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1178:(Shh), a secreted signaling molecule, which plays a critical role in development. Shh functions in diverse processes in development, including patterning limb bud tissue differentiation. The Shh signaling network behaves as a bistable switch, allowing the cell to abruptly switch states at precise Shh concentrations.
1279:
is an elaboration—a multi-stable "over center" system used to create irreversible motion. The pawl goes over center as it is turned in the forward direction. In this case, "over center" refers to the ratchet being stable and "locked" in a given position until clicked forward again; it has nothing to
1252:
Bistability as applied in the design of mechanical systems is more commonly said to be "over centre"—that is, work is done on the system to move it just past the peak, at which point the mechanism goes "over centre" to its secondary stable position. The result is a toggle-type action- work applied to
1159:
Bistability can be modified to be more robust and to tolerate significant changes in concentrations of reactants, while still maintaining its "switch-like" character. Feedback on both the activator of a system and inhibitor make the system able to tolerate a wide range of concentrations. An example
234:
is an attribute of certain optical devices where two resonant transmissions states are possible and stable, dependent on the input. Bistability can also arise in biochemical systems, where it creates digital, switch-like outputs from the constituent chemical concentrations and activities. It is often
1021:
gives rise to a pair of new fixed points emerging, one stable and the other unstable, at a critical value of the parameter. The unstable solution can then form another saddle-node bifurcation with the initial stable solution at a higher value of the parameter, leaving only the higher fixed solution.
1012:
oocyte maturation, mammalian calcium signal transduction, and polarity in budding yeast, incorporate multiple positive feedback loops with different time scales (slow and fast). Having multiple linked positive feedback loops with different time scales ("dual-time switches") allows for (a) increased
1007:
Bistability can be generated by a positive feedback loop with an ultrasensitive regulatory step. Positive feedback loops, such as the simple X activates Y and Y activates X motif, essentially link output signals to their input signals and have been noted to be an important regulatory motif in
1016:
Bistability can also arise in a biochemical system only for a particular range of parameter values, where the parameter can often be interpreted as the strength of the feedback. In several typical examples, the system has only one stable fixed point at low values of the parameter. A
153:. The switch lever is designed to rest in the "on" or "off" position, but not between the two. Bistable behavior can occur in mechanical linkages, electronic circuits, nonlinear optical systems, chemical reactions, and physiological and biological systems.
172:, an unstable equilibrium point, must lie between the two minima. At rest, a particle will be in one of the minimum equilibrium positions, because that corresponds to the state of lowest energy. The maximum can be visualized as a barrier between them.
1271:
An even more common example of an over-center device is an ordinary electric wall switch. These switches are often designed to snap firmly into the "on" or "off" position once the toggle handle has been moved a certain distance past the center-point.
1191:
loop wherein the Gli transcription factors activate the enhanced transcription of a repressor (Ptc). This signaling network illustrates the simultaneous positive and negative feedback loops whose exquisite sensitivity helps create a bistable switch.
1558:
to show practically how to see bistability captured by a saddle-node bifurcation diagram and the hysteresis behaviours when the bifurcation parameter is increased or decreased slowly over the tipping points and a protein gets turned 'On' or turned
1245:
1111:
94:. A surface shaped like this with two "low points" can act as a bistable system; a ball resting on the surface can only be stable at those two positions, such as balls marked "1" and "2". Between the two is a local maximum
1186:
transcription is activated by Shh, and their gene products act as transcriptional activators for their own expression and for targets downstream of Shh signaling. Simultaneously, the Shh signaling network is controlled by a
1259:
are a common method of achieving an "over centre" action. A spring attached to a simple two position ratchet-type mechanism can create a button or plunger that is clicked or toggled between two mechanical states. Many
1236:, which is bi-stability in the frequency space. Here trajectories can shoot between two stable limit cycles, and thus show similar characteristics as normal bi-stability when measured inside a Poincare section.
377:
1164:, thus allowing for progression of a cell into mitosis. Without this double feedback, the system would still be bistable, but would not be able to tolerate such a wide range of concentrations.
320:
875:
2226:
Nielsen; Dolganov, Nadia A.; Rasmussen, Thomas; Otto, Glen; Miller, Michael C.; Felt, Stephen A.; Torreilles, Stéphanie; Schoolnik, Gary K.; et al. (2010). Isberg, Ralph R. (ed.).
