What is life? This question is still much debated in science. After the discovery of the structure of DNA by Watson and Crick in 1953, and the more recent advances in DNA sequencing technology, living organisms have become primarily viewed as being defined by their genes.
But there is more to life than genetics alone. In fact, a more "holistic" view is emerging in which the essence of life is considered to reside in the complex collection of chemical reactions that enable an organism to grow, repair, and reproduce itself. In other words, life as a network of self-sustaining chemical reactions. This alternative view could have important consequences for many areas of science, for example the way we might treat diseases like cancer, search for possible life on other planets or grow artificial donor organs. And now there is mathematical evidence that at least one particular living organism (the well-studied bacterium E. coli) is indeed such a self-sustaining reaction network, thus formally supporting this alternative view of life.
Living systems are able to produce, through self-regulated chemical reactions, all the necessary components to repair and reproduce themselves, in such a way as to maintain the continued functionality of the system as a whole. Think of it as an autonomous robot that is capable of harnessing its own energy, repairing itself, and perhaps even building fully-functioning copies of itself. A robot, though, that is based on chemical reactions instead of mechanical principles. And one that was not designed and constructed by humans, but that originated spontaneously from basic chemistry, and subsequently evolved into more and more diverse and wonderfully complex forms.
Already several decades ago, this view of life was described in terms of an autocatalytic set: a chemical reaction network that is able to (collectively) reproduce itself from a basic food source. An essential element in this concept is that of catalysis. A catalyst is a molecule that speeds up the rate at which a chemical reaction happens, without being "used up" in that reaction. Almost all organic reactions (i.e., chemical reactions that happen in living systems) are catalysed. Most of these organic reactions can also happen without their catalyst, but they would proceed too slowly, and would not be synchronised sufficiently, for life to exist. So, catalysts are essential in providing and regulating the functionality of the chemical reaction networks that give rise to, and sustain, life.
An autocatalytic set can now be defined as a particular kind of reaction network (i.e., a set of interconnected chemical reactions and the molecules involved in them) such that:
1. each reaction in the set is catalysed by at least one of the molecules from the set itself, and
2. each molecule in the set can be produced from a basic food source by using only reactions from the set itself.
食物来源的一个子集of molecule types which are assumed to be directly available from the environment (i.e., those elements that occur naturally in the air, rocks, and oceans). The above definition captures the idea of life as a self-regulating (part 1) and self-sustaining (part 2) chemical reaction network. A simple example is given in Fig. 1.
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Fig. 1: A simple example of an autocatalytic set consisting of a reaction network with just two reactions. Black dots represent molecule types, and white boxes represent chemical reactions. Solid black arrows indicate reactants going into and products coming out of a reaction, while dashed grey arrows indicate catalysis. With the four molecule types at the bottom comprising the food source, this reaction network forms an autocatalytic set, where the two molecule types at the top mutually catalyse each other's production from the food set.
This concept of autocatalytic sets was originally introduced by evolutionary biologist Stuart Kauffman. Over the past few years, my colleague Mike Steel and I have taken Kauffman's original concept, made it mathematically more rigorous, and studied it extensively both theoretically and computationally. We also constructed an efficient computer algorithm to detect autocatalytic sets in reaction networks. This has led to many useful and detailed insights into the possible emergence and further evolution of autocatalytic sets. However, many of our results were obtained from studying simple computer models of chemical reaction networks.
所以,为了测试这个概念(及其形式化)a real biological reaction network, we used our mathematical framework to investigate the existence of autocatalytic sets in the bacterium E. coli metabolism. Although commonly associated with food poisoning, most strands of E. coli are harmless, and form part of your normal gut flora. It produces vitamin K, and can help fight off other, harmful bacteria. Scientists have studied E. coli in great detail. As a consequence, its carefully reconstructed metabolic network (i.e., the set of all chemical reactions and interactions that occur in a living organism) is the most complete among all bacterial species. Together with Bill Martin and his postdoc Filipa Sousa, who are both experts on metabolism in the context of the origin and early evolution of life, we subjected the E. coli metabolic network to a formal autocatalytic sets analysis.
When we provided this network as input to our computer program, the result we got back was that 98% of the more than 1800 reactions in E. coli's metabolism indeed form an autocatalytic set. Moreover, our results also recover certain properties of this metabolic network that were assumed from a biological perspective, and which are now verified and supported in a mathematical way. For example, the autocatalytic set that exists in E. coli's metabolism exhibits a modular structure that corresponds well with known functional categories of metabolic reactions.
Furthermore, this autocatalytic set is quite robust against environmental variations, such as different food sets or the removal of random reactions or molecules. Using our formal framework, we can easily check how important each individual molecule or reaction is to the existence and sustainability of the full autocatalytic set. For example, we can remove a particular molecule or reaction from the metabolic network, and then use our computer algorithm again to check whether this reduced network still contains an autocatalytic set, and if so, how much smaller it is compared to the original one.
It turns out that there are many reactions and molecules that, upon removal, do not affect the original autocatalytic set at all, or only to a small extent. However, there are a few molecules and reactions that have a significant impact on the size of the autocatalytic set when they are removed from the network. This result clearly reflects the characteristic small-world network phenomenon (also commonly known as "six degrees of separation"), which has been observed in many natural systems. Some of these results are presented in Fig. 2.
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Fig. 2: The influence of individual molecule types on E. coli's autocatalytic set. Each black dot in this graph represents one of the around 1200 molecule types in the metabolic network of E. coli. The horizontal axis indicates in how many reactions in this network a molecule type is involved. The vertical axis indicates the size of the remaining autocatalytic set ("RAF size") after a given molecule type has been removed from the network. The cluster of dots in the top left represents molecules that are not involved in many reactions and, as a consequence, do not reduce the autocatalytic set significantly when they are removed. The cluster in the middle represents molecules that have a larger effect on the size of the autocatalytic set when removed (i.e., the size of the remaining autocatalytic set is smaller). The bottom cluster represents molecules that are involved in a larger number of reactions and which have a significant impact on the size of the autocatalytic set when removed. The fact that there are three very distinct clusters indicates a strong modular structure in the metabolic network of E. coli.
We can also consider different food sets and see how that affects the size of the autocatalytic set. We can even try to find the minimum food set that will still allow the original autocatalytic set to exist. Interestingly, such a minimum food set is not unique. E. coli's autocatalytic set exists for several different combinations of food molecules. This, again, provides mathematical support for the experimental observation that E. coli is able to grow on different combinations of nutrients, and that it has a high level of robustness.
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Our results were published in the Journal of Systems Chemistry. It clearly shows the strength and usefulness of the autocatalytic sets framework for studying real biological systems. Moreover, it provides (for the first time!) formal and convincing support for the alternative view of life as a self-regulating and self-sustaining chemical reaction network. Also, additional recent results show that our framework generalises over various alternative models and definitions, showing its wide applicability.
The availability and generality of this formal framework to study the existence, structure, and evolution of autocatalytic sets in chemical and biological reaction networks has opened up many new and exciting research directions. For example, in the context of the origin of life it will be interesting to investigate the metabolic networks of even simpler organisms. E. coli itself is already a highly evolved bacterium, unlikely to be fully representative of the primitive organisms that supposedly were in existence shortly after the origin of life. At the other end of the spectrum, ecologists are interested in studying entire ecosystems (networks of species interactions) in the context of autocatalytic sets. And it has even been argued that the economy might be an autocatalytic set!
The possibilities, and new insights that could be gained from them, seem endless. If autocatalytic sets are indeed an underlying and essential principle of life, then the analysis tools to study them more formally and extensively are now available. And thanks to these new analysis tools, the evidence is indisputable: we all have millions of autocatalytic sets in our gut.
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