Editing Hysteresis (section)

==In biology==

===Cell biology and genetics===
{{Main|Cell biology}}
Hysteresis in cell biology often follows [[Bistability#In biological and chemical systems|bistable systems]] where the same input state can lead to two different, stable outputs. Where bistability can lead to digital, switch-like outputs from the continuous inputs of chemical concentrations and activities, hysteresis makes these systems more resistant to noise. These systems are often characterized by higher values of the input required to switch into a particular state as compared to the input required to stay in the state, allowing for a transition that is not continuously reversible, and thus less susceptible to noise. 

==== Irreversible hysteresis ====
[[File:Irreversible_Hysteresis.png|thumb|Irreversible hysteresis graph]]
In the case of mitosis, irreversibility is essential to maintain the overall integrity of the system such that we have three designated checkpoints to account for this: G1/S, G2/M, and the spindle checkpoint.<ref>{{Cite journal |last1=Makar |first1=A. B. |last2=McMartin |first2=K. E. |last3=Palese |first3=M. |last4=Tephly |first4=T. R. |date=June 1975 |title=Formate assay in body fluids: application in methanol poisoning |url=https://pubmed.ncbi.nlm.nih.gov/1 |journal=Biochemical Medicine |volume=13 |issue=2 |pages=117–126 |doi=10.1016/0006-2944(75)90147-7 |issn=0006-2944 |pmid=1}}</ref> Irreversible hysteresis in this context ensures that once a cell commits to a specific phase (e.g., entering mitosis or DNA replication), it does not revert to a previous phase, even if conditions or regulatory signals change. Based on the irreversible hysteresis curve, there does exist an input at which the cell jumps to the next stable state, but there is no input that allows the cell to revert to its previous stable state, even when the input is 0, demonstrating irreversibility. Positive feedback is critical for generating hysteresis in the cell cycle. For example: In the G2/M transition, active CDK1 promotes the activation of more CDK1 molecules by inhibiting Wee1 (an inhibitor) and activating Cdc25 (a phosphatase that activates CDK1).<ref>{{Cite journal |last1=Schmidt |first1=Matthias |last2=Rohe |first2=Alexander |last3=Platzer |first3=Charlott |last4=Najjar |first4=Abdulkarim |last5=Erdmann |first5=Frank |last6=Sippl |first6=Wolfgang |date=2017-11-23 |title=Regulation of G2/M Transition by Inhibition of WEE1 and PKMYT1 Kinases |journal=Molecules |language=en |volume=22 |issue=12 |pages=2045 |doi=10.3390/molecules22122045 |doi-access=free |pmc=6149964 |pmid=29168755}}</ref> These loops lock the cell into its current state and amplify the activation of CDK1. Positive feedback also serves to create a bistable system where CDK1 is either fully inactivated or fully activated. Hysteresis prevents the cell from oscillating between these two states from small perturbations in signal (input).

==== Reversible hysteresis ====
[[File:Reversible_Hysteresis.png|thumb|Reversible hysteresis graph]]
A biochemical system that is under the control of reversible hysteresis has both forward and reverse trajectories. The system generally requires a higher [input] to proceed forward into the next bistable state then to exit from that stage. For example, cells undergoing [[cell division]] exhibit reversible hysteresis in that it takes a higher concentration of [[cyclin]]s to switch them from G2 phase into [[mitosis]] than to stay in mitosis once begun.<ref>{{cite journal |last1=Pomerening |first1=Joseph R. |last2=Sontag |first2=Eduardo D. |last3=Ferrell |first3=James E. |year=2003 |title=Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2 |journal=Nature Cell Biology |volume=5 |issue=4 |pages=346&ndash;251 |doi=10.1038/ncb954 |pmid=12629549 |s2cid=11047458}}</ref><ref>{{cite journal |author1=Ferrell JE Jr. |author2=Machleder EM |date=1998 |title=The biochemical basis of an all-or-none cell fate switch in Xenopus oocytes |journal=Science |volume=280 |issue=5365 |pages=895–8 |bibcode=1998Sci...280..895F |doi=10.1126/science.280.5365.895 |pmid=9572732}}</ref>  Additionally, because the [cyclin] required to reverse the cell back to the G2 phase is much lower than the [cycilin] to enter mitosis, this improved the bistability of mitosis because it is more resistance to weak or transient signals. Small perturbations the [input] will be unable to push the cell out of mitosis so easily.

