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Assembly theory is a framework for quantifying selection and evolution. When applied to molecule complexity, its authors show it to be the first technique that is experimentally verifiable, unlike other molecular complexity algorithms that lack experimental measures.

Background

The hypothesis was proposed by chemist Leroy Cronin in 2017 and developed by the team he leads at the University of Glasgow, then extended in collaboration with a team at Arizona State University led by astrobiologist Sara Imari Walker, in a paper released in 2021.

Assembly Theory conceptualizes objects not as point particles, but as entities defined by their possible formation histories. This allows objects to show evidence of selection, within well-defined boundaries of individuals or selected units. Combinatorial objects are important in chemistry, biology and technology, in which most objects of interest (if not all) are hierarchical modular structures. For any object an 'assembly space' can be defined as all recursively assembled pathways that produce this object. The 'assembly index' is the number of steps on a shortest path producing the object. For such shortest path, the assembly space captures the minimal memory, in terms of the minimal number of operations necessary to construct an object based on objects that could have existed in its past. The assembly is defined as "the total amount of selection necessary to produce an ensemble of observed objects"; for an ensemble containing ${\displaystyle N_{T}}$ objects in total, ${\displaystyle N}$ of which are unique, the assembly ${\displaystyle A}$ is defined to be

${\displaystyle A=\mathop {\sum } \limits _{i=1}^{N}{e}^{{a}_{i}}\left({\frac {{n}_{i}-1}{{N}_{\rm {T}}}}\right)}$,

where objects of type ${\displaystyle i}$ occur ${\displaystyle n_{i}}$ times and have assembly index ${\displaystyle a_{i}}$.

For example, the word 'abracadabra' contains 5 unique letters (a, b, c, d and r) and is 11 symbols long. It can be assembled from its constituents as a + b --> ab + r --> abr + a --> abra + c --> abrac + a --> abraca + d --> abracad + abra --> abracadabra, because 'abra' was already constructed at an earlier stage. Because this requires at least 7 steps, the assembly index is 7. The word ‘abracadrbaa’, of the same length, for example, has no repeats so has an assembly index of 10.

Take two binary strings ${\displaystyle C=}$ and ${\displaystyle D=}$ as another example. Both have the same length ${\displaystyle N=8}$ bits, both have the same Hamming weight ${\displaystyle N_{1}=N/2=4}$. However, the assembly index of the first string is ${\displaystyle a(C)=3}$ ("01" is assembled, joined with itself into "0101", and joined again with "0101" taken from the assembly pool), while the assembly index of the second string is ${\displaystyle a(D)=6}$, since in this case only "01" can be taken from the assembly pool.

In general, for K subunits of an object O the assembly index is bounded by ${\displaystyle \log _{2}(K)\leq a_{O}\leq K-1}$.

While other approaches can provide a measure of complexity, the researchers claim that assembly theory's molecular assembly number is the first to be measurable experimentally. Molecules with a high assembly index are very unlikely to form abiotically, and the probability of abiotic formation goes down as the value of the assembly index increases. The assembly index of a molecule can be obtained directly via spectroscopic methods. This method could be implemented in a fragmentation tandem mass spectrometry instrument to search for biosignatures.

The theory was extended to map chemical space with molecular assembly trees, demonstrating the application of this approach in drug discovery, in particular in research of new opiate-like molecules by connecting the "assembly pool elements through the same pattern in which they were disconnected from their parent compound(s)".

It is difficult to identify chemical signatures that are unique to life. For example, the Viking lander biological experiments detected molecules that could be explained by either living or natural non-living processes. It appears that only living samples can produce assembly index measurements above ~15. However, another paper demonstrated that abiotic chemical processes could form highly complex crystal structures whose assembly indices exceed this threshold. Authors conclude that "while the proposal of a biosignature based on a molecular assembly index of 15 is an intriguing and testable concept, the contention that only life can generate molecular structures with MA index ≥ 15 is in error".

Critical views

A paper published in the Journal of Molecular Evolution concludes that what "assembly theory really does is to detect and quantify bias caused by higher-level constraints in some well-defined rule-based worlds"; one "can use assembly theory to check whether something unexpected is going on in a very broad range of computational model worlds or universes".

Steven A. Benner is of the opinion that it "is transparently false that non-living systems cannot contain molecules that are complex, no matter how complexity is defined".

Hector Zenil is of the opinion that the discoverers of assembly theory "are unwilling to acknowledge that what defines an algorithm is not the use to which it is put but rather its structure and function".

