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{{more citations needed|date=September 2010}}

{{more citations needed|date=September 2010}}

A single chemical reaction is said to be autocatalytic if one of the reaction products is also a catalyst for the same or a coupled reaction. Such a reaction is called an autocatalytic reaction.

A single chemical reaction is said to be autocatalytic if one of the reaction products is also a catalyst for the same or a coupled reaction. Such a reaction is called an autocatalytic reaction.

==Chemical reactions==

==Chemical reactions化学反应==

<math> \alpha A + \beta B \rightleftharpoons \sigma S + \tau T</math>

<math> \alpha A + \beta B \rightleftharpoons \sigma S + \tau T</math>

 

===Chemical equilibrium===

===Chemical equilibrium化学平衡===

Here, the brackets indicate the concentration of the chemical species, in moles per liter, and k₊ and k₋ are rate constants.

Here, the brackets indicate the concentration of the chemical species, in moles per liter, and k₊ and k₋ are rate constants.

这里，括号表示化学物质的浓度，以摩尔/升为单位，k < sub > + </sub > 和 k < sub >-</sub > 是速率常数。

这里，括号表示化学物质的浓度，以摩尔/升为单位，k+和 k-是速率常数。

===Far from equilibrium===

===Far from equilibrium远离平衡===

===Autocatalytic reactions===

===Autocatalytic reactions自催化反应===

[[Image:Sigmoid curve for an autocatalytical reaction.jpg|256px|right|thumb|Sigmoid variation of product concentration in autocatalytic reactions]]

[[Image:Sigmoid curve for an autocatalytical reaction.jpg|256px|right|thumb|Sigmoid variation of product concentration in autocatalytic reactions]]

Autocatalytic reactions are those in which at least one of the products is a reactant. Perhaps the simplest autocatalytic reaction can be written   

Autocatalytic reactions are those in which at least one of the products is a reactant. Perhaps the simplest autocatalytic reaction can be written   

:<math>  A + B \rightleftharpoons 2B</math>

:<math>  A + B \rightleftharpoons 2B</math>

The graph for these equations is a sigmoid curve (specifically a logistic function), which is typical for autocatalytic reactions: these chemical reactions proceed slowly at the start (the induction period) because there is little catalyst present, the rate of reaction increases progressively as the reaction proceeds as the amount of catalyst increases and then it again slows down as the reactant concentration decreases. If the concentration of a reactant or product in an experiment follows a sigmoid curve, the reaction may be autocatalytic.

The graph for these equations is a sigmoid curve (specifically a logistic function), which is typical for autocatalytic reactions: these chemical reactions proceed slowly at the start (the induction period) because there is little catalyst present, the rate of reaction increases progressively as the reaction proceeds as the amount of catalyst increases and then it again slows down as the reactant concentration decreases. If the concentration of a reactant or product in an experiment follows a sigmoid curve, the reaction may be autocatalytic.

:<math>{d \over dt}[ B ] = + k_+ [ A ] [B ]  -k_{-} [B ]^2 \,</math>.

:<math>{d \over dt}[ B ] = + k_+ [ A ] [B ]  -k_{-} [B ]^2 \,</math>.

These kinetic equations apply for example to the acid-catalyzed hydrolysis of some esters to carboxylic acids and alcohols. In the hurricane example, hurricanes are formed from unequal heating within the atmosphere. The Earth's atmosphere is then far from thermal equilibrium. The order of the Earth's atmosphere increases, but at the expense of the order of the sun. The sun is becoming more disorderly as it ages and throws off light and material to the rest of the universe. The total disorder of the sun and the earth increases despite the fact that orderly hurricanes are generated on earth.

These kinetic equations apply for example to the acid-catalyzed hydrolysis of some esters to carboxylic acids and alcohols. In the hurricane example, hurricanes are formed from unequal heating within the atmosphere. The Earth's atmosphere is then far from thermal equilibrium. The order of the Earth's atmosphere increases, but at the expense of the order of the sun. The sun is becoming more disorderly as it ages and throws off light and material to the rest of the universe. The total disorder of the sun and the earth increases despite the fact that orderly hurricanes are generated on earth.

This reaction is one in which a molecule of species A interacts with a molecule of species B. The A molecule is converted into a B molecule. The final product consists of the original B molecule plus the B molecule created in the reaction.

This reaction is one in which a molecule of species A interacts with a molecule of species B. The A molecule is converted into a B molecule. The final product consists of the original B molecule plus the B molecule created in the reaction.

A chemical reaction cannot oscillate about a position of final equilibrium because the second law of thermodynamics requires that a thermodynamic system approach equilibrium and not recede from it. For a closed system at constant temperature and pressure, the Gibbs free energy must decrease continuously and not oscillate. However it is possible that the concentrations of some reaction intermediates oscillate, and also that the rate of formation of products oscillates.

