自催化

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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.^[1] 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.

一个单一的化学反应，如果其中一个反应产物也是同一反应或耦合反应的催化剂，则称为自催化反应。

[math]\displaystyle{ A + B \rightleftharpoons 2B }[/math]

【数学】 a + b 右/右/左/右/数学

A set of chemical reactions can be said to be "collectively autocatalytic" if a number of those reactions produce, as reaction products, catalysts for enough of the other reactions that the entire set of chemical reactions is self-sustaining given an input of energy and food molecules (see autocatalytic set).

with the rate equations (for an elementary reaction)

与速率方程(对于一个基本反应)

Chemical reactions

[math]\displaystyle{ {d \over dt}[ A ] =- k_+ [ A ] [B ] + k_{-} [B ]^2 \, }[/math]

[ a ] =-k _ + [ a ][ b ] + k _ {-}[ b ] ^ 2，</math >

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

[ b ] = + k _ + [ a ][ b ]-k _ {-}[ b ] ^ 2，</math > .

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.

这个反应是物种 a 的分子与物种 b 的分子相互作用的反应。A 分子转化成 b 分子。最终产物包括原来的 b 分子和在反应中产生的 b 分子。

A chemical reaction of two reactants and two products can be written as

The key feature of these rate equations is that they are nonlinear; the second term on the right varies as the square of the concentration of B. This feature can lead to multiple fixed points of the system, much like a quadratic equation can have multiple roots. Multiple fixed points allow for multiple states of the system. A system existing in multiple macroscopic states is more orderly (has lower entropy) than a system in a single state.

这些速率方程的关键特征是它们是非线性的; 右边的第二项随 b 浓度的平方变化。这个特性可以导致系统的多个固定点，就像一元二次方程可以有多个根一样。多个固定点允许系统的多个状态。一个存在于多个宏观状态的系统比一个处于单一状态的系统更有序(熵更低)。

[math]\displaystyle{ \alpha A + \beta B \rightleftharpoons \sigma S + \tau T }[/math]

The concentrations of A and B vary in time according to There must be at least some acid present initially to start the catalyzed mechanism; if not the reaction must start by an alternate uncatalyzed path which is usually slower. The above equations for the catalyzed mechanism would imply that the concentration of acid product remains zero forever.

A 和 b 的浓度在时间上有所不同，根据起初必须至少有一些酸存在才能开始催化机制; 如果没有，反应必须以一个备用的无催化路径开始，通常较慢。上述方程式的催化机制将意味着浓度的酸产品永远保持零。

where the Greek letters are stoichiometric coefficients and the capital Latin letters represent chemical species. The chemical reaction proceeds in both the forward and reverse direction. This equation is easily generalized to any number of reactants, products, and reactions.

Chemical equilibrium

In chemical equilibrium the forward and reverse reaction rates are such that each chemical species is being created at the same rate it is being destroyed. In other words, the rate of the forward reaction is equal to the rate of the reverse reaction.

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.

热力学第二定律指出，物理或化学系统及其周围环境(封闭系统)的无序(熵)必须随时间增加。任其自生自灭的系统变得越来越随机，像匀速运动这样的系统的有序能量最终会退化为粒子在热浴中的随机运动。

[math]\displaystyle{ k_+ [ A ]^\alpha [B ]^\beta = k_{-} [S ]^\sigma[T ]^\tau \, }[/math]

There are, however, many instances in which physical systems spontaneously become emergent or orderly. For example, despite the destruction they cause, hurricanes 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.

然而，在许多情况下，物理系统自发地变得涌现或有序。例如，尽管飓风造成了破坏，但与封闭房间中空气分子的随机运动相比，飓风有一个非常有序的涡旋运动。更引人注目的是化学系统创造的秩序，最引人注目的是与生命相关的秩序。

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

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. The light undergoes optical modulation instability, spontaneous dividing into a multitude of optical filaments, and the polymer system thereby forms filaments within the blend structure. The result is a new system that couples optical autocatalytic behavior to spinodal decomposition.

