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2025/12/31

Todays Wiki Article: Assembly Theory

For the communication theory about social interactions, see action assembly theory.

Assembly theory is a framework developed to quantify the complexity of molecules and objects by assessing the minimal number of steps required to assemble them from fundamental building blocks. Proposed by chemist Lee Cronin and his team, the theory assigns an assembly index to molecules, which serves as a measurable indicator of their structural complexity. Cronin and colleagues argue that this approach allows for experimental verification and has applications in understanding selection processes, evolution, and the identification of biosignatures in astrobiology.^[1] However, the usefulness of the approach has been disputed.

Background

The hypothesis was proposed by chemist Leroy Cronin in 2017 and developed by the team he leads at the University of Glasgow,^[2]^[3] then extended in collaboration with a team at Arizona State University led by astrobiologist Sara Imari Walker, in a paper released in 2021.^[4]

Assembly theory conceptualizes objects not as point particles, but as entities defined by their possible formation histories.^[5] This allows objects to show evidence of selection, within well-defined boundaries of individuals or selected units.^[5] Combinatorial objects are important in chemistry, biology and technology, in which most objects of interest (if not all) are hierarchical modular structures.^[5]For any object an 'assembly space' can be defined as all recursively assembled pathways that produce this object.^[5] The 'assembly index' is the number of steps on a shortest path producing the object.^[5] 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.^[5] The assembly is defined as "the total amount of selection necessary to produce an ensemble of observed objects"; for an ensemble containing $N_{T}$ objects in total, $N$ of which are unique, the assembly $A$ is defined to be

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

where $n_{i}$ denotes 'copy number', the number of occurrences of objects of type $i=\{1,2,\dots ,N\}$ having assembly index $a_{i}$ .^[5]

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.^[6] The word 'abracadrbaa', of the same length, for example, has no repeats so has an assembly index of 10.

Take two binary strings $C=[01010101]$ and $D=[00010111]$ as another example. Both have the same length $N=8$ bits, both have the same Hamming weight $N_{1}=N/2=4$ . However, the assembly index of the first string is $a(C)=3$ ("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 $a(D)=6$ , since in this case only "01" can be taken from the assembly pool.^{[citation needed]}

In general, for K subunits of an object O the assembly index is bounded by $\log _{2}(K)\leq a_{O}\leq K-1$ .^[3]

Once a pathway to assemble an object is discovered, the object can be reproduced. The rate of discovery of new objects can be defined by the expansion rate $k_{\text{d}}$ , introducing a discovery timescale $\tau _{\text{d}}\approx 1/k_{\text{d}}$ .^[5] To include copy number $n_{i}$ in the dynamics of assembly theory, a production timescale $\tau _{\text{p}}\approx 1/k_{\text{p}}$ is defined, where $k_{\text{p}}$ is the production rate of a specific object $i$ .^[5] Defining these two distinct timescales $\tau _{\text{d}}$ , for the initial discovery of an object, and $\tau _{\text{p}}$ , for making copies of existing objects, allows to determine the regimes in which selection is possible.^[5]

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.^[5] The assembly index of a molecule can be obtained directly via spectroscopic methods.^[5]^[1] This method could be implemented in a fragmentation tandem mass spectrometry instrument to search for biosignatures.^[1]

The theory was extended to map chemical space with molecular assembly trees, demonstrating the application of this approach in drug discovery,^[2] 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.^[7] For example, the Viking lander biological experiments detected molecules that could be explained by either living or natural non-living processes.^[8] It appears that only living samples can produce assembly index measurements above ~15.^[1] However, 2021, Cronin first explained how polyoxometalates could have large assembly indexes >15 in theory due to autocatalysis.^[9]

Critical views

Chemist Steven A. Benner has publicly criticized various aspects of assembly theory.^[10] Benner argues that it is transparently false that non-living systems, and with no life intervention, cannot contain molecules that are complex but people would be misled in thinking that because it was published in Nature journals after peer review, these papers must be right.

