Editing Protein (section)

== Mechanical properties ==

The [[Mechanical properties of biomaterials|mechanical properties]] of proteins are highly diverse and are often central to their biological function, as in the case of proteins like [[keratin]] and [[collagen]].<ref>{{cite journal | vauthors = Gosline J, Lillie M, Carrington E, Guerette P, Ortlepp C, Savage K | title = Elastic proteins: biological roles and mechanical properties | journal = Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences | volume = 357 | issue = 1418 | pages = 121–132 | date = February 2002 | pmid = 11911769 | pmc = 1692928 | doi = 10.1098/rstb.2001.1022 | veditors = Bailey AJ, Macmillan J, Shrewry PR, Tatham AS }}</ref> For instance, the ability of [[Muscle|muscle tissue]] to continually expand and contract is directly tied to the elastic properties of their underlying protein makeup.<ref>{{cite journal | vauthors = Maruyama K, Natori R, Nonomura Y | title = New elastic protein from muscle | journal = Nature | volume = 262 | issue = 5563 | pages = 58–60 | date = July 1976 | pmid = 934326 | doi = 10.1038/262058a0 | bibcode = 1976Natur.262...58M }}</ref><ref>{{cite journal | vauthors = Tskhovrebova L, Trinick J | title = Making muscle elastic: the structural basis of myomesin stretching | journal = PLOS Biology | volume = 10 | issue = 2 | pages = e1001264 | date = February 2012 | pmid = 22347814 | pmc = 3279349 | doi = 10.1371/journal.pbio.1001264 | doi-access = free }}</ref> Beyond fibrous proteins, the conformational dynamics of [[enzyme]]s<ref>{{cite journal | vauthors = Mizraji E, Acerenza L, Lin J | title = Viscoelastic models for enzymes with multiple conformational states | journal = Journal of Theoretical Biology | volume = 129 | issue = 2 | pages = 163–175 | date = November 1987 | pmid = 3455460 | doi = 10.1016/s0022-5193(87)80010-3 | bibcode = 1987JThBi.129..163M }}</ref>  and the structure of [[biological membrane]]s, among other biological functions, are governed by the mechanical properties of the proteins. Outside of their biological context, the unique mechanical properties of many proteins, along with their relative sustainability when compared to [[List of synthetic polymers|synthetic polymers]], have made them desirable targets for next-generation materials design.<ref>{{Cite journal | vauthors = Schiller T, Scheibel T |date=2024-04-18 |title=Bioinspired and biomimetic protein-based fibers and their applications |journal=Communications Materials |volume=5 |issue=1 |page=56 |doi=10.1038/s43246-024-00488-2 |doi-access=free |bibcode=2024CoMat...5...56S }}</ref><ref>{{cite journal | vauthors = Sun J, He H, Zhao K, Cheng W, Li Y, Zhang P, Wan S, Liu Y, Wang M, Li M, Wei Z, Li B, Zhang Y, Li C, Sun Y, Shen J, Li J, Wang F, Ma C, Tian Y, Su J, Chen D, Fan C, Zhang H, Liu K | title = Protein fibers with self-recoverable mechanical properties via dynamic imine chemistry | journal = Nature Communications | volume = 14 | issue = 1 | pages = 5348 | date = September 2023 | pmid = 37660126 | pmc = 10475138 | doi = 10.1038/s41467-023-41084-1 | bibcode = 2023NatCo..14.5348S }}</ref>

