Bistability
Encyclopedia
Bistability is a fundamental phenomenon in nature. Something that is bistable can be resting in either of two states. These rest states need not be symmetric with respect to stored energy. The defining characteristic of bistability is simply that two stable states (minima) are separated by a peak (maximum).
In physics, for an ensemble of particles, the bistability comes from the fact that its free energy
has three critical point
s. Two of them are minima and the last is a maximum. By mathematical arguments, the maximum must lie between the two minima. By default, the system state will be in either of the minima states, because that corresponds to the state of lowest energy. The maximum can be visualised as a barrier.
A transition from one state of minimal free energy requires some form of activation energy to penetrate the barrier (compare activation energy
and Arrhenius equation
for the chemical case). After the barrier has been reached, the system will relax into the next state of lowest energy again. The time it takes is usually attributed the relaxation time
. There might be uncertainty as to which state will be the new one, but it is often well defined in the situation.
Optical bistability
is an attribute of certain optical devices where two resonant transmissions states are possible and stable, dependent on the input.
progression, cellular differentiation
, and apoptosis
. It is also involved in loss of cellular homeostasis associated with early events in cancer
onset and in prion
diseases as well as in the origin of new species (speciation
).
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 links output signals to their input signals and have been noted to be an important regulatory motif in 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 Xenopus oocyte maturation, mammalian calcium signal transduction, and polarity in budding yeast, incorporate temporal (slow and fast) positive feedback loops, or more than one feedback loop that occurs at different times. By having two different temporal positive feedback loops or “dual-time switches” allows for (a) increased regulation: two switches that have independent changeable activation and deactivation times; and (b) linked feedback loops on multiple timescales can filter noise.
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 of this in cell biology is that activated CDK1 (Cyclin Dependent Kinase 1) activates is activator Cdc25 while at the same time inactivating its inactivator, Wee1, 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.
Bistability has also been described in the embryonic development of Drosophila melanogaster (the fruit fly). Examples are anterior-posterior and dorso-ventral axis formation and eye development .
A prime example of bistability in biological systems is that of Sonic hedgehog (Shh), a transcription factor of Drosophila, 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. gli1 and gli2 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 negative feedback 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.
Bistability can only arise in biological and chemical systems if three necessary conditions are fulfilled: positive feedback
, a mechanism to filter out small stimuli and a mechanism to prevent explosions.
Bistable chemical systems have been studied extensively to analyse relaxation kinetics, non-equilibrium thermodynamics
, stochastic resonance
, as well as climate change
.
Bistability is often accompanied by hysteresis
. On a population level, if many realisations of a bistable system are considered (e.g. many bistable cells (speciation
)), one typically observes bimodal distribution
s.
.
As an example of a common over-centre device, a ratchet
goes over centre as it is turned in the forward direction. In this case, "over centre" refers to the ratchet being stable and "locked" in a given position until clicked forward again; it has nothing to do with the ratchet being unable to turn in the reverse direction. Position "1" and position "2" in the figure above could be read as "current tooth" and "next tooth."
In physics, for an ensemble of particles, the bistability comes from the fact that its free energy
Thermodynamic free energy
The thermodynamic free energy is the amount of work that a thermodynamic system can perform. The concept is useful in the thermodynamics of chemical or thermal processes in engineering and science. The free energy is the internal energy of a system less the amount of energy that cannot be used to...
has three critical point
Critical point (thermodynamics)
In physical chemistry, thermodynamics, chemistry and condensed matter physics, a critical point, also called a critical state, specifies the conditions at which a phase boundary ceases to exist...
s. Two of them are minima and the last is a maximum. By mathematical arguments, the maximum must lie between the two minima. By default, the system state will be in either of the minima states, because that corresponds to the state of lowest energy. The maximum can be visualised as a barrier.