A paper published in the Journal of Molecular Evolution^[11] concludes that "the hype around Assembly Theory reflects rather unfavorably both on the authors and the scientific publication system in general". The author^[11] 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".

Another paper authored by a group of chemists and planetary scientists published in the Journal of the Royal Society Interface^[12]demonstrated that abiotic chemical processes have the potential to form crystal structures of great complexity — values exceeding the proposed abiotic/biotic divide of MA index = 15. They 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".

Two papers published in 2024 argue that assembly theory provides no insights beyond those already available using algorithmic complexity and Claude Shannon's information theory.^[13]^[14]

References

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.
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.
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.
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.
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. PMID 37794189.
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
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.
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.
Cronin, Leroy (2021). "Exploring the Hidden Constraints that Control the Self-Assembly of Nanomolecular Inorganic Clusters". Bulletin of Japan Society of Coordination Chemistry. 78: 11–17. doi:10.4019/bjscc.78.11.
Benner, Steven A. "Assembly Theory and Agnostic Life Finding – The Primordial Scoop". Retrieved 19 September 2023.
Jaeger, Johannes (2024). "Assembly Theory: What It Does and What It Does Not Do". Journal of Molecular Evolution. 92(2): 87–92. Bibcode:2024JMolE..92...87J. doi:10.1007/s00239-024-10163-2. PMC 10978598. PMID 38453740.
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). Bibcode:2024JRSI...2130632H. doi:10.1098/rsif.2023.0632. PMC 10878807. PMID 38378136.
Uthamacumaran, A.; Abrahão, F. S.; Kiani, N. A.; et al. (7 August 2024). "On the salient limitations of the methods of assembly theory and their classification of molecular biosignatures". npj Systems Biology and Applications. 10 (1): 82. arXiv:2210.00901. doi:10.1038/s41540-024-00403-y. PMC 11306634. PMID 39112510.
Abrahão, F. S.; Hernández-Orozco, S.; Kiani, N. A.; Tegnér, J.; Zenil, H. (23 September 2024). "Assembly Theory is an approximation to algorithmic complexity based on LZ compression that does not explain selection or evolution". PLOS Complex Systems. 1 e0000014. arXiv:2403.06629. doi:10.1371/journal.pcsy.0000014.

2025/12/28

Concord Wilshire announces builder and timeline for The Metropolitan redevelopment of Phoenix Metrocenter

Photo of metrocenter — The 64-acre project is designed to transform the former mall site into a walkable urban village that integrates light rail access with housing, entertainment, dining and retail. (File graphics/DigitalFreePress)

Staff Reports | Business & Construction

Concord Wilshire Capital has completed demolition of the former Metrocenter Mall and named Oakwood Homes as the exclusive residential builder for The Metropolitan, an $850 million mixed-use development in Phoenix.

The 64-acre project is designed to transform the former mall site into a walkable urban village that integrates light rail access with housing, entertainment, dining and retail, according to a press release.

“We are pleased to announce that we have selected Oakwood Homes, a division of Clayton Homes and a subsidiary of Berkshire Hathaway, as our exclusive residential builder and partner for The Metropolitan project,” said Nate Sirang, president of Concord Wilshire, in a prepared statement. “Their values, resources and design flexibility align with our goals and the needs of today’s housing market.”

Construction is scheduled to begin in April 2026 for three of the five planned residential communities, with the remaining two and the retail district starting in April 2027. Planned residential communities include:

Terra Court: 144 townhomes near the light rail, priced from the low $400,000s. All units have been pre-sold.
Luna Villas: 314 townhomes starting in the low $500,000s. Half of the units have been pre-sold.
Levante Apartments: A 350-unit multifamily project developed by Concord Wilshire and Hines, also fully pre-sold. A shared parking structure will serve both the apartments and retail center.
Brava: 290 premium townhomes, with construction beginning in April 2027 and prices starting in the low $600,000s.