1008:
cellular signal transduction because positive feedback loops can create switches with an all-or-nothing decision. Studies have shown that numerous biological systems, such as
1022:
Thus, at values of the parameter between the two critical values, the system has two stable solutions. An example of a dynamical system that demonstrates similar features is
540:
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Three-dimensional invariant measure for cellular-differentiation featuring a two-stable mode. The axes denote cell counts for three types of cells: progenitor (
902:
1160:
of this in cell biology is that activated CDK1 (Cyclin
Dependent Kinase 1) activates its activator Cdc25 while at the same time inactivating its inactivator,
1363:
1028:
1497:
Ket Hing Chong; Sandhya
Samarasinghe; Don Kulasiri & Jie Zheng (2015). "Computational techniques in mathematical modelling of biological switches".
1229:. In an ensemble average over the population, the result may simply look like a smooth transition, thus showing the value of single-cell resolution.
1966:
Wang, Yu-Chiun; Ferguson, Edwin L. (10 March 2005). "Spatial bistability of Dpp–receptor interactions during
Drosophila dorsal–ventral patterning".
121:. A ball located at this point, ball 3, is in equilibrium but unstable; the slightest disturbance will cause it to move to one of the stable points.
2124:
Lai, K., M.J. Robertson, and D.V. Schaffer, The sonic hedgehog signaling system as a bistable genetic switch. Biophys J, 2004. 86(5): pp. 2748–57.
175:
A system can transition from one state of minimal energy to the other if it is given enough activation energy to penetrate the barrier (compare
1907:
Lopes, Francisco J. P.; Vieira, Fernando M. C.; Holloway, David M.; Bisch, Paulo M.; Spirov, Alexander V.; Ohler, Uwe (26 September 2008).
142:
1351:
1481:
1454:
1248:
A ratchet in action. Each tooth in the ratchet together with the regions to either side of it constitutes a simple bistable mechanism.
1419:
2134:
Elf, J.; Ehrenberg, M. (2004). "Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases".
168:, which are the stable equilibrium points. These rest states need not have equal potential energy. By mathematical arguments, a
1303:
1214:. In bistable spatially extended systems the onset of local correlations and propagation of traveling waves have been analyzed.
1211:
1203:
1315:
328:
1444:
2309:
1471:
2294:
1509:
1013:
regulation: two switches that have independent changeable activation and deactivation times; and (b) noise filtering.
1801:"Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems"
1748:
Ferrell JE Jr.; Machleder EM (1998). "The biochemical basis of an all-or-none cell fate switch in
Xenopus oocytes".
1195:
Bistability can only arise in biological and chemical systems if three necessary conditions are fulfilled: positive
980:
Bistability is key for understanding basic phenomena of cellular functioning, such as decision-making processes in
257:
1512:; Gardner, Timothy S.; Cantor, Charles R. (2000). "Construction of a genetic toggle switch in Escherichia coli".
815:
1253:
the system below a threshold sufficient to send it 'over center' results in no change to the mechanism's state.
1507:
The tutorial provides a simple example illustration of bistability using a synthetic toggle switch proposed in
985:
248:
1221:. On a population level, if many realisations of a bistable system are considered (e.g. many bistable cells (
1018:
203:
20:
2277:
1613:
2228:"A Bistable Switch and Anatomical Site Control Vibrio cholerae Virulence Gene Expression in the Intestine"
1571:"Solution of the chemical master equation by radial basis functions approximation with interface tracking"
1503:
For detailed techniques of mathematical modelling of bistability, see the tutorial by Chong et al. (2015)
878:
754:
approaches −1 over time. Thus, the dynamics are "bistable". The final state of the system can be either
219:
1171:(the fruit fly). Examples are anterior-posterior and dorso-ventral axis formation and eye development.
2078:"Modeling bistable cell-fate choices in the Drosophila eye: qualitative and quantitative perspectives"
2030:
1975:
1920:
1812:
1757:
1521:
1226:
1207:
211:
2278:"Snap bracelets from tape measures - Bistable structures | Experiments | Naked Scientists"
1265:
2314:
1404:
231:
195:
149:
can be resting in either of two states. An example of a mechanical device which is bistable is a
1339:
2159:
1999:
1781:
1545:
882:
487:
218:
of binary data, with one state representing a "0" and the other state a "1". It is also used in
180:
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519:
693:
629:
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2107:
2058:
1991:
1948:
1889:
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1602:
1537:
1477:
1450:
1188:
176:
1199:, a mechanism to filter out small stimuli and a mechanism to prevent increase without bound.
