Assembly theory

Last updated September 22, 2024

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. This approach allows for experimental verification and has applications in understanding selection processes, evolution, and the identification of biosignatures in astrobiology.^[1]

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] refers to Hector Zenil's blog post^[12] "that identifies no less than eight fallacies of assembly theory". The paper also refers to the video essay by the same author,^[13] stating that it "summarizes these fallacies, and highlights conceptual/methodological limitations, and the pervasive failure by the proponents of assembly theory to acknowledge relevant previous work in the field of complexity science". The paper 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 ".

The group led by Hector Zenil, a former Senior researcher and faculty member from Oxford and Cambridge and currently an Associate Professor in Biomedical Engineering from King's College London,^[14] is cited to have reproduced the results of Assembly Theory with traditional statistical algorithms.^[15]

Another paper authored by a group of chemists and planetary scientists, including an author affiliated with NASA, published in the journal of the Royal Society Interface^[16] 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".

The paper also cites the papers and posts of Hector Zenil^[12] as questioning whether a single scalar value like the assembly index can be employed to adequately discriminate between living and nonliving systems, and pointing out the noticeable similarities of the Assembly Theory approach to uncited prior efforts to distinguish biotic from abiotic molecular compounds.^[17]

In particular, the paper mentions that Zenil and colleagues "may also have anticipated key conclusions of Assembly Theory by exploring connections among causal memory, selection, and evolution".^[16]^[18]

Related Research Articles

<span class="mw-page-title-main">Astrobiology</span> Science concerned with life in the universe

Astrobiology, is a scientific field within the life and environmental sciences that studies the origins, early evolution, distribution, and future of life in the universe by investigating its deterministic conditions and contingent events. As a discipline, astrobiology is founded on the premise that life may exist beyond Earth.

Computational chemistry is a branch of chemistry that uses computer simulations to assist in solving chemical problems. It uses methods of theoretical chemistry incorporated into computer programs to calculate the structures and properties of molecules, groups of molecules, and solids. The importance of this subject stems from the fact that, with the exception of some relatively recent findings related to the hydrogen molecular ion, achieving an accurate quantum mechanical depiction of chemical systems analytically, or in a closed form, is not feasible. The complexity inherent in the many-body problem exacerbates the challenge of providing detailed descriptions of quantum mechanical systems. While computational results normally complement information obtained by chemical experiments, it can occasionally predict unobserved chemical phenomena.

In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most modern equations of state are formulated in the Helmholtz free energy. Equations of state are useful in describing the properties of pure substances and mixtures in liquids, gases, and solid states as well as the state of matter in the interior of stars.

<span class="mw-page-title-main">Superparamagnetism</span> Form of magnetism

Superparamagnetism is a form of magnetism which appears in small ferromagnetic or ferrimagnetic nanoparticles. In sufficiently small nanoparticles, magnetization can randomly flip direction under the influence of temperature. The typical time between two flips is called the Néel relaxation time. In the absence of an external magnetic field, when the time used to measure the magnetization of the nanoparticles is much longer than the Néel relaxation time, their magnetization appears to be on average zero; they are said to be in the superparamagnetic state. In this state, an external magnetic field is able to magnetize the nanoparticles, similarly to a paramagnet. However, their magnetic susceptibility is much larger than that of paramagnets.

Stuart Alan Kauffman is an American medical doctor, theoretical biologist, and complex systems researcher who studies the origin of life on Earth. He was a professor at the University of Chicago, University of Pennsylvania, and University of Calgary. He is currently emeritus professor of biochemistry at the University of Pennsylvania and affiliate faculty at the Institute for Systems Biology. He has a number of awards including a MacArthur Fellowship and a Wiener Medal.

<span class="mw-page-title-main">Kinetic theory of gases</span> Understanding of gas properties in terms of molecular motion

The kinetic theory of gases is a simple classical model of the thermodynamic behavior of gases. It treats a gas as composed of numerous particles, too small to see with a microscope, which are constantly in random motion. Their collisions with each other and with the walls of their container are used to explain physical properties of the gas—for example, the relationship between its temperature, pressure, and volume. The particles are now known to be the atoms or molecules of the gas.

<span class="mw-page-title-main">Neutral theory of molecular evolution</span> Theory of evolution by changes at the molecular level

The neutral theory of molecular evolution holds that most evolutionary changes occur at the molecular level, and most of the variation within and between species are due to random genetic drift of mutant alleles that are selectively neutral. The theory applies only for evolution at the molecular level, and is compatible with phenotypic evolution being shaped by natural selection as postulated by Charles Darwin.

Density functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density. DFT is among the most popular and versatile methods available in condensed-matter physics, computational physics, and computational chemistry.

An instanton is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a finite, non-zero action, either in quantum mechanics or in quantum field theory. More precisely, it is a solution to the equations of motion of the classical field theory on a Euclidean spacetime.

A biosignature is any substance – such as an element, isotope, molecule, or phenomenon – that provides scientific evidence of past or present life on a planet. Measurable attributes of life include its physical or chemical structures, its use of free energy, and the production of biomass and wastes.

Förster resonance energy transfer (FRET), fluorescence resonance energy transfer, resonance energy transfer (RET) or electronic energy transfer (EET) is a mechanism describing energy transfer between two light-sensitive molecules (chromophores). A donor chromophore, initially in its electronic excited state, may transfer energy to an acceptor chromophore through nonradiative dipole–dipole coupling. The efficiency of this energy transfer is inversely proportional to the sixth power of the distance between donor and acceptor, making FRET extremely sensitive to small changes in distance.