[[Young's modulus]], ''E,''  is calculated as the axial stress σ over the resulting strain ε. It is a measure of the relative [[stiffness]] of a material. In the context of proteins, this stiffness often directly correlates to biological function. For example, [[collagen]], found in [[connective tissue]], [[bone]]s, and [[cartilage]], and [[keratin]], found in nails, claws, and hair, have observed stiffnesses that are several orders of magnitude higher than that of [[elastin]],<ref name="Guthold-2007">{{cite journal | vauthors = Guthold M, Liu W, Sparks EA, Jawerth LM, Peng L, Falvo M, Superfine R, Hantgan RR, Lord ST | title = A comparison of the mechanical and structural properties of fibrin fibers with other protein fibers | journal = Cell Biochemistry and Biophysics | volume = 49 | issue = 3 | pages = 165–181 | date = 2007-10-02 | pmid = 17952642 | pmc = 3010386 | doi = 10.1007/s12013-007-9001-4 }}</ref> which is though to give elasticity to structures such as [[blood vessel]]s, [[Lung|pulmonary tissue]], and [[Bladder|bladder tissue]], among others.<ref>{{cite journal | vauthors = Wang K, Meng X, Guo Z | title = Elastin Structure, Synthesis, Regulatory Mechanism and Relationship With Cardiovascular Diseases | journal = Frontiers in Cell and Developmental Biology | volume = 9 | pages = 596702 | date = 2021 | pmid = 34917605 | pmc = 8670233 | doi = 10.3389/fcell.2021.596702 | doi-access = free }}</ref><ref>{{cite journal | vauthors = Debelle L, Tamburro AM | title = Elastin: molecular description and function | journal = The International Journal of Biochemistry & Cell Biology | volume = 31 | issue = 2 | pages = 261–272 | date = February 1999 | pmid = 10216959 | doi = 10.1016/S1357-2725(98)00098-3 }}</ref> In comparison to this, [[globular protein]]s, such as [[Bovine serum albumin|Bovine Serum Albumin]], which float relatively freely in the [[cytosol]] and often function as enzymes (and thus undergoing frequent conformational changes) have comparably much lower Young's moduli.<ref name="Khoury-2019">{{cite journal | vauthors = Khoury LR, Popa I | title = Chemical unfolding of protein domains induces shape change in programmed protein hydrogels | journal = Nature Communications | volume = 10 | issue = 1 | pages = 5439 | date = November 2019 | pmid = 31784506 | pmc = 6884551 | doi = 10.1038/s41467-019-13312-0 | bibcode = 2019NatCo..10.5439K }}</ref><ref>{{cite journal | vauthors = Tan R, Shin J, Heo J, Cole BD, Hong J, Jang Y | title = Tuning the Structural Integrity and Mechanical Properties of Globular Protein Vesicles by Blending Crosslinkable and NonCrosslinkable Building Blocks | journal = Biomacromolecules | volume = 21 | issue = 10 | pages = 4336–4344 | date = October 2020 | pmid = 32955862 | doi = 10.1021/acs.biomac.0c01147 }}</ref>