See also

• List of interstellar and circumstellar molecules
• Word problem for groups

References

1. ^ Marshall SM, Mathis C, Carrick E, et al. (24 May 2021). "Identifying molecules as biosignatures with assembly theory and mass spectrometry". Nature Communications. 12 (3033): 3033. Bibcode:2021NatCo..12.3033M. doi:10.1038/s41467-021-23258-x. PMC 8144626. PMID 34031398.
2. ^ Liu, Yu; Mathis, Cole; Bajczyk, Michał Dariusz; Marshall, Stuart M.; Wilbraham, Liam; Cronin, Leroy (2021). "Exploring and mapping chemical space with molecular assembly trees". Science Advances. 7 (39): eabj2465. Bibcode:2021SciA....7J2465L. doi:10.1126/sciadv.abj2465. PMC 8462901. PMID 34559562.
3. ^ Marshall, Stuart M.; Murray, Alastair R. G.; Cronin, Leroy (2017). "A probabilistic framework for identifying biosignatures using Pathway Complexity". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 375 (2109). arXiv:1705.03460. Bibcode:2017RSPTA.37560342M. doi:10.1098/rsta.2016.0342. PMC 5686400. PMID 29133442.
4. Sara Imari Walker; Leroy Cronin; Alexa Drew; Shawn Domagal-Goldman; Theresa Fisher; Michael Line; Camerian Millsaps (7 April 2019). "Probabilistic Biosignature Frameworks". In Victoria Meadows; Giada Arney; Britney Schmidt; David J. Des Marais (eds.). Planetary Astrobiology. doi:10.2458/azu_uapress_9780816540068-ch018.
5. ^ Sharma, Abhishek; Czégel, Dániel; Lachmann, Michael; Kempes, Christopher P.; Walker, Sara I.; Cronin, Leroy (October 2023). "Assembly theory explains and quantifies selection and evolution". Nature. 622 (7982): 321–328. Bibcode:2023Natur.622..321S. doi:10.1038/s41586-023-06600-9. ISSN 1476-4687. PMC 10567559.
6. Mathis, Cole; Y. Patarroyo, Keith; Cronin, Lee. "Understanding Assembly Indices". Molecular Assembly. Cronin Group. Retrieved 26 March 2024. resulting in an Assembly Index of 7
7. Schwieterman, Edward W.; Kiang, Nancy Y.; Parenteau, Mary N.; Harman, Chester E.; Dassarma, Shiladitya; Fisher, Theresa M.; Arney, Giada N.; Hartnett, Hilairy E.; Reinhard, Christopher T.; Olson, Stephanie L.; Meadows, Victoria S.; Cockell, Charles S.; Walker, Sara I.; Grenfell, John Lee; Hegde, Siddharth; Rugheimer, Sarah; Hu, Renyu; Lyons, Timothy W. (2018). "Exoplanet Biosignatures: A Review of Remotely Detectable Signs of Life". Astrobiology. 18 (6): 663–708. arXiv:1705.05791. Bibcode:2018AsBio..18..663S. doi:10.1089/ast.2017.1729. PMC 6016574. PMID 29727196.
8. Plaxco KW, Gross M (12 August 2011). Astrobiology: A Brief Introduction. JHU Press. pp. 285–286. ISBN 978-1-4214-0194-2. Retrieved 16 July 2013.
9. ^ Hazen, Robert M.; Burns, Peter C.; Cleaves II, H. James; Downs, Robert T.; Krivovichev, Sergey V.; Wong, Michael L. (2024). "Molecular assembly indices of mineral heteropolyanions: some abiotic molecules are as complex as large biomolecules". Journal of the Royal Society Interface. 21 (211). doi:10.1098/rsif.2023.0632. PMC 10878807. This article incorporates text from this source, which is available under the CC BY 4.0 license.
10. Jaeger, Johannes (2024). "Assembly Theory: What It Does and What It Does Not Do". Journal of Molecular Evolution. doi:10.1007/s00239-024-10163-2.
11. Benner, Steven A. "Assembly Theory and Agnostic Life Finding – The Primordial Scoop". Retrieved 19 September 2023.
12. Zenil, Hector. "The 8 Fallacies of Assembly Theory – Medium". Retrieved 26 September 2023.

Further reading

• Resources in your library
• Resources in other libraries

• Cronin, Leroy; Walker, Sara Imari (3 June 2016). "Beyond prebiotic chemistry". Science. 352 (6290): 1174–1175. Bibcode:2016Sci...352.1174C. doi:10.1126/science.aaf6310. ISSN 0036-8075. PMID 27257242. S2CID 206649123.
• Cronin, Leroy; Krasnogor, Natalio; Davis, Benjamin G.; Alexander, Cameron; Robertson, Neil; Steinke, Joachim H. G.; Schroeder, Sven L. M.; Khlobystov, Andrei N.; Cooper, Geoff; Gardner, Paul M.; Siepmann, Peter (2006). "The imitation game—a computational chemical approach to recognizing life". Nature Biotechnology. 24 (10): 1203–1206. doi:10.1038/nbt1006-1203. ISSN 1546-1696. PMID 17033651. S2CID 4664573.
• Ball, Philip (4 May 2023). "A New Theory for the Assembly of Life in the Universe". Quanta Magazine.

• Extraterrestrial life
• Molecular biology techniques
• Theories