A chemical reaction cannot oscillate about a position of final equilibrium because the second law of thermodynamics requires that a thermodynamic system approach equilibrium and not recede from it. For a closed system at constant temperature and pressure, the Gibbs free energy must decrease continuously and not oscillate. However it is possible that the concentrations of some reaction intermediates oscillate, and also that the rate of formation of products oscillates.

方程[同构于捕食-食饵模型和双反应自催化模型。在这个例子中，狒狒和猎豹在自动催化反应中相当于两种不同的化学物种 x 和 y

方程[同构于捕食-食饵模型和双反应自催化模型。在这个例子中，狒狒和猎豹在自动催化反应中相当于两种不同的化学物种 x 和 y

==Creation of order==

==Creation of order秩序创立==

Consider a coupled set of two autocatalytic reactions in which the concentration of one of the reactants A is much larger than its equilibrium value. In this case, the forward reaction rate is so much larger than the reverse rates that we can neglect the reverse rates.

Consider a coupled set of two autocatalytic reactions in which the concentration of one of the reactants A is much larger than its equilibrium value. In this case, the forward reaction rate is so much larger than the reverse rates that we can neglect the reverse rates.

===Background===

===Background背景===

<math> A + X \rightarrow 2X</math>

<math> A + X \rightarrow 2X</math>

The [[second law of thermodynamics]] states that the disorder ([[entropy]]) of a physical or chemical system and its surroundings (a [[closed system]]) must increase with time. Systems left to themselves become increasingly [[random]], and orderly energy of a system like uniform motion degrades eventually to the random motion of particles in a [[heat bath]].

The [[second law of thermodynamics]] states that the disorder ([[entropy]]) of a physical or chemical system and its surroundings (a [[closed system]]) must increase with time. Systems left to themselves become increasingly [[random]], and orderly energy of a system like uniform motion degrades eventually to the random motion of particles in a [[heat bath]].

 

<math> X + Y \rightarrow 2Y</math>

<math> X + Y \rightarrow 2Y</math>

There are, however, many instances in which physical systems spontaneously become [[emergence|emergent]] or orderly. For example, despite the destruction they cause, [[hurricane]]s have a very orderly [[vortex]] motion when compared to the random motion of the air molecules in a closed room. Even more spectacular is the order created by chemical systems; the most dramatic being the order associated with life.

There are, however, many instances in which physical systems spontaneously become [[emergence|emergent]] or orderly. For example, despite the destruction they cause, [[hurricane]]s have a very orderly [[vortex]] motion when compared to the random motion of the air molecules in a closed room. Even more spectacular is the order created by chemical systems; the most dramatic being the order associated with life.

 

<math> Y \rightarrow E</math>

<math> Y \rightarrow E</math>

This is consistent with the Second Law, which requires that the total disorder of a system ''and its surroundings'' must increase with time. Order can be created in a system by an even greater decrease in order of the system's surroundings.<ref>{{cite book | author=Ilya Prigogine | title=From Being to Becoming: Time and Complexity in the Physical Sciences | location=San Francisco | publisher=W. H. Freeman | year=1980 | isbn=978-0-7167-1107-0 | author-link=Ilya Prigogine | url-access=registration | url=https://archive.org/details/frombeingtobecom00ipri }}

This is consistent with the Second Law, which requires that the total disorder of a system ''and its surroundings'' must increase with time. Order can be created in a system by an even greater decrease in order of the system's surroundings.<ref>{{cite book | author=Ilya Prigogine | title=From Being to Becoming: Time and Complexity in the Physical Sciences | location=San Francisco | publisher=W. H. Freeman | year=1980 | isbn=978-0-7167-1107-0 | author-link=Ilya Prigogine | url-access=registration | url=https://archive.org/details/frombeingtobecom00ipri }}

 

with the rate equations

with the rate equations

</ref> In the hurricane example, hurricanes are formed from unequal heating within the atmosphere. The Earth's atmosphere is then far from [[thermal equilibrium]]. The order of the Earth's atmosphere increases, but at the expense of the order of the sun. The sun is becoming more disorderly as it ages and throws off light and material to the rest of the universe. The total disorder of the sun and the earth increases despite the fact that orderly hurricanes are generated on earth.

</ref> In the hurricane example, hurricanes are formed from unequal heating within the atmosphere. The Earth's atmosphere is then far from [[thermal equilibrium]]. The order of the Earth's atmosphere increases, but at the expense of the order of the sun. The sun is becoming more disorderly as it ages and throws off light and material to the rest of the universe. The total disorder of the sun and the earth increases despite the fact that orderly hurricanes are generated on earth.

 

<math>{d \over dt}[ X ] =  k_1 [ A ] [X ]  - k_{2} [X ][Y ] \,</math>

<math>{d \over dt}[ X ] =  k_1 [ A ] [X ]  - k_{2} [X ][Y ] \,</math>

A similar example exists for living chemical systems. The sun provides energy to green plants. The green plants are food for other living chemical systems. The energy absorbed by plants and converted into chemical energy generates a system on earth that is orderly and far from [[chemical equilibrium]]. Here, the difference from chemical equilibrium is determined by an excess of reactants over the equilibrium amount. Once again, order on earth is generated at the expense of entropy increase of the sun. The total entropy of the earth and the rest of the universe increases, consistent with the Second Law.