A transition from one state of minimal free energy requires some form of activation energy to penetrate the barrier (compare activation energy
Activation energy
In chemistry, activation energy is a term introduced in 1889 by the Swedish scientist Svante Arrhenius that is defined as the energy that must be overcome in order for a chemical reaction to occur. Activation energy may also be defined as the minimum energy required to start a chemical reaction...
and Arrhenius equation
Arrhenius equation
The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of the reaction rate constant, and therefore, rate of a chemical reaction. The equation was first proposed by the Dutch chemist J. H. van 't Hoff in 1884; five years later in 1889, the Swedish...
for the chemical case). After the barrier has been reached, the system will relax into the next state of lowest energy again. The time it takes is usually attributed the relaxation time
Relaxation time
In the physical sciences, relaxation usually means the return of a perturbed system into equilibrium.Each relaxation process can be characterized by a relaxation time τ...
. There might be uncertainty as to which state will be the new one, but it is often well defined in the situation.
Optical bistability
Optical bistability
In optics, optical bistability is an attribute of certain optical devices where two resonant transmissions states are possible and stable, dependent on the input. Optical devices with a feedback mechanism, e.g. a laser, provide two methods of achieving bistability.*Absorptive bistability utilizes...
is an attribute of certain optical devices where two resonant transmissions states are possible and stable, dependent on the input.
In biological and chemical systems
Bistability is key for understanding basic phenomena of cellular functioning, such as decision-making processes in cell cycleCell cycle
The cell cycle, or cell-division cycle, is the series of events that takes place in a cell leading to its division and duplication . In cells without a nucleus , the cell cycle occurs via a process termed binary fission...
progression, cellular differentiation
Cellular differentiation
In developmental biology, cellular differentiation is the process by which a less specialized cell becomes a more specialized cell type. Differentiation occurs numerous times during the development of a multicellular organism as the organism changes from a simple zygote to a complex system of...
, and apoptosis
Apoptosis
Apoptosis is the process of programmed cell death that may occur in multicellular organisms. Biochemical events lead to characteristic cell changes and death. These changes include blebbing, cell shrinkage, nuclear fragmentation, chromatin condensation, and chromosomal DNA fragmentation...
. It is also involved in loss of cellular homeostasis associated with early events in cancer
Cancer
Cancer , known medically as a malignant neoplasm, is a large group of different diseases, all involving unregulated cell growth. In cancer, cells divide and grow uncontrollably, forming malignant tumors, and invade nearby parts of the body. The cancer may also spread to more distant parts of the...
onset and in prion
Prion
A prion is an infectious agent composed of protein in a misfolded form. This is in contrast to all other known infectious agents which must contain nucleic acids . The word prion, coined in 1982 by Stanley B. Prusiner, is a portmanteau derived from the words protein and infection...
diseases as well as in the origin of new species (speciation
Speciation
Speciation is the evolutionary process by which new biological species arise. The biologist Orator F. Cook seems to have been the first to coin the term 'speciation' for the splitting of lineages or 'cladogenesis,' as opposed to 'anagenesis' or 'phyletic evolution' occurring within lineages...
).
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 links output signals to their input signals and have been noted to be an important regulatory motif in 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 Xenopus oocyte maturation, mammalian calcium signal transduction, and polarity in budding yeast, incorporate temporal (slow and fast) positive feedback loops, or more than one feedback loop that occurs at different times. By having two different temporal positive feedback loops or “dual-time switches” allows for (a) increased regulation: two switches that have independent changeable activation and deactivation times; and (b) linked feedback loops on multiple timescales can filter noise.
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 of this in cell biology is that activated CDK1 (Cyclin Dependent Kinase 1) activates is activator Cdc25 while at the same time inactivating its inactivator, Wee1, 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.
Bistability has also been described in the embryonic development of Drosophila melanogaster (the fruit fly). Examples are anterior-posterior and dorso-ventral axis formation and eye development .
A prime example of bistability in biological systems is that of Sonic hedgehog (Shh), a transcription factor of Drosophila, 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. gli1 and gli2 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 negative feedback 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.