==== History and memory ====
In systems with bistability, the same input level can correspond to two distinct stable states (e.g., "low output" and "high output"). The actual state of the system depends on its history {{Ndash}}whether the input level was increasing (forward trajectory) or decreasing (backward trajectory). Thus, it is difficult to determine which state a cell is in if given only a bistability curve. The cell's ability to "remember" its prior state ensures stability and prevents it from switching states unnecessarily due to minor fluctuations in input.<ref>{{Cite journal |last1=Smith |first1=R. J. |last2=Bryant |first2=R. G. |date=1975-10-27 |title=Metal substitutions incarbonic anhydrase: a halide ion probe study |url=https://pubmed.ncbi.nlm.nih.gov/3 |journal=Biochemical and Biophysical Research Communications |volume=66 |issue=4 |pages=1281–1286 |doi=10.1016/0006-291x(75)90498-2 |issn=0006-291X |pmid=3}}</ref> This memory is often maintained through molecular feedback loops, such as positive feedback in signaling pathways, or the persistence of regulatory molecules like proteins or phosphorylated components.<ref>{{Cite journal |last1=Jiang |first1=Yanfei |last2=Hao |first2=Nan |date=2021-04-01 |title=Memorizing environmental signals through feedback and feedforward loops |journal=Current Opinion in Cell Biology |series=Cell Signalling |volume=69 |pages=96–102 |doi=10.1016/j.ceb.2020.11.008 |pmid=33549848 |pmc=8058236 |issn=0955-0674}}</ref> For example, the refractory period in action potentials is primarily controlled by history. Absolute refraction period prevents a volted-gated sodium channel from activating or refiring after it has just fired.<ref>{{Cite book |title=Human physiology |date=1983 |publisher=Springer |isbn=978-3-540-11669-1 |editor-last=Schmidt |editor-first=Robert F. |location=Berlin Heidelberg New York |editor-last2=Thews |editor-first2=Gerhard}}</ref> This is because following the absolute refractory period, the neuron is less excitable due to hyperpolarization caused by potassium efflux. This molecular inhibitory feedback creates a memory for the neuron or cell, so that the neuron does not fire too soon. As time passes, the neuron or cell will slowly lose the memory of having fired and will begin to fire again. Thus, memory is time-dependent, which is important in maintaining homeostasis and regulating many different biological processes.

==== Biochemical systems: regulating the cell cycle in ''xenopus laevis'' egg extracts ====
Cells advancing through the cell cycle must make an irreversible commitment to mitosis, ensuring they do not revert to interphase before successfully segregating their chromosomes. A mathematical model of cell-cycle progression in cell-free egg extracts from frogs suggests that hysteresis in the molecular control system drives these irreversible transitions into and out of mitosis.<ref>{{Cite journal |last1=Chow |first1=Y. W. |last2=Pietranico |first2=R. |last3=Mukerji |first3=A. |date=1975-10-27 |title=Studies of oxygen binding energy to hemoglobin molecule |url=https://pubmed.ncbi.nlm.nih.gov/6 |journal=Biochemical and Biophysical Research Communications |volume=66 |issue=4 |pages=1424–1431 |doi=10.1016/0006-291x(75)90518-5 |issn=0006-291X |pmid=6}}</ref> Here, Cdc2 (Cyclin-dependent kinase 1 or CDK1) is responsible for mitotic entry and exit such that binding of cyclin B forms a complex called Maturation-Promoting Factor (MPF).<ref>{{Cite journal |last1=Hoffmann |first1=I. |last2=Clarke |first2=P. R. |last3=Marcote |first3=M. J. |last4=Karsenti |first4=E. |last5=Draetta |first5=G. |date=January 1993 |title=Phosphorylation and activation of human cdc25-C by cdc2--cyclin B and its involvement in the self-amplification of MPF at mitosis |journal=The EMBO Journal |volume=12 |issue=1 |pages=53–63 |doi=10.1002/j.1460-2075.1993.tb05631.x |issn=0261-4189 |pmid=8428594|pmc=413175 }}</ref> The activation threshold for mitotic entry was found to be between 32 and 40 nM cyclin B in the frog extracts while the inactivation threshold for exiting mitosis was lower, between 16 and 24 nM cyclin B. The higher threshold for mitotic entry compared to the lower threshold for mitotic exit indicates hysteresis, a hallmark of history-dependent behavior in the system. Concentrations between 24 and 32 nM cyclin B demonstrated bistability, where the system could exist in either interphase or mitosis, depending on its prior state (history). Though, the cell cycle is not completely irreversible, the difference in thresholds is enough for growth and survival of the cells.