The Young's modulus of a single protein can be found through [[molecular dynamics]] simulation. Using either atomistic force-fields, such as [[CHARMM]] or [[GROMOS]], or coarse-grained forcefields like Martini,<ref>{{cite journal | vauthors = Souza PC, Alessandri R, Barnoud J, Thallmair S, Faustino I, Grünewald F, Patmanidis I, Abdizadeh H, Bruininks BM, Wassenaar TA, Kroon PC, Melcr J, Nieto V, Corradi V, Khan HM, Domański J, Javanainen M, Martinez-Seara H, Reuter N, Best RB, Vattulainen I, Monticelli L, Periole X, Tieleman DP, de Vries AH, Marrink SJ | title = Martini 3: a general purpose force field for coarse-grained molecular dynamics | journal = Nature Methods | volume = 18 | issue = 4 | pages = 382–388 | date = April 2021 | pmid = 33782607 | doi = 10.1038/s41592-021-01098-3 | url = https://pure.rug.nl/ws/files/190731140/s41592_021_01098_3.pdf }}</ref> a single protein molecule can be stretched by a uniaxial force while the resulting extension is recorded in order to calculate the strain.<ref>{{Cite web |title=Piotr Szymczak's Homepage |url=https://www.fuw.edu.pl/~piotrek/proteins.html |access-date=2024-05-13 |website=www.fuw.edu.pl}}</ref><ref>{{cite journal | vauthors = Mapplebeck S, Booth J, Shalashilin D | title = Simulation of protein pulling dynamics on second time scale with boxed molecular dynamics | journal = The Journal of Chemical Physics | volume = 155 | issue = 8 | pages = 085101 | date = August 2021 | pmid = 34470356 | doi = 10.1063/5.0059321 | bibcode = 2021JChPh.155h5101M | doi-access = free }}</ref> Experimentally, methods such as [[atomic force microscopy]] can be used to obtain similar data.<ref>{{cite journal | vauthors = Carrion-Vazquez M, Marszalek PE, Oberhauser AF, Fernandez JM | title = Atomic force microscopy captures length phenotypes in single proteins | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 96 | issue = 20 | pages = 11288–11292 | date = September 1999 | pmid = 10500169 | pmc = 18026 | doi = 10.1073/pnas.96.20.11288 | doi-access = free | bibcode = 1999PNAS...9611288C }}</ref> The internal dynamics of proteins involve subtle elastic and plastic deformations induced by [[Viscoelasticity|viscoelastic]] forces, which can be probed by nano-[[rheology]] techniques.<ref>{{Cite journal |last=Weinreb |first=Eyal |last2=McBride |first2=John M. |last3=Siek |first3=Marta |last4=Rougemont |first4=Jacques |last5=Renault |first5=Renaud |last6=Peleg |first6=Yoav |last7=Unger |first7=Tamar |last8=Albeck |first8=Shira |last9=Fridmann-Sirkis |first9=Yael |last10=Lushchekina |first10=Sofya |last11=Sussman |first11=Joel L. |last12=Grzybowski |first12=Bartosz A. |last13=Zocchi |first13=Giovanni |last14=Eckmann |first14=Jean-Pierre |last15=Moses |first15=Elisha |date=2025-03-28 |title=Enzymes as viscoelastic catalytic machines |url=https://www.nature.com/articles/s41567-025-02825-9 |journal=Nature Physics |language=en |pages=1–12 |doi=10.1038/s41567-025-02825-9 |issn=1745-2481}}</ref> These estimates yield typical spring constants around ''k ≈'' 100 pN/nm, equivalent to Yonung's moduli of ''E ≈'' 100 MPa, and typical friction coefficients of ''γ'' ≈ 0.1 pN·s/nm, corresponding to viscosity of ''η'' ≈ 0.01 pN·s/nm<sup>2</sup> = 10<sup>7</sup>cP (that is, 10<sup>7</sup> more viscous than water). 