Bistability can only arise in biological and chemical systems if three necessary conditions are fulfilled: positive feedback
Feedback
Feedback describes the situation when output from an event or phenomenon in the past will influence an occurrence or occurrences of the same Feedback describes the situation when output from (or information about the result of) an event or phenomenon in the past will influence an occurrence or...
, a mechanism to filter out small stimuli and a mechanism to prevent explosions.
Bistable chemical systems have been studied extensively to analyse relaxation kinetics, non-equilibrium thermodynamics
Non-equilibrium thermodynamics
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium; for they are changing or can be triggered to change over time, and are continuously and discontinuously...
, stochastic resonance
Stochastic resonance
Stochastic resonance is a phenomenon that occurs in a threshold measurement system when an appropriate measure of information transfer is maximized in the presence of a non-zero level of stochastic input noise thereby lowering the response...
, as well as climate change
Climate change
Climate change is a significant and lasting change in the statistical distribution of weather patterns over periods ranging from decades to millions of years. It may be a change in average weather conditions or the distribution of events around that average...
.
Bistability is often accompanied by hysteresis
Hysteresis
Hysteresis is the dependence of a system not just on its current environment but also on its past. This dependence arises because the system can be in more than one internal state. To predict its future evolution, either its internal state or its history must be known. If a given input alternately...
. On a population level, if many realisations of a bistable system are considered (e.g. many bistable cells (speciation
Speciation
Speciation is the evolutionary process by which new biological species arise. The biologist Orator F. Cook seems to have been the first to coin the term 'speciation' for the splitting of lineages or 'cladogenesis,' as opposed to 'anagenesis' or 'phyletic evolution' occurring within lineages...
)), one typically observes bimodal distribution
Bimodal distribution
In statistics, a bimodal distribution is a continuous probability distribution with two different modes. These appear as distinct peaks in the probability density function, as shown in Figure 1....
s.
In mechanical systems
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. An especially common method of achieving an "over centre" action is to use a springSpring (device)
A spring is an elastic object used to store mechanical energy. Springs are usually made out of spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication...
.
As an example of a common over-centre device, a ratchet
Ratchet (device)
A ratchet is a device that allows continuous linear or rotary motion in only one direction while preventing motion in the opposite direction. Because most socket wrenches today use ratcheting handles, the term "ratchet" alone is often used to refer to a ratcheting wrench, and the terms "ratchet"...
goes over centre as it is turned in the forward direction. In this case, "over centre" refers to the ratchet being stable and "locked" in a given position until clicked forward again; it has nothing to do with the ratchet being unable to turn in the reverse direction. Position "1" and position "2" in the figure above could be read as "current tooth" and "next tooth."
See also
- ferroelectric, ferromagnetic, hysteresisHysteresisHysteresis is the dependence of a system not just on its current environment but also on its past. This dependence arises because the system can be in more than one internal state. To predict its future evolution, either its internal state or its history must be known. If a given input alternately...
, bistable perception - astable multivibrator, monostable multivibrator.
- Schmitt trigger
- strong Allee effectAllee effectThe Allee effect is a phenomenon in biology characterized by a positive correlation between population density and the per capita population growth rate in very small populations.-Description:...
- Multistable perceptionMultistable perceptionMultistable perceptual phenomena are a form of perceptual phenomena in which there are unpredictable sequences of spontaneous subjective changes...
describes the spontaneous or exogenous alternation of different percepts in face of the same physical stimulusStimulus (physiology)In physiology, a stimulus is a detectable change in the internal or external environment. The ability of an organism or organ to respond to external stimuli is called sensitivity....
.
- Interferometric modulator displayInterferometric modulator displayInterferometric modulator display is a technology used in electronic visual displays that can create various colors via interference of reflected light...
, a bistable reflective display technology found in mirasol displays by QualcommQualcommQualcomm is an American global telecommunication corporation that designs, manufactures and markets digital wireless telecommunications products and services based on its code division multiple access technology and other technologies. Headquartered in San Diego, CA, USA...
External links
- http://www.answers.com/topic/optical-bistability
- BiStable Reed Sensor