生命科学的（代数）数学原理——生物为什么能繁殖？（中英对照）

【摘要】为了破解生物繁殖之谜，我首先指出了生命复制的三个特点：1）生命复制是靠生物自己完成的，2）生命复制是全成分复制，也即复制中生物的每一种化学成分都得到了复制，3）生命复制是减（负）熵复制；并因此推演出下述（自）复制定律：自复制物质是生命（生物）繁殖的根本原因。复制定律的真实性是毋庸置疑的：如果一个生物复制了自己（后代），那么制造者无疑就在（亲体）生物体内。换句话说，该生物的某一部分（或全部分）物质是制造者。这样，该制造者必定是自复制物质，因为既然它制造了一个生物（后代），那它必定制造了后代的所有部分包括与制造者相同的那部分。

关键词：生命；复制；数学；定律。

导言

某些重要而基本的定律往往看上去像是同义反复的废话或不言自明的垃圾，例如“A=A”（同一律），又如“F=-F’”（牛顿第三定律）。生命科学的最基本定律，（自）复制定律，看起来似乎也是这样。

豌豆为什么能繁殖（复制）豌豆，细菌为什么能繁殖（复制）细菌？这是长期困扰生命科学家及哲学家的难题。但几乎无人想到过它的谜底竟能如此简单：几乎是同义反复。

要认识这一问题，我们需要做的仅仅是：先去了解一下生命（生物）复制是什么，然后寻找它的原因，最后我们就会找到（自）复制定律。而那是打开生命秘密的一把鈅匙。   

生命（生物）复制

世界上所谓的复制或拷贝有很多，如文件复制、照片拷贝、电影拷贝、复制建筑物、复制机器等，然而，它们都不是生物复制。那么什么是生命（生物）复制呢？生命（生物）复制有下列特点：

1）   生物复制是靠生物自己完成的。文件的复制是由抄写员或复印机完成的，照片、电影拷贝是由拷贝机完成的，建筑物的复制是由建筑工人及其机械设备完成的，飞机不能繁殖飞机、坦克不能制造坦克……它们没有一个能完成自己的复制。唯有生物能靠自己完成复制：豌豆繁殖豌豆，西瓜复制西瓜，大肠杆菌制造大肠杆菌。

2) 生命复制应该被称为全成分制复，也即生物的每一种化学成分都得到复制。我们可以用大肠杆菌作为例子来说明这一点。我们知道细菌的细胞可以由1个繁殖成2个。我们表示为1 细胞→1 细胞，这里“→” 应该读作“制造”。

由于1 细胞→1 细胞， 1 细胞成了2细胞。这是细胞繁殖的事实。细胞是由它的化学物质组成的。这里当1 细胞→1 细胞时一套（细菌）细胞的物质变成了2套。也就是说，只要细菌生存环境保持不变一个克隆系内的每个细胞将含有同样的物质成分。如此的复制就是全成分复制。我提供4点（常识）事实来支持这一判断。（i）所有生物物质（比如青霉素、胰岛素、结核菌素，等等）都是可再生的。（ii）来自同一克隆的每个细胞的物质成分是相同的。（iii）如果一位科学家发现了某种细胞或细菌能产生一种新物质（比如说是大肠菌素），那么全世界学者都可要求自己也能重复这一发现，无论如何这一发现应能在上述细胞（或细菌）的克隆后代得到重复：否则这一发现将得不到承认。（iv）根据分子生物学（教科书）我们知道细胞（或细菌）自身的物质可归类如下：首先是转录参与者，即DNA（基因组）及转录酶系物质；其次是DNA（作为模板）与转录酶系（作为执行转录者）合作转录的直接产物，也即RNA（含mRNA, rRNA, tRNA 及其它各种RNA）；第三是RNA（翻译）的产物也即蛋白质（包括酶）；第四是酶的产物（例如碳水化合物、酯类等其它有机物质）。由于一个克隆系内细胞的第一类（基因组及转录酶系）物质是固定的，所以只要生存环境不变它的直接及间接产物也即第二、第三、第四类物质也将是固定的。

3）生命复制是负熵制造 (Schrödinger 1944）。每个个体、细胞甚至有机多聚体分子比起它的原料都是熵更低的产品。所以除非制造者耗了能、做了功，否则就不可能制造出生物。这样的复制就是减熵或负熵复制。换句话说，一切不耗能不做功的制造决不是生物制造。同样，一切无须耗能、无须做功的复制决不是生命复制。

 （自）复制定律

由生物复制我们可推演出生命科学的基本定律：（自）复制定律。

现在我们来证明它。

已知细胞能制造细胞，也即“细胞→细胞”（或1细胞成为2细胞）。

细胞是由它的化学物质组成的，所以, “细胞→细胞”必定要依赖于细胞物质成分的复制（没有物质哪有物质组成的细胞）。换句话说，没有物质成分的复制就不会有生物繁殖。所以我们必须要去探查细胞的一套化学（包括结构性与功能性）物质为什么能被复制。

我们用ΣA 来代表一套细胞物质，也即，ΣA= A₁，A₂，A₃……A_x……A_n。“A”应读作“细胞的化学成分”。每一个“A”我们给一个顺序号：1, 2, 3...x…n；细胞成分的总数是n，而x 代表小于n 的任意正整数。

这样全成分复制就可表达为 

ΣA→ΣA，也即 A₁, A₂, A₃……A_x……A_n→A₁, A₂, A₃……A_x……A_n

这里我们不能断定制造者包含了整个ΣA。我们能断定的只是制造者必定在ΣA之中。我们用ΔA 来代表这个未知的制造者，也即ΣA→ΣA 实际是ΔA→ΣA。ΔA可能是一种A （如A₁或A_x），两种A （如A₁、A_x 或A₃、A_x+1），三种A （如A₁、A₇、A₁₁或任何其它三种A），也可能是四种A……x种A……甚至n种A （即ΣA）。然而，ΔA→ΣA 就等于

ΔA→ΔA+（ΣA-ΔA）。最终我们就得到了 ΔA→ΔA及ΔA→（ΣA-ΔA)。

我们把证明过程简化如下：

已知 细胞→细胞，这必须立足于ΣA→ΣA。

然而，ΣA→ΣA实际是ΔA→ΣA。

接着，“ΔA→ΣA”等于“ΔA→ΔA+(ΣA-ΔA)”。

所以我们得到了ΔA→ΔA以及ΔA→(ΣA-ΔA)。

根据以上结果我们就得到如下（自）复制定律：任何能全成分复制的物都是由自复制物质创建的。换句话说，自复制物质是生命（生物）复制的根本原因。没有自复制物质就不会有生命（生物）复制。这样的话，没有自复制物质也就不会有生命（生物）。

自复制定律的原理既简单又毋庸置疑。比如说，设想有10个囚犯越狱了。我们能断定这一事件的肇事者必定在此10人之中，可能是其中的1人或某2人、3人……甚至10个人全部。

所以我们得到：肇事者→10人（越狱）。

同样，我们可把“肇事者→10人”（越狱）写成“肇事者→肇事者+（10人-肇事者）。

那就是说，肇事者不仅是自己越狱，还造成了其余（10人-肇事者）人越狱。

这就得到了越狱定律：越狱肇事者是任何越狱事件的根本原由。所以，没有越狱制造者就不会有越狱事件。

晚近，我又找到甚至更简单的证明方法：

已知 细胞→细胞。它意味着ΣA→ΣA首先应该成立。而该式表明ΣA中必有制造ΣA的制造者。那么这个制造者一定能复制自己，因为它本身是ΣA的一部分（或全部）。

这也适用于越狱定律：已知10人越狱。这意味着10人中的一部分或全部分制造了该事件。所以肇事者必定造成了自己的越狱因为肇事者就是10人中的一部分或全部分。

（自）复制定律指出的乃是生命（生物）复制的内幕真理。所以，只要全成分复制是生物界事实，（自）复制定律就是真理。这是世人应该认清的。

（自）复制定律是揭开生命秘密的钥匙。

由于一个生物的全部物质都是自复制物质的产品，所以就会存在下述事实：1）自复制物质决定了一个生物能拥有哪些物质以及（必然地也能决定了）哪些性状。2）所有生物的复制必然建立在其自复制物质复制的基础之上。所以没有自复制物质便不会有后代。可见，自复制物质必须由亲代传给后代并成为后代的物质基础；换句话说，它是生物的遗传物质。那就是说，生物的制造者、自复制物质、遗传物质是同一事物。

从此我们懂得了：生命科学就是研究（自）复制物质的科学；生物就是由（自）复制物质创建的能全成分复制（自己）的物。生命是什么？生命就是生物的特有能力：复制自己的能力。如果有人发现一种新物，它除了能复制自己之外没有任何其它生气，它依然是一种新的生物。

从此我们还得知：生命科学（生物学）在世界科学的地图上已有了自己的坐标。它是化学的一个分支，这个分支的原点就是自复制化学物质。 

此外，（自）复制定律将为生命起源的探索提供一个入口这是可以想象到的。

参考文献：

[1] Schrödinger, Erwin (1944) What is Life－the Physical Aspect of the Living Cell. Cambridge, University Press. Chapter VI.

          Mathematical (algebra) principle of life science

        —Why can living things reproduce?

Abstract

Towards an understanding of the mysteries of the reproduction of life, I have described the three features of life replication: 1) life replication is accomplished by itself, 2) life replication is the replication of all components, in which every chemical component of the organism is replicated, 3) life replication is replication with decreasing entropy; then consequently derived the following law of self-replication: the self-replicating material(s) is the root cause of life (organisms) reproduction. It is indisputable that the law of self-replication is true: if an organism replicates itself into offspring, the producer must be in the organism (parent). In other words, part (or all) of the materials of this organism are the producer. Thus, the producer must be the self-replicating material, because it produced an organism (offspring), and it must have produced all parts of the offspring, including the part that is identical to itself (the producer).   

Keywords: life；replicate；mathematics；law

Introduction

Some important and basic law often looks like a tautology or self-evident to nonsense rubbish, such as “A=A” (the law of identity) and “F=-F’” (Newton’s third law of motion). This seems to be the case also for the basic law of life science−─the law of self-replication.

Why can a pea reproduce (replicate) new peas? Why can a bacterial cell reproduce (replicate) new cells? This is a difficult problem that has long puzzled life scientists and philosophers. But few thought it could be so simple: the answer is almost a tautology.

To understand this problem, all we is must do is first realize what life (organisms) replication is, then we must look for its cause, to ultimately discover the law of self-replication. This is the key to unlocking the secrets of life.

Life (organisms) replication

There are many so-called replication or copying processes in the world, such as file replication, photocopying, film copying, building clones, and machine clones; however, these do not constitute life (organisms) replication. Then, what is life (organisms) replication? Life (organisms) replication has the following features:   

1) Life replication is accomplished by itself. File replication is performed by copyist or printer, photocopying or film copying is done by a copy-machine, a building’s clone is built by workers with their equipment─aircraft can’t reproduce aircraft, tanks can’t reproduce tanks─none of these can accomplish their own replication. Only organisms can accomplish replication by themselves: peas reproduce peas, melons replicate melons, and cells of Escherichia coli replicate cells of E. coli.   

2) Life replication should be called replication of all components, in which every chemical component of the organism is replicated. We can explain this using E. coli cells as an example. We know that one bacterial cell can reproduce into two bacterial cells. We can express this as

“1 cell→1 cell”, reading “→” as “produces”.

During the process of “1 cell→1 cell”, one cell becomes two cells. This is a fact of cell replication. A cell is formed by its chemical substances. Here one set of bacterial substances becomes two sets when “1 cell→1 cell”. That is to say, each cell of a clone contains the same components if the bacterial living environment remains unchanged. Such replication is the replication of all components. I provide four commonly known facts to support this statement. (i) All biological materials (such as penicillin, insulin, tuberculin) are renewable. (ii) The material composition of each cell from a clone should be the same. (iii) If a scientist discovered that a certain bacterium could produce a new material (such as colicin), then scholars all over the world would attempt to repeat such a finding. Such a finding must be able to be repeated in this bacterium’s clonal offspring, otherwise the findings would not be accepted. (iv) From molecular biology textbooks, we know that the materials of a cell can be summarized as follows: first, the components of transcription, i.e. DNA (genome) and transcriptase system materials; second, the direct products of transcription undertaken as collaboration between DNA template and the transcription system (the operator of transcription), namely RNA (including mRNA, rRNA, and tRNA); third, RNA-translation products, i.e. proteins (including enzymes); fourth, enzymatic  products (such as carbohydrates and lipids). Because the materials of the first class (the genome and transcriptase system) are fixed, their direct and indirect products, i.e. the second, third, and fourth classes, will also be fixed if the living environment remains constant.   

3) Life replication is replication with decreasing entropy (Schrödinger 1944). Every individual, cell, and even organic polymer molecule has lower entropy than the total entropy of its raw materials; therefore no organism could be produced unless its producer consumes energy and does work. In other words, all productions that do not consume energy and do no work can never be life productions. Similarly, replications that consume no energy and do no work can never be life replication.

The law of self-replication

From life replication we can derive the basic law of life science: the law of self-replication.

Now let us to prove it. 

It is known that a cell can produce a cell, i.e., “cell→cell” (or one cell becomes two cells). 

As a cell is formed by its chemical components, so “cell→cell” must rely on the replication of the cell’s components (without substances, how could there be a cell formed by substances?). In other words, if there was no replication of components, there would be no life reproduction. Therefore, we must seek why a cell’s set of chemical (including structural and functional) components is replicated.

We use ΣA to represent a set of components, i.e., ΣA= A₁，A₂，A₃……A_x……A_n。

“A” should be read “cell’s chemical components”. We give every “A” a serial number: 1, 2, 3...x…n, the total number of them is n, and x represents any positive integer less than n. 

Thus, replication of all components can be expressed as

ΣA→ΣA, i.e., A₁, A₂, A₃……A_x……A_n→A₁, A₂, A₃……A_x……A_n

Here we cannot judge that producer comprises the entire ΣA. We can judge only that the  producer must be within ΣA. We use ΔA to represent this unknown producer, namely

ΣA→ΣA is really ΔA→ΣA. ΔA maybe one A (e.g. A₁ or A_x), two As (e.g. A₁, A_x or A₃, A_x+1), three As (e.g. A₁, A₇, A₁₁ or any other three A), four As…xAs……even nAs (i.e.,ΣA). However, ΔA→ΣA is equal to ΔA→ΔA+(ΣA-ΔA). Final we obtain ΔA→ΔA with ΔA→(ΣA-ΔA).

We can simply express the proof process as follows:

It is known that cell→cell.

This must be based on ΣA→ΣA.

However, ΣA→ΣA is really ΔA→ΣA. 

Equally, “ΔA→ΣA” is equal to “ΔA→ΔA+(ΣA-ΔA) ”.

Therefore, we arrive at ΔA→ΔA, with ΔA→(ΣA-ΔA).

According to the outcome above, we can obtain the following law of self-replication:

Anything that is able to replicate all its own components is created by self-replicating material(s). In other words, self-replicating material(s) are the root cause of life (organism) reproduction. Without self-replicating material(s), there can be no life (organism) reproduction. Thus, with no self-replicating material(s), there can be no life (organisms).

This principle of the law of self-replication is simple and undeniable. Let us imagine, for example, there were 10 prisoners breaking out of jail. We can surmise that, among the 10 men, there must be at least one instigator of this incident, and this could be one, two, three, or even all 10 of the prisoners.

So we get: instigator→10 (out of jail). Also, “instigator→10” is equal to “instigator→instigator+(10-instigator)”.

That is to say, instigator(s) gets not only himself (or themselves) out of jail but also the others (10-instigator).  

Here the law of jail-breaking is: the instigator(s) of jail-breaking are the root cause of any jail-breaking occurrence. Accordingly, if there are no instigator(s), there will be no jail-breaking.

Recently, I have found an even simpler method of proof:

It is known that cell→cell. This suggests that ΣA→ΣA should exist first.

This expression tell us that, within ΣA, there must be a producer able to produce ΣA.

So, the producer must be able to replicate itself, because itself is a part (or all) of ΣA. 

This also holds true for the law of jail-breaking: 10 prisoners breaking out of a jail are known. That means that some or all of the 10 men instigated the incident. Thus, the instigator must himself break out of the jail, because the instigator is a part (or all) of these 10 men.

What is pointed out by the law of self-replication is the truth “behind the scenes” of life reproduction. Therefore, as long as the replication of all components is a biological fact, then the law of self-replication is a truth. This is what the world should clearly recognize.

The law of self-replication is the key to unlocking the secrets of life.

Because all the materials of an organism are the products of this organism’s self-replicating material, the following truths exist: 1) the self-replicating material determines what materials (and therefore, characteristics) an organism can have; and 2) the replication of all living things must be based on the replication of their self-replicating material. Therefore, if there is no self-replicating material, there can be no offspring. Consequently, the self-replicating material must be passed from parent(s) to offspring, and become the physical basis of the offspring; in other words, it is the hereditary material of living things. That is to say, the producer of living things, the self-replicating material─ the hereditary material─ is the same object.

We now understand: life science is the science of (self)-replicating material(s), and a living thing is able to replicate all its own components that are created by the self-replicating material(s). What is life? Life is no other than the special ability of the living thing: the ability to replicate itself. If one finds a new object that has no expression of life other than to replicate itself, it is still a new living thing.

We also know that from now on, life science (biology) has its own coordinates on the world map of sciences. It is a branch of chemistry, and the origin of this branch is chemical self-replicating substance(s).

Moreover, it is imaginable that law of self-replication could indicate a clue for exploring the origin of life.

Reference:

[1] Schrödinger, Erwin (1944) What is Life－the Physical Aspect of the Living Cell. Cambridge, University Press. Chapter VI.