A similar example exists for living chemical systems. The sun provides energy to green plants. The green plants are food for other living chemical systems. The energy absorbed by plants and converted into chemical energy generates a system on earth that is orderly and far from [[chemical equilibrium]]. Here, the difference from chemical equilibrium is determined by an excess of reactants over the equilibrium amount. Once again, order on earth is generated at the expense of entropy increase of the sun. The total entropy of the earth and the rest of the universe increases, consistent with the Second Law.

 

<math>{d \over dt}[ Y ] =  k_2 [ X ] [Y ]  - k_{3} [Y ] \,</math>.

<math>{d \over dt}[ Y ] =  k_2 [ X ] [Y ]  - k_{3} [Y ] \,</math>.

Some autocatalytic reactions also generate order in a system at the expense of its surroundings. For example, ([[clock reactions]]) have [[reaction intermediate|intermediates]] whose concentrations oscillate in time, corresponding to temporal order. Other reactions generate spatial separation of [[chemical species]] corresponding to spatial order. More complex reactions are involved in [[metabolic pathway]]s and [[metabolic network]]s in [[biological systems]].

Some autocatalytic reactions also generate order in a system at the expense of its surroundings. For example, ([[clock reactions]]) have [[reaction intermediate|intermediates]] whose concentrations oscillate in time, corresponding to temporal order. Other reactions generate spatial separation of [[chemical species]] corresponding to spatial order. More complex reactions are involved in [[metabolic pathway]]s and [[metabolic network]]s in [[biological systems]].

 

Here, we have neglected the depletion of the reactant A, since its concentration is so large. The rate constants for the three reactions are <math>k_1</math>, <math>k_2</math>, and <math>k_3</math>, respectively.

Here, we have neglected the depletion of the reactant A, since its concentration is so large. The rate constants for the three reactions are <math>k_1</math>, <math>k_2</math>, and <math>k_3</math>, respectively.

在这里，我们忽略了反应物 a 的耗尽，因为它的浓度很大。这三个反应的速率常数分别是 < math > k _ 1 </math > ，< math > k _ 2 </math > ，和 < math > k _ 3 </math > 。

在这里，我们忽略了反应物 a 的耗尽，因为它的浓度很大。这三个反应的速率常数分别是k1,k2,k3 。

The transition to order as the distance from equilibrium increases is not usually continuous. Order typically appears abruptly. The threshold between the disorder of chemical equilibrium and order is known as a [[phase transition]]. The conditions for a phase transition can be determined with the mathematical machinery of [[non-equilibrium thermodynamics]].

The transition to order as the distance from equilibrium increases is not usually continuous. Order typically appears abruptly. The threshold between the disorder of chemical equilibrium and order is known as a [[phase transition]]. The conditions for a phase transition can be determined with the mathematical machinery of [[non-equilibrium thermodynamics]].

 

This system of rate equations is known as the Lotka–Volterra equation and is most closely associated with population dynamics in predator–prey relationships. This system of equations can yield oscillating concentrations of the reaction intermediates X and Y. The amplitude of the oscillations depends on the concentration of A (which decreases without oscillation). Such oscillations are a form of emergent temporal order that is not present in equilibrium.

This system of rate equations is known as the Lotka–Volterra equation and is most closely associated with population dynamics in predator–prey relationships. This system of equations can yield oscillating concentrations of the reaction intermediates X and Y. The amplitude of the oscillations depends on the concentration of A (which decreases without oscillation). Such oscillations are a form of emergent temporal order that is not present in equilibrium.

这个速率方程组被称为 Lotka-Volterra 方程，在捕食者-食饵关系中与族群动态最密切相关。这个方程组可以产生反应中间体 x 和 y 的振荡浓度。振荡的振幅取决于 a 的浓度(a 的浓度下降而没有振荡)。这种振荡是一种涌现的时间顺序，在平衡中不存在。

这个速率方程组被称为 Lotka-Volterra 方程，在捕食者-食饵关系中与族群动态最密切相关。这个方程组可以产生反应中间体 x 和 y 的振荡浓度。振荡的振幅取决于 a 的浓度(a 的浓度下降而没有振荡)。这种振荡是一种涌现的时间顺序，在平衡中不存在。

===Temporal order===

===Temporal order时间顺序===

A chemical reaction cannot oscillate about a position of final [[chemical equilibrium|equilibrium]] because the second law of thermodynamics requires that a [[thermodynamic system]] approach equilibrium and not recede from it. For a closed system at constant temperature and pressure, the [[Gibbs free energy]] must decrease continuously and not oscillate. However it is possible that the concentrations of some [[reaction intermediate]]s oscillate, and also that the ''rate'' of formation of products oscillates.<ref>Espenson, J.H. ''Chemical Kinetics and Reaction Mechanisms'' (2nd ed., McGraw-Hill 2002) p.190 {{ISBN|0-07-288362-6}}</ref>

