus3 levels. This effect is achieved due to the slower time scales involved in the transcription of intermediate Far1, such that the total Far1 activity reaches its equilibrium value slowly, and for transient changes in Fus3 concentration, the response of the system depends on the Far1 concentration achieved with the transient value. Experiments in this type of hysteresis benefit from the ability to change the concentration of the inputs with time. The mechanisms are often elucidated by allowing independent control of the concentration of the key intermediate, for instance, by using an inducible promoter.

Biochemical systems can also show hysteresis-like output when slowly varying states that are not directly monitored are involved, as in the case of the cell cycle arrest in yeast exposed to mating pheromone. Here, the duration of cell cycle arrest depends not only on the final level of input Fus3, but also on the previously achieved Fus3 levels. This effect is achieved due to the slower time scales involved in the transcription of intermediate Far1, such that the total Far1 activity reaches its equilibrium value slowly, and for transient changes in Fus3 concentration, the response of the system depends on the Far1 concentration achieved with the transient value. Experiments in this type of hysteresis benefit from the ability to change the concentration of the inputs with time. The mechanisms are often elucidated by allowing independent control of the concentration of the key intermediate, for instance, by using an inducible promoter.

{{Main|Chromatin}}
Darlington in his classic works on [[genetics]]<ref>{{cite book |last1=Darlington |first1=C. D. |title=Recent Advances in Cytology (Genes, Cells, & Organisms)  |edition=Second |publisher=P. Blakiston's Son & Co. | year=1937 |url=https://www.biodiversitylibrary.org/ia/recentadvancesin00darl |isbn=978-0-8240-1376-9 }}</ref><ref>{{cite book |last1=Rieger |first1=R. |last2=Michaelis |first2=A.  |last3=M. M. |year=1968 |title=A Glossary of Genetics and Cytogenetics: Classical and Molecular |publisher= [[Springer Science+Business Media|Springer]] |edition=Third |isbn=978-3-540-04316-4}}</ref> discussed hysteresis of the [[chromosomes]], by which he meant "failure of the external form of the chromosomes to respond immediately to the internal stresses due to changes in their molecular spiral", as they lie in a somewhat rigid medium in the limited space of the [[cell nucleus]].

{{Main|Morphogen}}
In [[developmental biology]], cell type diversity is regulated by long range-acting signaling molecules called [[morphogens]] that pattern uniform pools of cells in a concentration- and time-dependent manner. The morphogen [[sonic hedgehog]] (Shh), for example, acts on [[limb bud]] and [[neural progenitors]] to induce expression of a set of [[homeodomain]]-containing [[transcription factors]] to subdivide these tissues into distinct domains. It has been shown that these tissues have a 'memory' of previous exposure to Shh.<ref>{{cite journal
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|first1=B. D.
|last2= Scherz
|first2=P. J.
|last3= Nissim
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|last5= McMahon
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|last6= Tabin
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|year = 2004
|title = Evidence for an expansion-based temporal Shh gradient in specifying vertebrate digit identities
|journal = Cell
|pmid = 15315763
|volume = 118
|issue = 4
|pages = 517–28
|doi =10.1016/j.cell.2004.07.024 |s2cid=16280983
|doi-access= free
}}</ref>
In neural tissue, this hysteresis is regulated by a homeodomain (HD) feedback circuit that amplifies Shh signaling.<ref>{{Cite journal 
| last1 = Lek | first1 = M. 
| last2 = Dias | first2 = J. M. 
| last3 = Marklund | first3 = U. 
| last4 = Uhde | first4 = C. W. 
| last5 = Kurdija | first5 = S. 
| last6 = Lei | first6 = Q. 
| last7 = Sussel | first7 = L. 
| last8 = Rubenstein | first8 = J. L. 
| last9 = Matise | first9 = M. P. 
| last10 = Arnold | first10 = H. -H. 
| last11 = Jessell | first11 = T. M. 
| last12 = Ericson | first12 = J. 
| doi = 10.1242/dev.054288 
| title = A homeodomain feedback circuit underlies step-function interpretation of a Shh morphogen gradient during ventral neural patterning 
| journal = Development 
| volume = 137 
| issue = 23 
| pages = 4051–4060 
| year = 2010 
| pmid = 21062862 
| doi-access = free 
}}</ref> In this circuit, expression of [[Gli]] transcription factors, the executors of the Shh pathway, is suppressed. Glis are processed to repressor forms (GliR) in the absence of Shh, but in the presence of Shh, a proportion of Glis are maintained as full-length proteins allowed to translocate to the nucleus, where they act as activators (GliA) of transcription. By reducing Gli expression then, the HD transcription factors reduce the total amount of Gli (GliT), so a higher proportion of GliT can be stabilized as GliA for the same concentration of Shh.