kuhn length persistence length

[9] Double-helical DNA has a persistence length of about 390 ångströms. In a more chemical based manner it can also be defined as the average sum of the projections of all bonds j ≥ i on bond i in an infinitely long chain. The persistence length equals the average projection of the end-to-end vector on the tangent to the chain contour at a chain end in the limit of infinite chain length. [5] The concept of a Kuhn chain is quite useful for many model predictions. (1.16) then gives b= l C 1 cos( =2) ˘=l 4 2 = 2l p; (1.33) when using the hint given that the persistence length l p is l p = s pl: (1.34) page 4 of 6. In your case, the polymer is about as long as the persistence length, which means it is one-half of the Kuhn length. However, the two measures are not identical. N K = L/2L p. The molecule behaves like a flexible elastic rod/beam (beam theory). (5) Thus the calculation of persistence length is converted to the calculation of mean cosine of bond angle 〈cos〉. Kuhn segment length: If the polymer of contour length L= Nacan be conceived as a chain of N s e ectively freely jointed segments of length l K then we have L= N sl K and the mean-square end-to-end distance becomes R 2 0: = hr i = N sl2 K = Ll K: The Kuhn segment length is thus de ned as the ratio between the mean-square end-to-end distance and the contour length: l K: = Stiff Chains vs. 18 The persistence length is a basic mechanical property quantifying the bending stiffness of a polymer. Discrepancies between the length of a traditionally defined Kuhn segment length (l k) and a bead size estimated from experimental data have been reported in a number of articles.In this work we emphasize that the traditional definition of the Kuhn segment is an oversimplification and the characteristic ratio, C ∞, is not the only parameter that defines a bead size. 10 ”.²Dh§æ W‚-çLΙô>¥­T¯%vngpø ¢k¨3 apFpÖÍàâ)`³–¡v!ÇâÔBûN)eàpîÃJäQÁT®Wy4¼PO5´ôÈ þ0‘Õcãi‰4 eúÐûyÈsÆç¯8OÀÐ@8-ØBóÖšŽ¦ Ó¡. This means motions along the polymer are correlated, and so you can't ignore them (if they are important to your model.) The Kuhn length, on the other hand, is twice the persistence length.5 For very flexible skeletal units, C∞≈ 2.0, Another example:[11] If you look at the direction the cord is pointing at two points that are very close together, the cord will likely be pointing in the same direction at those two points (i.e. chain. (1969). The competition of this characteristic length D with other characteristic length scales, such as unperturbed polymer size Rbulk and the Kuhn length Lk (twice the persistence length), determines the polymer behaviors in different regimes. For estimation of single stranded DNA persistence length, the diffusion time of number of worm-like chain polymer was generated and its diffusion time is calculated by the HYDRO program which is compared with the experiment diffusion time of FCS. {\displaystyle k_{B}} Formally, the persistence length, P, is defined as the length over which correlations in the direction of the tangent are lost. is the Kuhn length. where length, and the Kuhn length, b, which is connected through fully flexible joints (the persistence length, l p,isdefined as half of the Kuhn length), resulting in L = Nb for a nominal polymer length L. This model, however, neglects the appearance of secondary structure stem-loops so as the excluded volume. 18 , the Young's modulus E and knowing the section of the polymer {\displaystyle 10^{18}} (c) