View source for Mosaic Q

== The Proteins Mosaic Q Pattern ==


<StructureSection load='1a3n' size='340' side='right' 
caption='Human hemoglobin (PDB: 1A3N) colored by amino acid 
chemical type (hydrophobic, polar, acidic, basic, special), revealing the Mosaic Q pattern.' 
scene='11/1109349/Hemoglobin_mosaicq/2'>
<small>
Francisco Javier Lobo Cabrera, Ph.D (francisco.lobo6@gmail.com)<br>
Prof. José Antonio Prado-Bassas, Facultad de Matemáticas, Universidad de Sevilla (bassas@us.es)<br>
María Ángeles García-Rosado Delgado, MSc (mariagarrodel@gmail.com)
</small>


The '''Mosaic Q''' is a structural pattern observed in protein 
three-dimensional structures, in which amino acids of the same 
chemical type tend to cluster spatially in groups of specific size 
and geometry. Large-scale analysis of over 160,000 X-ray determined 
structures in the RCSB PDB suggests that this clustering can be 
described by a highly conserved empirical law (R² = 0.979) that 
depends primarily on protein size (number of residues).<ref name="paper">Lobo-Cabrera FJ. 
A Constant Proportion in Protein Structure. 
bioRxiv. DOI:10.1101/500025. 
An updated version of the manuscript is available at 
https://github.com/UPO-Sevilla-Fco-Javier-Lobo-Cabrera/clustering_trait_proteins/blob/main/Manuscript_and_Supplementary_Materials_v4.pdf</ref>
Stochastic simulations prove that the experimental law that quantifies the pattern is dependent on a specific configuration of cluster size and geometry. In parallel, independent visual verification of this pattern is being carried out through the Proteins Mosaic Q Project, a citizen science initiative that enables distributed inspection of protein structures using standardized visualization protocols ([https://proteins-mosaic-q.org project website],[https://proteins-mosaic-q.org/repository/ repository]). The project has been registered and accepted in external platforms such as [https://scistarter.org/proteins-mosaic-q-project SciStarter]<ref name="scistarter">Proteins Mosaic Q Project. SciStarter. 
Available at: https://scistarter.org/proteins-mosaic-q-project. 
Last accessed: Monday, May 4th 2026.</ref>, [https://fairsharing.org/8206 FAIRsharing]<ref name="fairsharing">FAIRsharing.org: Proteins Mosaic Q Project Repository. 
FAIRsharing ID: https://fairsharing.org/8206. 
Last edited: Monday, May 4th 2026, 12:07. Last editor: delphinedauga. 
Last accessed: Monday, May 4th 2026, 14:38.</ref>,[https://citizenscience.eu/project/686 EU-Citizen.Science]<ref name="eucitizen">Proteins Mosaic Q Project. EU-Citizen.Science. 
Available at: https://citizenscience.eu/project/686. 
Last accessed: Monday, May 4th 2026.</ref> and [https://osf.io/42kjn/ Open Science Framework]<ref name="osf">Proteins Mosaic Q Project. Open Science Framework. 
Available at: https://osf.io/42kjn/. 
Last accessed: Monday, May 4th 2026.</ref>, providing additional transparency and independent verification pathways.


'''What is the Mosaic Q Pattern?'''

Alongside the well-known hydrophobic core, where hydrophobic residues tend to coalesce, residues of the same chemical category (polar, acidic, basic, or special) appear to assemble into short contiguous clusters, with an average length of around eight residues. This organization is referred to as the '''Mosaic Q model''', in which clusters of approximately 8 residues of the same chemical type coexist within the protein structure alongside the hydrophobic core. At present, the model provides an empirical description of a statistical regularity observed in protein structures. The overall relationship between spatial clustering and protein size is illustrated schematically below.

[[Image:MosaicQ_overview.png|center|800px|Schematic overview of the Mosaic Q pattern across proteins of different shapes and sizes, and its empirical relationship with protein size.]]

Stochastic simulations demonstrate that the shape of the experimental Q-n curve does depend on the number of residues per cluster and on cluster geometry. In this manner, it is shown that a good aproximation for the experimental results is a model where, in addition to the existence of a hydrophobic core, the rest of amino acids are grouped together according to their residue type (polar, basic, acidic, special) in clusters of approximately 8 residues. 

[[Image:MosaicQ_simulations.png|center|600px|Stochastic simulations of different cluster size configurations and their effect on Q–n scaling behavior. The experimental trend (red) is shown for reference.]]