A chemical reaction cannot oscillate about a position of final [[chemical equilibrium|equilibrium]] because the second law of thermodynamics requires that a [[thermodynamic system]] approach equilibrium and not recede from it. For a closed system at constant temperature and pressure, the [[Gibbs free energy]] must decrease continuously and not oscillate. However it is possible that the concentrations of some [[reaction intermediate]]s oscillate, and also that the ''rate'' of formation of products oscillates.<ref>Espenson, J.H. ''Chemical Kinetics and Reaction Mechanisms'' (2nd ed., McGraw-Hill 2002) p.190 {{ISBN|0-07-288362-6}}</ref>

 

====Idealized example: Lotka–Volterra equation理想化例子：Lotka–Volterra 等式====

====Idealized example: Lotka–Volterra equation====

Another example of a system that demonstrates temporal order is the Brusselator (see Prigogine reference). It is characterized by the reactions

Another example of a system that demonstrates temporal order is the Brusselator (see Prigogine reference). It is characterized by the reactions

Consider a coupled set of two autocatalytic reactions in which the concentration of one of the reactants A is much larger than its equilibrium value. In this case, the forward reaction rate is so much larger than the reverse rates that we can neglect the reverse rates.

Consider a coupled set of two autocatalytic reactions in which the concentration of one of the reactants A is much larger than its equilibrium value. In this case, the forward reaction rate is so much larger than the reverse rates that we can neglect the reverse rates.

 

<math> A \rightarrow X</math>

<math> A \rightarrow X</math>

The Brusselator in the unstable regime. A=1. B=2.5. X(0)=1. Y(0)=0. The system approaches a [[limit cycle. For B<1+A the system is stable and approaches a fixed point.]]

The Brusselator in the unstable regime. A=1. B=2.5. X(0)=1. Y(0)=0. The system approaches a [[limit cycle. For B<1+A the system is stable and approaches a fixed point.]]

不稳定政权中的布鲁塞尔人。1.2.5.X (0) = 1.Y (0) = 0.该系统接近[极限环]。对于 b < 1 + a，系统是稳定的，并且接近一个固定点。]

不稳定政权中的布鲁塞尔振子。 A=1. B=2.5. X(0)=1. Y(0)=0.该系统接近[极限环]。对于 b < 1 + a，系统是稳定的，并且接近一个固定点。]

The Brusselator has a fixed point at

The Brusselator has a fixed point at

====Another idealized example: Brusselator====

====Another idealized example: Brusselator另一个理想化模型：布鲁塞尔振子====

leading to an oscillation of the system. Unlike the Lotka-Volterra equation, the oscillations of the Brusselator do not depend on the amount of reactant present initially. Instead, after sufficient time, the oscillations approach a limit cycle.

leading to an oscillation of the system. Unlike the Lotka-Volterra equation, the oscillations of the Brusselator do not depend on the amount of reactant present initially. Instead, after sufficient time, the oscillations approach a limit cycle.

:<math>  X \rightarrow E</math>

:<math>  X \rightarrow E</math>

An idealized example of spatial spontaneous symmetry breaking is the case in which we have two boxes of material separated by a permeable membrane so that material can diffuse between the two boxes. It is assumed that identical Brusselators are in each box with nearly identical initial conditions. (see Prigogine reference)

An idealized example of spatial spontaneous symmetry breaking is the case in which we have two boxes of material separated by a permeable membrane so that material can diffuse between the two boxes. It is assumed that identical Brusselators are in each box with nearly identical initial conditions. (see Prigogine reference)

一个理想化的空间自发对称性破缺的例子是，我们有两个盒子的材料被一个可渗透的薄膜分开，这样材料可以在两个盒子之间扩散。我们假设在每个盒子中都有相同的布鲁塞尔子，并且具有几乎相同的初始条件。(见 Prigogine 参考文献)

一个理想化的空间自发对称性破缺的例子是，我们有两个盒子的材料被一个可渗透的薄膜分开，这样材料可以在两个盒子之间扩散。我们假设在每个盒子中都有相同的布鲁塞尔振子，并且具有几乎相同的初始条件。(见 Prigogine 参考文献)

If the system is initiated with the same conditions in each box, then a small fluctuation will lead to separation of materials between the two boxes. One box will have a predominance of X, and the other will have a predominance of Y.

If the system is initiated with the same conditions in each box, then a small fluctuation will lead to separation of materials between the two boxes. One box will have a predominance of X, and the other will have a predominance of Y.

如果系统启动时每个箱子的条件相同，那么一个小的波动将导致两个箱子之间的物料分离。一个盒子将具有 x 的优势，而另一个盒子将具有 y 的优势。

如果系统启动时每个盒子的条件相同，那么一个小的波动将导致两个盒子之间的物料分离。一个盒子将具有 x 的优势，而另一个盒子将具有 y 的优势。

:<math>[ Y ] =  {B \over A}    \,</math>.

:<math>[ Y ] =  {B \over A}    \,</math>.