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2239:
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37:
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43:
1860:"Feedback regulation of opposing enzymes generates robust, all-or-none bistable responses"
1409:
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728:
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Bistable chemical systems have been studied extensively to analyze relaxation kinetics,
2254:
2227:
2203:
2178:
2102:
2077:
2053:
2018:
1943:
1909:"Spatial Bistability Generates hunchback Expression Sharpness in the Drosophila Embryo"
1908:
1884:
1859:
1711:
1684:
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1597:
1570:
1380:
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1139:
1119:
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939:
919:
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992:. It is also involved in loss of cellular homeostasis associated with early events in
2303:
1396:
1392:
1261:
223:
199:
169:
165:
24:
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1785:
183:
for the chemical case). After the barrier has been reached, assuming the system has
2017:
Umulis, D. M.; Mihaela Serpe; Michael B. O’Connor; Hans G. Othmer (1 August 2006).
2003:
1504:
1414:
1106:{\displaystyle {\frac {\mathrm {d} x}{\mathrm {d} t}}=r+{\frac {x^{5}}{1+x^{5}}}-x}
215:
150:
125:
1549:
2244:
1933:
1769:
32:
1645:
1875:
1587:
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1244:
1222:
1218:
1001:
981:
236:
2076:
Graham, T. G. W.; Tabei, S. M. A.; Dinner, A. R.; Rebay, I. (22 June 2010).
2043:
2019:"Robust, bistable patterning of the dorsal surface of the Drosophila embryo"
1825:
989:
2263:
2212:
2194:
2155:
2111:
2062:
1995:
1952:
1893:
1844:
1720:
1701:
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1606:
1541:
812:
The appearance of a bistable region can be understood for the model system
2147:
1777:
1629:"Multistable switches and their role in cellular differentiation networks"
1738:
O. Brandman, J. E. Ferrell Jr., R. Li, T. Meyer, Science 310, 496 (2005).
1423:
1196:
207:
1987:
1422:, a bistable reflective display technology found in mirasol displays by
2093:
184:
2179:"Stochastic transitions in a bistable reaction system on the membrane"
1533:
993:
568:), while the other two points are stable. The direction of change of
1167:
Bistability has also been described in the embryonic development of
1280:
do with the ratchet being unable to turn in the reverse direction.
912:
1243:
997:
911:
690:
approaches 1 over time, but if the initial condition is negative (
187:, it will relax into the other minimum state in a time called the
124:
31:
1174:
A prime example of bistability in biological systems is that of
1161:
1554:. The tutorial also uses the dynamical system software XPPAUT
325:
This system describes a ball rolling down a curve with shape
2177:
Kochanczyk, M.; Jaruszewicz, J.; Lipniacki, T. (July 2013).
1383:– the generalized case of more than two stable points
1268:
retractable pens employ this type of bistable mechanism.
1734:
1732:
1730:
1685:"The smallest chemical reaction system with bistability"
16:
Quality of a system having two stable equilibrium states
1799:
Angeli, David; Ferrell, JE; Sontag, Eduardo D (2003).
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1031:
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372:{\displaystyle {\frac {y^{4}}{4}}-{\frac {y^{2}}{2}}}
331:
260:
206:, a circuit which is a fundamental building block of
100:
73:
46:
1446:
Academic Press
Dictionary of Science and Technology
976:). Pro-osteoblast stimulus promotes P→O transition.
1148:
1128:
1105:
1000:diseases as well as in the origin of new species (
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1627:Ghaffarizadeh A, Flann NS, Podgorski GJ (2014).
1505:http://www.mssanz.org.au/modsim2015/C2/chong.pdf
202:data. It is the essential characteristic of the
160:field, bistability stems from the fact that the
2023:Proceedings of the National Academy of Sciences
1569:Kryven, I.; Röblitz, S.; Schütte, Ch. (2015).
40:of a bistable system; it has two local minima
1473:Advanced Quantum Mechanics: A Practical Guide
1449:. Gulf Professional publishing. p. 267.
8:
315:{\displaystyle {\frac {dy}{dt}}=y(1-y^{2}).}
1556:http://www.math.pitt.edu/~bard/xpp/xpp.html
1476:. Cambridge University Press. p. 291.
1232:A specific type of instability is known as
870:{\displaystyle {\frac {dy}{dt}}=y(r-y^{2})}
597:over time depends on the initial condition
251:, one of the simplest bistable systems is
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626:. If the initial condition is positive (
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1470:Nazarov, Yuli V.; Danon, Jeroen (2013).