It must be noted, however, that the mosaic must be understood as a highly conserved pattern in protein structure, where exceptions may occur for different biological/evolutionary reasons, although the signal for this model is strong (R^2=0.978). Visual inspection of multiple PDB structures also point that the conclusions of the computational analysis are apparently valid. This is the basis for the validation mechanism by multiple independent observers, as discussed later, in the citizen-science aspect of this project. Indeed, the pattern can be visualized using a color scheme based on amino acid chemical type:

* '''White''': hydrophobic residues (Ala, Val, Ile, Leu, Met, Phe, Tyr, Trp).
* '''Green''': polar residues (Ser, Thr, Asn, Gln).
* '''Orange''': acidic residues (Asp, Glu).
* '''Blue''': basic residues (Arg, His, Lys).
* '''Cyan''': special residues (Cys, Sec, Gly, Pro); not included in standard Q calculation.

Amino acid chemical type classification follows established literature: acidic residues (Asp, Glu)<ref name="acidic">Agius C, Von Tucher S, Poppenberger B, Rozhon W. 
Quantification of glutamate and aspartate by ultra-high performance liquid chromatography. 
Molecules. 2018;23(6):1389. DOI:10.3390/molecules23061389.</ref>, basic residues (Arg, His, Lys)<ref name="basic">Li C, et al. 
Molecular selective binding of basic amino acids by a water-soluble pillar[5]arene. 
Chem Commun. 2013;49:1924–6. DOI:10.1039/c3cc38622h.</ref>, polar residues (Ser, Thr, Asn, Gln)<ref name="polar">Brinzei M, Stefaniu A, Iulian O, Ciocirlan O. 
Density functional theory (DFT) and thermodynamics calculations of amino acids with 
polar uncharged side chains. 
Chem Proc. 2021;3(1):56. DOI:10.3390/ecsoc-24-08420.</ref>, and hydrophobic residues (Ala, Val, Ile, Leu, Met, Phe, Tyr, Trp)<ref name="hydrophobic">Akbarbaglu Z, 
Tamjidi F, Sarabandi K, Ayaseh A. 
Physicochemical characteristics and antioxidant stability of spray-dried soy peptide fractions. 
Food Sci Nutr. 2023;7:3949–58. DOI:10.1002/fsn3.3381.</ref>. Special residues (Cys, Sec, Gly, Pro) are treated separately following Bak et al.<ref name="cys">Bak DW, Bechtel TJ, Falco JA, Weerapana E. 
Cysteine reactivity across the subcellular universe. 
Curr Opin Chem Biol. 2019;48:96–105. DOI:10.1016/j.cbpa.2018.11.002.</ref>, Arnér<ref name="sec">Arnér ESJ. 
Selenoproteins — What unique properties can arise with selenocysteine in place of cysteine? 
Exp Cell Res. 2010;316(8):1296–303. DOI:10.1016/j.yexcr.2010.02.032.</ref>, Imamoto et al.<ref name="gly">Imamoto Y, et al. 
Diverse roles of glycine residues conserved in photoactive yellow proteins. 
Biophys J. 2008;94(9):3620–8. DOI:10.1529/biophysj.107.123414.</ref> and Ho et al.<ref name="pro">Ho BK, et al. 
The flexibility in the proline ring couples to the protein backbone. 
Protein Sci. 2005;14(4):1011–8. DOI:10.1110/ps.041156905.</ref>

In all the examples, structures are rendered in spacefill Van der Waals representation, restricted to protein atoms, using the following Jmol script:

 select ala or val or ile or leu or met or phe or tyr or trp; color white;
 select ser or thr or asn or gln; color green;
 select asp or glu; color orange;
 select arg or his or lys; color blue;
 select cys or sec or gly or pro; color cyan;
 select all; spacefill vdw;
 restrict protein;

== Quantification: The Mosaic Q Descriptor ==

The degree of spatial clustering is quantified using the '''Mosaic Q descriptor'''. 
The position of each residue in space is defined by its α-carbon atom. 
Residues are classified into four chemical types: acidic (Asp, Glu), 
basic (Arg, His, Lys), polar (Ser, Thr, Asn, Gln) and hydrophobic 
(Ala, Val, Ile, Leu, Met, Phe, Tyr, Trp). Special residues 
(Cys, Sec, Gly, Pro) are excluded from the standard Q calculation. 
Q is defined as the sum of squared inverse Euclidean distances between 
α-carbons of residues of the same chemical type. For each ordered pair 
of residues (i, j) of the same chemical type, the contribution is 1/d²(i,j), 
where d(i,j) is the Euclidean distance between the α-carbons of residues i 
and j, measured in Ångströms. This is summed over all ordered pairs within 
each chemical type, that is acidic (A), basic (B), polar (P) and hydrophobic (H):