Hysteric thresholds in biological systems are not definite and can be recalibrated. For example, unreplicated DNA or chromosomes inhibits Cdc25 phosphatase and maintains Wee1 kinase activity.<ref>{{Cite journal |last1=Perry |first1=Jennifer A. |last2=Kornbluth |first2=Sally |date=2007-05-04 |title=Cdc25 and Wee1: analogous opposites? |journal=Cell Division |language=en |volume=2 |pages=12 |doi=10.1186/1747-1028-2-12 |doi-access=free |pmc=1868713 |pmid=17480229}}</ref> This prevents the activation of Cyclin B-Cdc2, effectively raising the threshold for mitotic entry. As a result, the cell delays the transition to mitosis until replication is complete, ensuring genomic integrity. Other instances may be DNA damage and unattached chromosomes during the spindle assembly checkpoint.<ref>{{Cite journal |last1=Marniemi |first1=J. |last2=Parkki |first2=M. G. |date=1975-09-01 |title=Radiochemical assay of glutathione S-epoxide transferase and its enhancement by phenobarbital in rat liver in vivo |url=https://pubmed.ncbi.nlm.nih.gov/9 |journal=Biochemical Pharmacology |volume=24 |issue=17 |pages=1569–1572 |doi=10.1016/0006-2952(75)90080-5 |issn=0006-2952 |pmid=9}}</ref>

==== 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
|last1 = Harfe
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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
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|doi =10.1016/j.cell.2004.07.024 |s2cid=16280983
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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. 
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| last8 = Rubenstein | first8 = J. L. 
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| last10 = Arnold | first10 = H. -H. 
| last11 = Jessell | first11 = T. M. 
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| 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.

===Immunology===

There is some evidence that [[T cell]]s exhibit hysteresis in that it takes a lower signal threshold to [[T cell activation|activate T cells]] that have been previously activated. [[Ras GTPase]] activation is required for downstream effector functions of activated T cells.<ref>{{Cite journal 
| last1 = Das | first1 = J. 
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| doi = 10.1016/j.cell.2008.11.051 
| title = Digital Signaling and Hysteresis Characterize Ras Activation in Lymphoid Cells 
| journal = Cell 
| volume = 136 
| issue = 2 
| pages = 337–351 
| year = 2009 
| pmid = 19167334 
| pmc =2662698 
}}</ref> Triggering of the T cell receptor induces high levels of Ras activation, which results in higher levels of GTP-bound (active) Ras at the cell surface. Since higher levels of active Ras have accumulated at the cell surface in T cells that have been previously stimulated by strong engagement of the T cell receptor, weaker subsequent T cell receptor signals received shortly afterwards will deliver the same level of activation due to the presence of higher levels of already activated Ras as compared to a naïve cell.

===Neuroscience===
{{See also|Refractory period (physiology)}}
The property by which some [[neuron]]s do not return to their basal conditions from a stimulated condition immediately after removal of the stimulus is an example of hysteresis.

===Neuropsychology===
{{Main|Context-dependent memory|State-dependent memory}}

[[Neuropsychology]], in exploring the [[neural correlates of consciousness]], interfaces with [[#Neuroscience|neuroscience]], although the complexity of the [[central nervous system]] is a challenge to its study (that is, its operation resists easy [[reductionism#In science|reduction]]). [[Context-dependent memory]] and [[state-dependent memory]] show hysteretic aspects of [[neurocognition]].