1435:
1287:
1156:is the parameter, acting as the input.
809:, depending on the initial conditions.
2183:Journal of the Royal Society Interface
7:
1217:Bistability is often accompanied by
379:, and has three equilibrium points:
214:. A bistable device can store one
1046:
1036:
908:In biological and chemical systems
129:Light switch, a bistable mechanism
14:
1420:Interferometric modulator display
1612:
1362:
1350:
1338:
1326:
1314:
1302:
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877:which undergoes a supercritical
247:In the mathematical language of
1443:Morris, Christopher G. (1992).
1204:non-equilibrium thermodynamics
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194:Bistability is widely used in
1:
2245:10.1371/journal.ppat.1001102
1934:10.1371/journal.pcbi.1000184
1770:10.1126/science.280.5365.895
1357:Safety hammer of a revolver
1225:)), one typically observes
2331:
1913:PLOS Computational Biology
1646:10.1186/1471-2105-15-s7-s7
535:{\displaystyle y\approx 0}
18:
1876:10.1016/j.cub.2008.02.035
1588:10.1186/s12918-015-0210-y
718:{\displaystyle y(0)<0}
654:{\displaystyle y(0)>0}
143:stable equilibrium states
141:means the system has two
986:cellular differentiation
249:dynamic systems analysis
2044:10.1073/pnas.0510398103
1858:Ferrell JE Jr. (2008).
1826:10.1073/pnas.0308265100
1297:An animal foothold trap
1169:Drosophila melanogaster
1019:saddle-node bifurcation
21:Flip-flop (electronics)
2195:10.1098/rsif.2013.0151
1702:10.1186/1752-0509-3-90
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243:Mathematical modelling
220:relaxation oscillators
130:
122:
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88:
61:
1247:
1240:In mechanical systems
1227:bimodal distributions
1151:
1131:
1108:
971:
951:
931:
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883:bifurcation parameter
879:pitchfork bifurcation
872:
804:
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749:
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661:), then the solution
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542:will not converge to
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114:{\displaystyle x_{3}}
89:
87:{\displaystyle x_{2}}
62:
60:{\displaystyle x_{1}}
35:
19:For electronics, see
2295:BiStable Reed Sensor
1208:stochastic resonance
1140:
1120:
1029:
960:
956:), and chondrocyte (
940:
920:
888:
816:
802:{\displaystyle y=-1}
784:
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747:{\displaystyle y(t)}
729:
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683:{\displaystyle y(t)}
665:
630:
619:{\displaystyle y(0)}
601:
590:{\displaystyle y(t)}
572:
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520:
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453:{\displaystyle y=-1}
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212:semiconductor memory
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71:
44:
2310:Digital electronics
2148:10.1049/sb:20045021
2035:2006PNAS..10311613U
2029:(31): 11613–11618.
1988:10.1038/nature03318
1980:2005Natur.434..229W
1925:2008PLSCB...4E0184L
1817:2004PNAS..101.1822A
1762:1998Sci...280..895F
1689:BMC Systems Biology
1683:Wilhelm, T (2009).
1575:BMC Systems Biology
1526:2000Natur.403..339G
1415:strong Allee effect
1405:bistable perception
1136:is the output, and
773:{\displaystyle y=1}
561:{\displaystyle y=0}
509:{\displaystyle y=0}
479:{\displaystyle y=0}
460:. The middle point
424:{\displaystyle y=0}
398:{\displaystyle y=1}
232:Optical bistability
196:digital electronics
2094:10.1242/dev.044826
1633:BMC Bioinformatics
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158:conservative force
147:bistable structure
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84:
57:
2088:(14): 2265–2278.
1974:(7030): 229–234.
1510:Collins, James J.
1189:negative feedback
1149:{\displaystyle r}
1129:{\displaystyle x}
1095:
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969:{\displaystyle x}
949:{\displaystyle y}
929:{\displaystyle z}
897:{\displaystyle r}
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2136:Systems Biology
2133:
2132:
2128:
2123:
2119:
2075:
2074:
2070:
2016:
2015:
2011:
1965:
1964:
1960:
1919:(9): e1000184.
1906:
1905:
1901:
1864:Current Biology
1857:
1856:
1852:
1798:
1797:
1793:
1756:(5365): 895–8.