“Oakwood Homes is thrilled to partner with Concord Wilshire in constructing the residential townhome communities at The Metropolitan,” said Ryan Smith, chief operating officer of Oakwood Homes. “The communities will feature a blend of Spanish Colonial and Contemporary Mediterranean design elements. We look forward to delivering the finished townhomes efficiently.”

Diversified Partners, a Scottsdale-based commercial and retail real estate firm, is leading development of The Loop at The Metropolitan, a retail and entertainment district. The Loop will include 116,000 square feet of boutique retail, rooftop restaurants, an event center, park plaza, live music venues, a splash pad and a weekly farmers market. It will also feature The Track at the Loop, a landscaped pedestrian and bike pathway connecting the development to nearby transit lines.

“The Loop will be where The Metropolitan comes to life,” said Walt Brown, CEO of Diversified Partners. “It’s not just about shopping or dining—it’s about creating a sense of place where people want to be.”

The project is led by Concord Wilshire in partnership with TLG Investment Partners, a Fort Lauderdale-based firm led by Leland Pillsbury and Christopher Nieberding, and CDS International Holdings, a family office led by Bill Milmoe.

2025/12/25

The Zombie Debts Making Wall Street Rich | Bloomberg Investigates

2025/12/23

Todays Thought

Every noon as the clock hands arrive at twelve, / I want to tie the two arms together, / And walk out of the bank carrying time in bags.

-Robert Bly, poet (23 Dec 1926-2021)

2025/12/19

Todays Word

A.Word.A.Day

with Anu Garg

deserts

PRONUNCIATION:

(di-ZUHRTS)

MEANING:

noun: Something that is deserved.

ETYMOLOGY:

From Latin deservire (to serve zealously). Earliest documented use: 1297.

NOTES:

This word survives almost entirely inside the phrase just deserts, meaning punishment or reward that fits the deed. Despite appearances, this has nothing to do with cakes, or arid landscapes. In movies, after a lifetime of crime, villains often get their just deserts. In real life, they get elected.

The world may be in disarray, but at least we can keep the language straight:

desert (di-ZUHRT), as in “to receive just deserts”
from Latin deservire (to serve zealously)

desert (di-ZUHRT), as in “to desert the army”
from Latin deserere (to abandon)

desert (DEZ-uhrt), as in “the Sahara”
from Latin deserere (to abandon)

dessert (di-ZUHRT), as in “fat-free dessert”
from French desservir (to clear the table)

dissert (di-SUHRT), as in “to speak or write at length”
from Latin disserere (to arrange, examine)

USAGE:

“[Carol Burnett’s] favorites starred Jimmy Stewart, and ‘the bad guys always got their just deserts’.”
Julieanne Smolinski; Whatever Happened to Fun?; Harper’s Bazaar (New York); Mar 2024.

See more usage examples of deserts in Vocabulary.com’s dictionary.

2025/12/17

Rose Nylund Scandinavian

Rose Nylund from

The Golden Girls used many nonsensical, humorous words from her fictional hometown of St. Olaf, Minnesota, often describing complex emotions or situations with unique terms like "garconanokin" (a person you don't want to share with) or "tutenbobels" (butt cheeks), blending made-up words with slightly real Scandinavian-sounding roots, like "vanskapskaka" (friendship cake). These unique phrases, often nonsensical gibberish or descriptive, became a hallmark of her character.

Examples of Rose's St. Olaf Words:

Garconanokin: Someone undesirable; literally, the moment dog poop turns white.
Tutenbobels: Buttocks.
Vanskapskaka: A friendship cake (from Swedish vänskapskaka).
Gerflokennokkin: A special St. Olaf dish.
Ugel Flugel: Hide-and-seek for adults.
Vertugenflürgen: Meaning "I'm not one to blow my own horn".
Kaflügenachen: Someone who parks in a handicapped spot without a permit.

Origin & Meaning:
These words weren't real Scandinavian words but were invented for the show, inspired by Norwegian-American culture, to reflect Rose's naive yet detailed view of her small town. They added to the show's humor and defined her character.