The fixed point becomes unstable when

The fixed point becomes unstable when

 

Real examples of clock reactions are the Belousov–Zhabotinsky reaction (BZ reaction), the Briggs–Rauscher reaction, the Bray–Liebhafsky reaction and the iodine clock reaction. These are oscillatory reactions, and the concentration of products and reactants can be approximated in terms of damped oscillations.

Real examples of clock reactions are the Belousov–Zhabotinsky reaction (BZ reaction), the Briggs–Rauscher reaction, the Bray–Liebhafsky reaction and the iodine clock reaction. These are oscillatory reactions, and the concentration of products and reactants can be approximated in terms of damped oscillations.

===Spatial order===

===Spatial order空间秩序===

The details of the process are quite involved, however, a section of the process is autocatalyzed by phosphofructokinase (PFK). This portion of the process is responsible for oscillations in the pathway that lead to the process oscillating between an active and an inactive form. Thus, the autocatalytic reaction can modulate the process.

The details of the process are quite involved, however, a section of the process is autocatalyzed by phosphofructokinase (PFK). This portion of the process is responsible for oscillations in the pathway that lead to the process oscillating between an active and an inactive form. Thus, the autocatalytic reaction can modulate the process.

The initial amounts of reactants determine the distance from a chemical equilibrium of the system. The greater the initial concentrations the further the system is from equilibrium. As the initial concentration increases, an abrupt change in order occurs. This abrupt change is known as phase transition. At the phase transition, fluctuations in macroscopic quantities, such as chemical concentrations, increase as the system oscillates between the more ordered state (lower entropy, such as ice) and the more disordered state (higher entropy, such as liquid water). Also, at the phase transition, macroscopic equations, such as the rate equations, fail. Rate equations can be derived from microscopic considerations. The derivations typically rely on a mean field theory approximation to microscopic dynamical equations. Mean field theory breaks down in the presence of large fluctuations (see Mean field theory article for a discussion).  Therefore, since large fluctuations occur in the neighborhood of a phase transition, macroscopic equations, such as rate equations, fail. As the initial concentration increases further, the system settles into an ordered state in which fluctuations are again small. (see Prigogine reference)

The initial amounts of reactants determine the distance from a chemical equilibrium of the system. The greater the initial concentrations the further the system is from equilibrium. As the initial concentration increases, an abrupt change in order occurs. This abrupt change is known as phase transition. At the phase transition, fluctuations in macroscopic quantities, such as chemical concentrations, increase as the system oscillates between the more ordered state (lower entropy, such as ice) and the more disordered state (higher entropy, such as liquid water). Also, at the phase transition, macroscopic equations, such as the rate equations, fail. Rate equations can be derived from microscopic considerations. The derivations typically rely on a mean field theory approximation to microscopic dynamical equations. Mean field theory breaks down in the presence of large fluctuations (see Mean field theory article for a discussion).  Therefore, since large fluctuations occur in the neighborhood of a phase transition, macroscopic equations, such as rate equations, fail. As the initial concentration increases further, the system settles into an ordered state in which fluctuations are again small. (see Prigogine reference)

反应物的初始数量决定了反应体系到化学平衡的距离。初始浓度越大，系统离平衡越远。随着初始浓度的增加，有序发生突变。这种突然的变化称为相变。在相变过程中，宏观量(如化学浓度)的涨落会随着系统在更有序的状态(如冰)和更无序的状态(如液态水)之间振荡而增加。此外，在相变时，宏观方程，如速率方程，失败。速率方程可以从微观考虑推导出来。推导通常依赖于平均场理论对微观动力学方程的近似。在存在大的波动时，平均场理论崩溃了(见平均场理论文章的讨论)。因此，由于大的波动发生在附近的相变，宏观方程，如速率方程，失败。随着初始浓度的进一步增加，系统进入有序状态，波动再次变小。(见 Prigogine 参考文献)

反应物的初始量决定了与体系化学平衡的距离。初始浓度越大，系统离平衡越远。随着初始浓度的增加，顺序发生突变。这种突变被称为相变。在相变阶段，宏观量的波动，如化学浓度，随着系统在更有序的状态（低熵，如冰）和更无序的状态（更高的熵，如液态水）之间振荡而增加。同样，在相变过程中，宏观方程，如速率方程，会失效。速率方程可以从微观角度推导出来。推导通常依赖于对微观动力学方程的平均场理论近似。平均场理论在大波动的存在下会崩溃（见平均场理论文章的讨论）。因此，由于大的波动发生在相变附近，宏观方程，如速率方程，失败了。随着初始浓度的进一步增加，系统进入有序状态，在这种状态下波动又很小(见 Prigogine 参考文献)

:<math>{d \over dt}[ Y_2 ] =  [B ] [X_2 ] - [ X_2 ]^2 [Y_2 ]  + D_y\left( Y_1 - Y_2\right)  \,</math>

:<math>{d \over dt}[ Y_2 ] =  [B ] [X_2 ] - [ X_2 ]^2 [Y_2 ]  + D_y\left( Y_1 - Y_2\right)  \,</math>

==Real examples==

==Real examples实例==

In 1995 Stuart Kauffman proposed that life initially arose as autocatalytic chemical networks.