At the macroscopic level, the Young's modulus of cross-linked protein networks can be obtained through more traditional [[mechanical testing]]. Experimentally observed values for a few proteins can be seen below.
{| class="wikitable"
|+Elasticity of Various Proteins
!Protein
!Protein Class
!Young's modulus
|-
|Keratin (Cross-Linked)
|Fibrous
|1.5-10 GPa<ref>{{Cite journal | vauthors = McKittrick J, Chen PY, Bodde SG, Yang W, Novitskaya EE, Meyers MA |date=2012-04-03 |title=The Structure, Functions, and Mechanical Properties of Keratin |url=http://link.springer.com/10.1007/s11837-012-0302-8 |journal=JOM |volume=64 |issue=4 |pages=449–468 |doi=10.1007/s11837-012-0302-8 |bibcode=2012JOM....64d.449M}}</ref>
|-
|Elastin (Cross-Linked)
|Fibrous
|1 MPa<ref name="Guthold-2007" />
|-
|Fibrin (Cross-linked)
|Fibrous
|1-10 MPa<ref name="Guthold-2007" />
|-
|Collagen (Cross-linked)
|Fibrous
|5-7.5 GPa<ref name="Guthold-2007" /><ref>{{cite journal | vauthors = Yang L, van der Werf KO, Fitié CF, Bennink ML, Dijkstra PJ, Feijen J | title = Mechanical properties of native and cross-linked type I collagen fibrils | journal = Biophysical Journal | volume = 94 | issue = 6 | pages = 2204–2211 | date = March 2008 | pmid = 18032556 | pmc = 2257912 | doi = 10.1529/biophysj.107.111013 | bibcode = 2008BpJ....94.2204Y }}</ref>
|-
|Resilin (Cross-Linked)
|Fibrous
|1-2 MPa<ref name="Guthold-2007" />
|-
|Bovine Serum Albumin (Cross-Linked)
|Globular 
|2.5-15 KPa<ref name="Khoury-2019" />
|-
|β-Barrel Outer Membrane Proteins
|Membrane
|20-45 GPa<ref>{{cite journal | vauthors = Lessen HJ, Fleming PJ, Fleming KG, Sodt AJ | title = Building Blocks of the Outer Membrane: Calculating a General Elastic Energy Model for β-Barrel Membrane Proteins | journal = Journal of Chemical Theory and Computation | volume = 14 | issue = 8 | pages = 4487–4497 | date = August 2018 | pmid = 29979594 | pmc = 6191857 | doi = 10.1021/acs.jctc.8b00377 }}</ref>
|}
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=== Viscosity ===
In addition to serving as enzymes within the cell, [[globular protein]]s often act as key transport molecules. For instance, [[Serum albumin|Serum Albumins]], a key component of [[blood]], are necessary for the transport of a multitude of small molecules throughout the body.<ref>{{cite journal | vauthors = Mishra V, Heath RJ | title = Structural and Biochemical Features of Human Serum Albumin Essential for Eukaryotic Cell Culture | journal = International Journal of Molecular Sciences | volume = 22 | issue = 16 | pages = 8411 | date = August 2021 | pmid = 34445120 | pmc = 8395139 | doi = 10.3390/ijms22168411 | doi-access = free }}</ref> Because of this, the concentration dependent behavior of these proteins in solution is directly tied to the function of the [[circulatory system]]. One way of quantifying this behavior is through the [[viscosity]] of the solution.{{Citation needed|date=December 2024}}

Viscosity, η, is generally given is a measure of a fluid's resistance to deformation. It can be calculated as the ratio between the applied stress and the rate of change of the resulting shear strain, that is, the rate of deformation. Viscosity of complex liquid mixtures, such as blood, often depends strongly on temperature and solute concentration.<ref name="Spencer_2024">{{cite journal | vauthors = Spencer SJ, Ranganathan VT, Yethiraj A, Andrews GT | title = Concentration Dependence of Elastic and Viscoelastic Properties of Aqueous Solutions of Ficoll and Bovine Serum Albumin by Brillouin Light Scattering Spectroscopy | journal = Langmuir: The ACS Journal of Surfaces and Colloids | volume = 40 | issue = 9 | pages = 4615–4622 | date = March 2024 | pmid = 38387073 | doi = 10.1021/acs.langmuir.3c02967 | arxiv = 2309.10967 }}</ref> For serum albumin, specifically [[bovine serum albumin]], the following relation between viscosity and [[temperature]] and [[concentration]] can be used.<ref>{{cite journal | vauthors = Monkos K | title = Viscosity of bovine serum albumin aqueous solutions as a function of temperature and concentration | journal = International Journal of Biological Macromolecules | volume = 18 | issue = 1–2 | pages = 61–68 | date = February 1996 | pmid = 8852754 | doi = 10.1016/0141-8130(95)01057-2 }}</ref>

<math>\eta = \exp\left[ \frac{c}{\alpha-\beta\ c}\left(-B +D T + \frac{\Delta E}{R T}\right)\right] </math>

Where ''c'' is the concentration, ''T'' is the temperature, ''R'' is the [[gas constant]], and α, β, ''B'', ''D'', and Δ''E'' are all material-based property constants. This equation has the form of an [[Arrhenius equation]], assigning viscosity an exponential dependence on temperature and concentration.
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