1747:
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1410:Schmitt trigger
1377:
1370:
1367:
1358:
1355:
1346:
1343:
1334:
1331:
1322:
1321:A toggle switch
1319:
1310:
1309:A slap bracelet
1307:
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1138:
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1118:
1117:
1084:
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1067:
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1027:
1026:
958:
957:
938:
937:
936:), osteoblast (
918:
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910:
886:
885:
854:
829:
821:
814:
813:
782:
781:
756:
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727:
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692:
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663:
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628:
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492:
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407:
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381:
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354:
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327:
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296:
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256:
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228:Schmitt trigger
189:relaxation time
101:
96:
95:
74:
69:
68:
47:
42:
41:
36:A graph of the
28:
17:
12:
11:
5:
2328:
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2289:External links
2287:
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2283:
2269:
2232:PLOS Pathogens
2218:
2169:
2142:(2): 230–236.
2126:
2117:
2068:
2009:
1958:
1899:
1850:
1791:
1740:
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1489:
1483:978-1139619028
1482:
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1456:978-0122004001
1455:
1434:
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1431:
1428:
1427:
1426:
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1407:
1390:
1384:
1381:Multistability
1376:
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1212:climate change
1176:Sonic hedgehog
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516:is stable but
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277:
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244:
241:
224:multivibrators
108:
104:
81:
77:
54:
50:
15:
13:
10:
9:
6:
4:
3:
2:
2327:
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2256:
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2214:
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1981:
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1837:
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1822:
1818:
1814:
1811:(7): 1822–7.
1810:
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1802:
1795:
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1787:
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1779:
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1397:ferromagnetic
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1393:ferroelectric
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1379:
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1374:
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1224:
1220:
1215:
1213:
1210:, as well as
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1200:
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1185:
1181:
1177:
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1170:
1165:
1163:
1157:
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1123:
1100:
1097:
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1078:
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1024:
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1011:
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996:onset and in
995:
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764:
761:
738:
732:
712:
709:
703:
697:
674:
668:
648:
645:
639:
633:
610:
604:
581:
575:
555:
552:
549:
529:
526:
523:
503:
500:
497:
489:
473:
470:
467:
447:
444:
441:
438:
418:
415:
412:
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389:
386:
364:
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355:
349:
344:
339:
335:
309:
301:
297:
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284:
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254:
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225:
221:
217:
213:
209:
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201:
197:
192:
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173:
171:
170:local maximum
167:
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148:
144:
140:
136:
127:
106:
102:
79:
75:
52:
48:
39:
34:
30:
26:
25:Multivibrator
22:
2272:
2235:
2231:
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2172:
2139:
2135:
2129:
2120:
2085:
2081:
2071:
2026:
2022:
2012:
1971:
1967:
1961:
1916:
1912:
1902:
1867:
1863:
1853:
1808:
1804:
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1636:
1632:
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1492:
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1179:
1173:
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1166:
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1015:
1009:
1006:
979:
811:
324:
246:
193:
174:
166:local minima
155:
151:light switch
146:
138:
132:
29:
2082:Development
1345:Mouse traps
1234:modehopping
139:bistability
2315:2 (number)
2304:Categories
1501:: 578–584.
1499:Modsim2015
1430:References
1401:hysteresis
1388:psychology
1333:A snapclip
1266:rollerball
1223:speciation
1219:hysteresis
1002:speciation
982:cell cycle
237:hysteresis
226:, and the
1581:(1): 67.
1262:ballpoint
1098:−
990:apoptosis
852:−
794:−
527:≈
445:−
350:−
294:−
208:computers
204:flip-flop
2264:20862321
2238:(9): 1.
2213:23635492
2164:17770042
2156:17051695
2112:20570936
2063:16864795
1996:15759004
1953:18818726
1894:18364225
1845:14766974
1786:34863795
1721:19737387
1665:25078021
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1542:10659857
1424:Qualcomm
1375:See also
1197:feedback
725:), then
164:has two
2255:2940755
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2103:2889600
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2031:Bibcode
2004:4415152
1976:Bibcode
1944:2527687
1921:Bibcode
1885:2832910
1813:Bibcode
1778:9572732
1758:Bibcode
1750:Science
1712:2749052
1656:4110729
1598:4599742
1522:Bibcode
1284:Gallery
1257:Springs
1010:Xenopus
185:damping
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2000:S2CID
1782:S2CID
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998:prion
881:with
156:In a
133:In a
2260:PMID
2209:PMID
2152:PMID
2108:PMID
2059:PMID
1992:PMID
1949:PMID
1890:PMID
1841:PMID
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1717:PMID
1661:PMID
1603:PMID
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