In 1995 Stuart Kauffman proposed that life initially arose as autocatalytic chemical networks.

British ethologist Richard Dawkins wrote about autocatalysis as a potential explanation for abiogenesis in his 2004 book The Ancestor's Tale.  He cites experiments performed by Julius Rebek and his colleagues at the Scripps Research Institute in California in which they combined amino adenosine and pentafluorophenyl ester with the autocatalyst amino adenosine triacid ester (AATE).  One system from the experiment contained variants of AATE which catalyzed the synthesis of themselves.  This experiment demonstrated the possibility that autocatalysts could exhibit competition within a population of entities with heredity, which could be interpreted as a rudimentary form of natural selection, and that certain environmental changes (such as irradiation) could alter the chemical structure of some of these self-replicating molecules (an analog for mutation) in such ways that could either boost or interfere with its ability to react, thus boosting or interfering with its ability to replicate and spread in the population.

British ethologist Richard Dawkins wrote about autocatalysis as a potential explanation for abiogenesis in his 2004 book The Ancestor's Tale.  He cites experiments performed by Julius Rebek and his colleagues at the Scripps Research Institute in California in which they combined amino adenosine and pentafluorophenyl ester with the autocatalyst amino adenosine triacid ester (AATE).  One system from the experiment contained variants of AATE which catalyzed the synthesis of themselves.  This experiment demonstrated the possibility that autocatalysts could exhibit competition within a population of entities with heredity, which could be interpreted as a rudimentary form of natural selection, and that certain environmental changes (such as irradiation) could alter the chemical structure of some of these self-replicating molecules (an analog for mutation) in such ways that could either boost or interfere with its ability to react, thus boosting or interfering with its ability to replicate and spread in the population.

英国动物行为学家理查德 · 道金斯在他2004年出版的《祖先的故事》一书中提到了自我催化作为自然发生的潜在解释。他引用了 Julius Rebek 和他的同事们在加利福尼亚斯克里普斯研究所进行的实验，他们将氨基腺苷和五氟苯酯与氨基腺苷三酸酯(AATE)结合在一起。实验中的一个系统包含了催化自身合成的 AATE 的变体。这项实验证明了这样一种可能性，即自动催化剂可以在具有遗传性的实体群体中展现竞争，这可以被解释为一种基本的自然选择形式，而且某些环境变化(如辐照)可以改变某些自我复制分子(变异的类似物)的化学结构，这种方式可以增强或干扰其反应能力，从而增强或干扰其复制和在群体中传播的能力。

英国动物行为学家 Richard Dawkins在他2004年出版的《祖先的故事》一书中提到了自我催化作为自然发生的潜在解释。他引用了 Julius Rebek 和他的同事们在加利福尼亚斯克里普斯研究所进行的实验，他们将氨基腺苷和五氟苯酯与氨基腺苷三酸酯(AATE)结合在一起。实验中的一个系统包含了催化自身合成的 AATE 的变体。这项实验证明了这样一种可能性，即自动催化剂可以在具有遗传性的实体群体中展现竞争，这可以被解释为一种基本的自然选择形式，而且某些环境变化(如辐照)可以改变某些自我复制分子(变异的类似物)的化学结构，这种方式可以增强或干扰其反应能力，从而增强或干扰其复制和在群体中传播的能力。

== Optics example ==

== Optics example光学实例 ==

Autocatalysis plays a major role in the processes of life.  Two researchers who have emphasized its role in the origins of life are Robert Ulanowicz  and Stuart Kauffman.

Autocatalysis plays a major role in the processes of life.  Two researchers who have emphasized its role in the origins of life are Robert Ulanowicz  and Stuart Kauffman.

Another autocatalytic system is one driven by light coupled to photo-polymerization reactions. In a process termed optical autocatalysis, positive feedback is created between light intensity and photo-polymerization rate, via polymerization-induced increases in the refractive index. Light's preference to occupy regions of higher refractive index results in leakage of light into regions of higher molecular weight, thereby amplifying the photo-chemical reaction. The positive feedback may be expressed as:<ref name=":0">{{Cite journal|last=Biria|first=Saeid|last2=Malley|first2=Phillip P. A.|last3=Kahan|first3=Tara F.|last4=Hosein|first4=Ian D.|date=2016-11-15|title=Optical Autocatalysis Establishes Novel Spatial Dynamics in Phase Separation of Polymer Blends during Photocuring|journal=ACS Macro Letters|volume=5|issue=11|pages=1237–1241|doi=10.1021/acsmacrolett.6b00659}}</ref>