[[Image:MosaicQ_equation.png|center|600px|Formal definition of the Q descriptor.]]

where for each type, i and j range independently over all residues of that type (i ≠ j). Note that each pair is counted twice in this formulation, 
consistent with the original definition. An alternative descriptor, Q_alt, 
also includes special residues:

[[Image:MosaicQ_alt_equation.png|center|210px|Formal definition of the Q_alt descriptor, extending Q to include special residues.]]

where S denotes special residues (Cys, Sec, Gly, Pro), and i and j range over all residues of that type (i ≠ j). Higher Q values indicate stronger spatial clustering, although their interpretation should be considered in relation to protein size. The empirical law found relates Q linearly to the 
number of residues (n) with very limited variance (R² = 0.978), indicating 
that proteins of similar size tend to display similar Q values, largely 
independent of fold, conformation or organism of origin:

[[Image:MosaicQ_empirical_law.png|center|600px|Fig. 1. Empirical law relating Q to the number of residues (n) across >160,000 X-ray structures in the RCSB PDB (R² = 0.978).]]

An analogous empirical law holds for Q_alt:

[[Image:MosaicQ_alt_empirical_law.png|center|600px|Fig. 1B. Empirical law relating Q_alt to the number of residues (n).]]

The Q descriptor is implemented in the [https://pypi.org/project/protein-mosaic-q/ protein-mosaic-q] PyPI package, also registered in [https://bio.tools/protein-mosaic-q bio.tools]<ref name="biotools">protein-mosaic-q. bio.tools. 
Available at: https://bio.tools/protein-mosaic-q. 
Last accessed: Monday, May 4th 2026.</ref>. 
Given a PDB or CIF file, it can be computed as follows:

 mosaicq protein.pdb
 mosaicq protein.cif --metric Q_alt

where the <code>--metric Q_alt</code> parameter selects Q_alt instead of the default Q.


Source code is available at 
[https://github.com/UPO-Sevilla-Fco-Javier-Lobo-Cabrera/clustering_trait_proteins GitHub].

== Exploring the pattern's presence in well-known proteins ==

Although the statistical analysis suggests that the Mosaic Q pattern is 
broadly conserved across protein structures, it is instructive to visualize 
it in some well-known examples spanning different sizes, folds and biological 
functions. Accordingly, this Proteopedia entry enables interactive 3D 
exploration of the Mosaic Q pattern across representative protein structures, 
enabling the Proteopedia community, with its deep expertise in protein 
structural biology, to assess and contribute to the project's effort.

Click on any protein name below to load it in the viewer:

* <scene name='11/1109349/Cas9_mosaicq/1'>CRISPR-Cas9 (PDB: 4UN3)</scene> RNA-guided endonuclease, large and functionally diverse structure.
* <scene name='11/1109349/Nucleosome_mosaicq/1'>Nucleosome (PDB: 8Y3E)</scene> fundamental unit of chromatin, histone octamer core.
* <scene name='11/1109349/P53_mosaicq/1'>Tumor Suppressor p53 (PDB: 1TUP)</scene> critical tumor suppressor, DNA-binding and tetramerization domains.
* <scene name='11/1109349/Hemoglobin_mosaicq/2'>Human Hemoglobin (PDB: 1A3N)</scene> oxygen-transport protein, four subunits (two α and two β chains).
* <scene name='11/1109349/Rubisco_mosaicq/1'>RuBisCO (PDB: 5IU0)</scene> key enzyme in carbon fixation, large hexadecameric assembly.


== Independent Verification Through Citizen Science ==

The '''Proteins Mosaic Q Project''' is an open citizen science initiative designed to facilitate independent verification of the observed pattern through reproducible visualization workflows.

The project is registered in multiple external platforms and open science registries, including:

* [https://fairsharing.org/8206 FAIRsharing]<ref name="fairsharing"/>
* [https://scistarter.org/proteins-mosaic-q-project SciStarter]<ref name="scistarter"/>
* [https://citizenscience.eu/project/686 EU-Citizen.Science]<ref name="eucitizen"/>
* [https://bio.tools/protein-mosaic-q bio.tools]<ref name="biotools"/>
* [https://osf.io/42kjn/ Open Science Framework]<ref name="osf">Proteins Mosaic Q Project. Open Science Framework. 
Available at: https://osf.io/42kjn/. 
Last accessed: Monday, May 4th 2026.</ref>

Participants can generate independent visual evidence by applying a standardized representation to protein structures from the RCSB PDB. This approach does not replace statistical analysis, but provides a complementary layer of transparency and reproducibility through distributed inspection of individual cases.

== References ==
<references/>

</StructureSection>