这与第二定律是一致的，第二定律要求一个系统及其周围环境的总体无序必须随着时间的推移而增加。在一个系统中，秩序可以通过对系统周围环境的更大程度的降低来创建。光经历光学调制不稳定性，自发地分裂成许多光学纤维，聚合物系统因此在混合结构中形成纤维。其结果是一个新的系统，将光学自动催化行为与失稳相分离相结合。

Far from equilibrium

Far from equilibrium, the forward and reverse reaction rates no longer balance and the concentration of reactants and products is no longer constant. For every forward reaction [math]\displaystyle{ \alpha }[/math] molecules of A are destroyed. For every reverse reaction [math]\displaystyle{ \alpha }[/math] molecules of A are created. In the case of an elementary reaction step the reaction order in each direction equals the molecularity, so that the rate of change in the number of moles of A is then

It is known that an important metabolic cycle, glycolysis, displays temporal order. Glycolysis consists of the degradation of one molecule of glucose and the overall production of two molecules of ATP. The process is therefore of great importance to the energetics of living cells. The global glycolysis reaction involves glucose, ADP, NAD, pyruvate, ATP, and NADH.

众所周知，一个重要的代谢循环，糖酵解，显示时间顺序。糖酵解是由一个葡萄糖分子的降解和两个 ATP 分子的全部产生组成。因此，这个过程对活细胞的能量学来说是非常重要的。糖酵解反应包括葡萄糖、 ADP、 NAD、丙酮酸、 ATP 和 NADH。

[math]\displaystyle{ {d \over dt}[ A ] =-\alpha k_+ [ A ]^\alpha [B ]^\beta +\alpha k_{-} [S ]^\sigma[T ]^\tau \, }[/math]

[math]\displaystyle{ {d \over dt}[ B ] =-\beta k_+ [ A ]^\alpha [B ]^\beta +\beta k_{-} [S ]^\sigma[T ]^\tau \, }[/math]

[math]\ce{ glucose{} + 2ADP{} + 2P_\mathit{i}{} + 2NAD -> 2(pyruvate){} + 2ATP{} + 2NADH }[/math].

< chem > glucose {} + 2ADP {} + 2P _ mathit { i }{} + 2NAD-> 2(丙酮酸盐){} + 2ATP {} + 2NADH </chem > 。

[math]\displaystyle{ {d \over dt}[ S ] =\sigma k_+ [ A ]^\alpha [B ]^\beta -\sigma k_{-} [S ]^\sigma[T ]^\tau \, }[/math]

[math]\displaystyle{ {d \over dt}[ T ] =\tau k_+ [ A ]^\alpha [B ]^\beta -\tau k_{-} [S ]^\sigma[T ]^\tau \, }[/math]

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.

该过程的细节相当复杂，然而，该过程的一部分是由磷酸果糖激酶(PFK)自催化的。这部分的过程负责振荡的路径，导致过程之间的振荡活跃和非活跃的形式。因此，自催化反应可以调节这一过程。

This system of equations has a single stable fixed point when the forward rates and the reverse rates are equal (when [math]\displaystyle{ {d \over dt}=0 }[/math] for every species). This means that the system evolves to the equilibrium state, and this is the only state to which it evolves.^[2]

Autocatalytic reactions

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, which is used to establish the initial geometry needed to generate the arbitrary final geometry. It has been successfully done in the wet oxidation of [math]\displaystyle{ Al_xGa_{1-x}As }[/math] to obtain arbitrary shaped layers of [math]\displaystyle{ AlO_x }[/math].

利用自催化反应结合反应扩散系统理论的结果来设计薄层是可能的。自催化过程允许控制氧化前沿的非线性行为，用于建立生成任意最终几何所需的初始几何。在湿式氧化法中，成功地获得了任意形状的氧化铝层。

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^[1]

[math]\displaystyle{ A + B \rightleftharpoons 2B }[/math]

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)

with the rate equations (for an elementary reaction)

[math]\displaystyle{ {d \over dt}[ A ] =- k_+ [ A ] [B ] + k_{-} [B ]^2 \, }[/math]

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

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.

不对称自催化反应发生在反应产物是手性的情况下，因此可以作为手性催化剂自身生产。这种类型的反应，比如 Soai 反应，具有将非常小的对映体过量百分数放大成大的反应的特性。这被认为是生物同手性起源的重要步骤。

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.

The key feature of these rate equations is that they are nonlinear; the second term on the right varies as the square of the concentration of B. This feature can lead to multiple fixed points of the system, much like a quadratic equation can have multiple roots. Multiple fixed points allow for multiple states of the system. A system existing in multiple macroscopic states is more orderly (has lower entropy) than a system in a single state.