===Respiratory physiology===
Lung hysteresis is evident when observing the [[Lung compliance|compliance of a lung]] on inspiration versus expiration. The difference in [[Compliance (physiology)|compliance]] (Δvolume/Δpressure) is due to the additional energy required to overcome surface tension forces during inspiration to recruit and inflate additional alveoli.<ref>{{cite journal|last1=Escolar|first1=J. D.|first2=A. |last2=Escolar|title=Lung histeresis: a morphological view|journal=Histology and Histopathology Cellular and Molecular Biology|year=2004|volume=19|issue=1|pages=159&ndash;166|pmid=14702184|url=http://www.hh.um.es/pdf/Vol_19/19_1/Escolar-19-159-166-2004.pdf|access-date=1 March 2011}}</ref>

The [[transpulmonary pressure]] vs Volume curve of inhalation is different from the Pressure vs Volume curve of exhalation, the difference being described as hysteresis. Lung volume at any given pressure during inhalation is less than the lung volume at any given pressure during exhalation.<ref name="isbn0-7817-5152-7">{{cite book |first1=John B. |last1=West |title=Respiratory physiology: the essentials |publisher=[[Lippincott Williams & Wilkins]] |location=Hagerstown, MD |year=2005 |isbn=978-0-7817-5152-0}}</ref>

=== Voice and speech physiology ===
A hysteresis effect may be observed in voicing onset versus offset.<ref>{{Cite journal|title = A theoretical study of the hysteresis phenomenon at vocal fold oscillation onset–offset|journal = The Journal of the Acoustical Society of America|date = 1999|issn = 0001-4966|pages = 423–431|volume = 105|issue = 1|doi = 10.1121/1.424572|pmid = 9921668|first = Jorge C.|last = Lucero|bibcode = 1999ASAJ..105..423L }}</ref> The threshold value of the subglottal pressure required to start the vocal fold vibration is lower than the threshold value at which the vibration stops, when other parameters are kept constant. In utterances of vowel-voiceless consonant-vowel sequences during speech, the intraoral pressure is lower at the voice onset of the second vowel compared to the voice offset of the first vowel, the oral airflow is lower, the transglottal pressure is larger and the glottal width is smaller.

===Ecology and epidemiology===

Hysteresis is a commonly encountered phenomenon in ecology and epidemiology, where the observed equilibrium of a system can not be predicted solely based on environmental variables, but also requires knowledge of the system's past history. Notable examples include the theory of [[spruce budworm]] outbreaks and behavioral-effects on disease transmission.<ref>{{cite book
 |last=Strogatz
 |first=Stephen H.
 |author-link=Steven Strogatz
 |date=1994
 |title=Nonlinear Dynamics and Chaos
 |url=
 |location=
 |publisher=Perseus Books Publishing
 |pages= 73–79
 |isbn=0-7382-0453-6
}}</ref>

It is commonly examined in relation to [[critical transition]]s between ecosystem or community types in which dominant competitors or entire landscapes can change in a largely irreversible fashion.<ref>{{cite journal
| last1      = Sternberg
| first1     = Leonel Da Silveira Lobo
| date       = 21 December 2001
| title      = Savanna–forest hysteresis in the tropics
| url        = https://onlinelibrary.wiley.com/doi/abs/10.1046/j.1466-822X.2001.00243.x
| journal    = Global Ecology and Biogeography
| volume     = 10
| issue      = 4
| pages      = 369–378
| doi = 10.1046/j.1466-822X.2001.00243.x
| bibcode = 2001GloEB..10..369D
}}</ref><ref>{{cite journal
| last1      = Beisner
| first1     = BE
| last2      = Haydon
| first2     = DT
| last3      = Cuddington
| first3     = K
| date       = 1 September 2003
| title      = Alternative stable states in ecology
| journal    = Frontiers in Ecology and the Environment
| volume     = 1
| issue      = 7
| pages      = 376–382
| doi        = 10.2307/3868190
| jstor = 3868190
| doi-access= free
}}</ref>