A single-molecule magnet (SMM) is a metal-organic compound that has superparamagnetic behavior below a certain blocking temperature at the molecular scale. In this temperature range, an SMM exhibits magnetic hysteresis of purely molecular origin. In contrast to conventional bulk magnets and molecule-based magnets, collective long-range magnetic ordering of magnetic moments is not necessary.

Fluorescence correlation spectroscopy (FCS) is a statistical analysis, via time correlation, of stationary fluctuations of the fluorescence intensity. Its theoretical underpinning originated from L. Onsager's regression hypothesis. The analysis provides kinetic parameters of the physical processes underlying the fluctuations. One of the interesting applications of this is an analysis of the concentration fluctuations of fluorescent particles (molecules) in solution. In this application, the fluorescence emitted from a very tiny space in solution containing a small number of fluorescent particles (molecules) is observed. The fluorescence intensity is fluctuating due to Brownian motion of the particles. In other words, the number of the particles in the sub-space defined by the optical system is randomly changing around the average number. The analysis gives the average number of fluorescent particles and average diffusion time, when the particle is passing through the space. Eventually, both the concentration and size of the particle (molecule) are determined. Both parameters are important in biochemical research, biophysics, and chemistry.

In probability theory, the Gillespie algorithm generates a statistically correct trajectory of a stochastic equation system for which the reaction rates are known. It was created by Joseph L. Doob and others, presented by Dan Gillespie in 1976, and popularized in 1977 in a paper where he uses it to simulate chemical or biochemical systems of reactions efficiently and accurately using limited computational power. As computers have become faster, the algorithm has been used to simulate increasingly complex systems. The algorithm is particularly useful for simulating reactions within cells, where the number of reagents is low and keeping track of every single reaction is computationally feasible. Mathematically, it is a variant of a dynamic Monte Carlo method and similar to the kinetic Monte Carlo methods. It is used heavily in computational systems biology.

Research concerning the relationship between the thermodynamic quantity entropy and both the origin and evolution of life began around the turn of the 20th century. In 1910 American historian Henry Adams printed and distributed to university libraries and history professors the small volume A Letter to American Teachers of History proposing a theory of history based on the second law of thermodynamics and on the principle of entropy.

Fluorescence cross-correlation spectroscopy (FCCS) is a spectroscopic technique that examines the interactions of fluorescent particles of different colours as they randomly diffuse through a microscopic detection volume over time, under steady conditions.

<span class="mw-page-title-main">Viscosity</span> Resistance of a fluid to shear deformation

The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity is defined scientifically as a force multiplied by a time divided by an area. Thus its SI units are newton-seconds per square meter, or pascal-seconds.

In bioinformatics, alignment-free sequence analysis approaches to molecular sequence and structure data provide alternatives over alignment-based approaches.

The Virtual Planetary Laboratory (VPL) is a virtual institute based at the University of Washington that studies how to detect exoplanetary habitability and their potential biosignatures. First formed in 2001, the VPL is part of the NASA Astrobiology Institute (NAI) and connects more than fifty researchers at twenty institutions together in an interdisciplinary effort. VPL is also part of the Nexus for Exoplanet System Science (NExSS) network, with principal investigator Victoria Meadows leading the NExSS VPL team.

In network science, the network entropy is a disorder measure derived from information theory to describe the level of randomness and the amount of information encoded in a graph. It is a relevant metric to quantitatively characterize real complex networks and can also be used to quantify network complexity

References

1 2 3 4 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.
1 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.
1 2 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.
1 2 3 4 5 6 7 8 9 10 11 12 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.
1 2 Jaeger, Johannes (2024). "Assembly Theory: What It Does and What It Does Not Do". Journal of Molecular Evolution. 92 (2): 87–92. doi: 10.1007/s00239-024-10163-2 . PMC 10978598 . PMID 38453740.
1 2 Zenil, Hector. "The 8 Fallacies of Assembly Theory". Medium. Retrieved 26 September 2023.
↑ "Lee Cronin's Assembly Theory Disputed & Debunked by Dr. Hector Zenil". YouTube . January 2024. Retrieved 13 March 2024.
↑ "Dr Hector Zenil" . Retrieved 17 March 2024.
↑ Uthamacumaran, Abicumaran; Abrahão, Felipe S.; Kiani, Narsis; Zenil, Hector (2022). "On the Salient Limitations of the Methods of Assembly Theory and their Classification of Molecular Biosignatures". arXiv: 2210.00901 [cs.IT].
1 2 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 . PMID 38378136.
↑ Zenil, Hector; Kiani, Narsis A.; Shang, M-M; Tegnér, Jesper (2018). "Algorithmic complexity and reprogrammability of chemical structure networks". Parallel Processing Letters. 28 (1850005). arXiv: 1802.05856 . doi:10.1142/S0129626418500056.
↑ Hernández-Orozco, Santiago; Kiani, Narsis A.; Zenil, Hector (2018). "Algorithmically probable mutations reproduce aspects of evolution, such as convergence rate, genetic memory and modularity". Royal Society Open Science. 5 (8). arXiv: 1709.00268 . doi:10.1098/rsos.180399. PMID 30225028.

Assembly theory

Contents

Background

Critical views

See also

Related Research Articles

References

Further reading