Another autocatalytic system is one driven by light coupled to photo-polymerization reactions. In a process termed optical autocatalysis, positive feedback is created between light intensity and photo-polymerization rate, via polymerization-induced increases in the refractive index. Light's preference to occupy regions of higher refractive index results in leakage of light into regions of higher molecular weight, thereby amplifying the photo-chemical reaction. The positive feedback may be expressed as:<ref name=":0">{{Cite journal|last=Biria|first=Saeid|last2=Malley|first2=Phillip P. A.|last3=Kahan|first3=Tara F.|last4=Hosein|first4=Ian D.|date=2016-11-15|title=Optical Autocatalysis Establishes Novel Spatial Dynamics in Phase Separation of Polymer Blends during Photocuring|journal=ACS Macro Letters|volume=5|issue=11|pages=1237–1241|doi=10.1021/acsmacrolett.6b00659}}</ref>

Autocatalysis occurs in the initial transcripts of rRNA. The introns are capable of excising themselves by the process of two nucleophilic transesterification reactions. The RNA able to do this is sometimes referred to as a ribozyme.  Additionally, the citric acid cycle is an autocatalytic cycle run in reverse.

Autocatalysis occurs in the initial transcripts of rRNA. The introns are capable of excising themselves by the process of two nucleophilic transesterification reactions. The RNA able to do this is sometimes referred to as a ribozyme.  Additionally, the citric acid cycle is an autocatalytic cycle run in reverse.

自我催化发生在 rna 的最初转录本中。这些内含子能够通过两个亲核酯交换反应反应自我激活。能够做到这一点的 RNA 有时被称为核酶。此外，三羧酸循环是一种反向运行的自动催化循环。

自我催化发生在RNA的最初转录本中。这些内含子能够通过两个亲核酯交换反应反应自我激活。能够做到这一点的 RNA 有时被称为核酶。此外，三羧酸循环是一种反向运行的自动催化循环。

:<math>\text{polymerization rate} \to \text{molecular weight}/\text{refractive index} \to \text{intensity}</math>

:<math>\text{polymerization rate} \to \text{molecular weight}/\text{refractive index} \to \text{intensity}</math>

==Biological example==

==Biological example生物实例==

</ref> Glycolysis consists of the degradation of one molecule of glucose and the overall production of two molecules of [[Adenosine triphosphate|ATP]]. The process is therefore of great importance to the energetics of living cells. The global glycolysis reaction involves [[glucose]], [[Adenosine diphosphate|ADP]], [[Nicotinamide adenine dinucleotide|NAD]], [[Pyruvic acid|pyruvate]], [[Adenosine triphosphate|ATP]], and NADH.

</ref> Glycolysis consists of the degradation of one molecule of glucose and the overall production of two molecules of [[Adenosine triphosphate|ATP]]. The process is therefore of great importance to the energetics of living cells. The global glycolysis reaction involves [[glucose]], [[Adenosine diphosphate|ADP]], [[Nicotinamide adenine dinucleotide|NAD]], [[Pyruvic acid|pyruvate]], [[Adenosine triphosphate|ATP]], and NADH.

 

The details of the process are quite involved, however, a section of the process is autocatalyzed by [[phosphofructokinase]] (PFK). This portion of the process is responsible for oscillations in the pathway that lead to the process oscillating between an active and an inactive form. Thus, the autocatalytic reaction can modulate the process.

The details of the process are quite involved, however, a section of the process is autocatalyzed by [[phosphofructokinase]] (PFK). This portion of the process is responsible for oscillations in the pathway that lead to the process oscillating between an active and an inactive form. Thus, the autocatalytic reaction can modulate the process.

 

==Shape tailoring of thin layers薄层剪裁==

==Shape tailoring of thin layers==

It is possible to use the results from an autocatalytic reaction coupled with [[reaction–diffusion system]] theory to tailor the design of a thin layer. The autocatalytic process allows controlling the nonlinear behavior of the oxidation [[Front (physics)|front]], which is used to establish the initial geometry needed to generate the arbitrary final geometry.<ref>{{cite journal |last1=Alfaro-Bittner |first1=K. |last2=Rojas |first2=R.G. |last3=Lafleur |first3=G. |last4=Calvez |first4=S. |last5=Almuneau |first5=G. |last6=Clerc |first6=M.G. |last7=Barbay |first7=S. |title=Modeling the Lateral Wet Oxidation of into Arbitrary Mesa Geometries |journal=Physical Review Applied|date=22 April 2019|volume=11 |issue=4|page=044067|doi=10.1103/PhysRevApplied.11.044067|url=https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.11.044067}}</ref> It has been successfully done in the wet oxidation of <math>Al_xGa_{1-x}As</math> to obtain arbitrary shaped layers of <math>AlO_x</math>.