The concentrations of A and B vary in time according to^[1]^[3]

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

1995年，斯图尔特 · 考夫曼提出生命最初是以自催化化学网络的形式出现的。

[math]\displaystyle{ [A]=\frac{[A]_0+[B]_0}{1+\frac{[B]_0}{[A]_0}e^{([A]_0+[B]_0)kt}} }[/math]

and

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。

[math]\displaystyle{ [B]=\frac{[A]_0+[B]_0}{1+\frac{[A]_0}{[B]_0}e^{-([A]_0+[B]_0)kt}} }[/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.

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.

自动催化在生命过程中起着重要的作用。强调罗伯特·尤兰维奇在生命起源中的作用的两位研究人员是斯图尔特 · 考夫曼和斯图尔特 · 考夫曼。

These kinetic equations apply for example to the acid-catalyzed hydrolysis of some esters to carboxylic acids and alcohols.^[3] There must be at least some acid present initially to start the catalyzed mechanism; if not the reaction must start by an alternate uncatalyzed path which is usually slower. The above equations for the catalyzed mechanism would imply that the concentration of acid product remains zero forever.^[3]

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。

Creation of order

Ultimately, biological metabolism itself can be seen as a vast autocatalytic set, in that all of the molecular constituents of a biological cell are produced by reactions involving this same set of molecules.

最终，生物的新陈代谢本身可以被看作是一个巨大的自我催化装置，因为一个生物细胞的所有分子成分都是由包含同一组分子的反应产生的。

Background

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.

There are, however, many instances in which physical systems spontaneously become emergent or orderly. For example, despite the destruction they cause, hurricanes 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.

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.^[4] 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.

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.

Some autocatalytic reactions also generate order in a system at the expense of its surroundings. For example, (clock reactions) have 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 pathways and metabolic networks in biological systems.

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.

Temporal order

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.^[5]

Idealized example: Lotka–Volterra equation

The Lotka–Volterra equation is isomorphic with the predator–prey model and the two-reaction autocatalytic model. In this example baboons and cheetahs are equivalent to two different chemical species X and Y in autocatalytic 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.

[math]\displaystyle{ A + X \rightarrow 2X }[/math]

[math]\displaystyle{ X + Y \rightarrow 2Y }[/math]

[math]\displaystyle{ Y \rightarrow E }[/math]

Category:Catalysis

类别: 催化

This page was moved from wikipedia:en:Autocatalysis. Its edit history can be viewed at 自催化/edithistory

↑ ^1.0 ^1.1 ^1.2 Steinfeld J.I., Francisco J.S. and Hase W.L. Chemical Kinetics and Dynamics (2nd ed., Prentice-Hall 1999) p.151-2

↑ Ross, John; Garcia-Colin, Leopoldo S. (March 1989). "Thermodynamics of chemical systems far from equilibrium". The Journal of Physical Chemistry. 93 (5): 2091–2092. doi:10.1021/j100342a075.

↑ ^3.0 ^3.1 ^3.2 Moore J.W. and Pearson R.G. Kinetics and Mechanism (John Wiley 1981) p.26

↑ Ilya Prigogine (1980). From Being to Becoming: Time and Complexity in the Physical Sciences. San Francisco: W. H. Freeman. ISBN 978-0-7167-1107-0. https://archive.org/details/frombeingtobecom00ipri.

↑ Espenson, J.H. Chemical Kinetics and Reaction Mechanisms (2nd ed., McGraw-Hill 2002) p.190

[Steinfeld-1] 1.0 ^1.1 ^1.2 Steinfeld J.I., Francisco J.S. and Hase W.L. Chemical Kinetics and Dynamics (2nd ed., Prentice-Hall 1999) p.151-2
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[2] Ross, John; Garcia-Colin, Leopoldo S. (March 1989). "Thermodynamics of chemical systems far from equilibrium". The Journal of Physical Chemistry. 93 (5): 2091–2092. doi:10.1021/j100342a075.

[Moore-3] 3.0 ^3.1 ^3.2 Moore J.W. and Pearson R.G. Kinetics and Mechanism (John Wiley 1981) p.26
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[4] Ilya Prigogine (1980). From Being to Becoming: Time and Complexity in the Physical Sciences. San Francisco: W. H. Freeman. ISBN 978-0-7167-1107-0. https://archive.org/details/frombeingtobecom00ipri.

[5] Espenson, J.H. Chemical Kinetics and Reaction Mechanisms (2nd ed., McGraw-Hill 2002) p.190
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