It is possible to use the results from an autocatalytic reaction coupled with [[reaction–diffusion system]] theory to tailor the design of a thin layer. The autocatalytic process allows controlling the nonlinear behavior of the oxidation [[Front (physics)|front]], which is used to establish the initial geometry needed to generate the arbitrary final geometry.<ref>{{cite journal |last1=Alfaro-Bittner |first1=K. |last2=Rojas |first2=R.G. |last3=Lafleur |first3=G. |last4=Calvez |first4=S. |last5=Almuneau |first5=G. |last6=Clerc |first6=M.G. |last7=Barbay |first7=S. |title=Modeling the Lateral Wet Oxidation of into Arbitrary Mesa Geometries |journal=Physical Review Applied|date=22 April 2019|volume=11 |issue=4|page=044067|doi=10.1103/PhysRevApplied.11.044067|url=https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.11.044067}}</ref> It has been successfully done in the wet oxidation of <math>Al_xGa_{1-x}As</math> to obtain arbitrary shaped layers of <math>AlO_x</math>.

 

==Phase transitions相变==

==Phase transitions==

The initial amounts of reactants determine the distance from a chemical equilibrium of the system. The greater the initial concentrations the further the system is from equilibrium. As the initial concentration increases, an abrupt change in [[entropy|order]] occurs. This abrupt change is known as [[phase transition]]. At the phase transition, fluctuations in macroscopic quantities, such as chemical concentrations, increase as the system oscillates between the more ordered state (lower entropy, such as ice) and the more disordered state (higher entropy, such as liquid water). Also, at the phase transition, macroscopic equations, such as the rate equations, fail. Rate equations can be derived from microscopic considerations. The derivations typically rely on a [[mean field theory]] approximation to microscopic dynamical equations. Mean field theory breaks down in the presence of large fluctuations (see [[Mean field theory]] article for a discussion).  Therefore, since large fluctuations occur in the neighborhood of a phase transition, macroscopic equations, such as rate equations, fail. As the initial concentration increases further, the system settles into an ordered state in which fluctuations are again small. (see Prigogine reference)

The initial amounts of reactants determine the distance from a chemical equilibrium of the system. The greater the initial concentrations the further the system is from equilibrium. As the initial concentration increases, an abrupt change in [[entropy|order]] occurs. This abrupt change is known as [[phase transition]]. At the phase transition, fluctuations in macroscopic quantities, such as chemical concentrations, increase as the system oscillates between the more ordered state (lower entropy, such as ice) and the more disordered state (higher entropy, such as liquid water). Also, at the phase transition, macroscopic equations, such as the rate equations, fail. Rate equations can be derived from microscopic considerations. The derivations typically rely on a [[mean field theory]] approximation to microscopic dynamical equations. Mean field theory breaks down in the presence of large fluctuations (see [[Mean field theory]] article for a discussion).  Therefore, since large fluctuations occur in the neighborhood of a phase transition, macroscopic equations, such as rate equations, fail. As the initial concentration increases further, the system settles into an ordered state in which fluctuations are again small. (see Prigogine reference)

 

==Asymmetric autocatalysis不对称自催化 ==

==Asymmetric autocatalysis==

Asymmetric autocatalysis occurs when the reaction product is [[chiral]] and thus acts as a chiral catalyst for its own production. Reactions of this type, such as the [[Soai reaction]], have the property that they can amplify a very small [[enantiomeric excess]] into a large one. This has been proposed as an important step in the origin of biological [[homochirality]].<ref name="Soai2001">{{cite journal|vauthors=Soai K, Sato I, Shibata T | title=Asymmetric autocatalysis and the origin of chiral homogeneity in organic compounds. | journal=The Chemical Record | year= 2001 | volume= 1 | issue= 4 | pages= 321–32 | pmid=11893072 | doi= 10.1002/tcr.1017| pmc= }}</ref>

Asymmetric autocatalysis occurs when the reaction product is [[chiral]] and thus acts as a chiral catalyst for its own production. Reactions of this type, such as the [[Soai reaction]], have the property that they can amplify a very small [[enantiomeric excess]] into a large one. This has been proposed as an important step in the origin of biological [[homochirality]].<ref name="Soai2001">{{cite journal|vauthors=Soai K, Sato I, Shibata T | title=Asymmetric autocatalysis and the origin of chiral homogeneity in organic compounds. | journal=The Chemical Record | year= 2001 | volume= 1 | issue= 4 | pages= 321–32 | pmid=11893072 | doi= 10.1002/tcr.1017| pmc= }}</ref>

 

== Role in origin of life生命起源中的角色 ==

== Role in origin of life ==

In 1995 [[Stuart Kauffman]] proposed that life initially arose as autocatalytic chemical networks.<ref>{{cite book|author=Stuart Kauffman|title=At Home in the Universe: The Search for the Laws of Self-Organization and Complexity|isbn=978-0-19-509599-9|publisher=Oxford University Press|year=1995|url-access=registration|url=https://archive.org/details/athomeinuniverse00kauf_0}}</ref>

In 1995 [[Stuart Kauffman]] proposed that life initially arose as autocatalytic chemical networks.<ref>{{cite book|author=Stuart Kauffman|title=At Home in the Universe: The Search for the Laws of Self-Organization and Complexity|isbn=978-0-19-509599-9|publisher=Oxford University Press|year=1995|url-access=registration|url=https://archive.org/details/athomeinuniverse00kauf_0}}</ref>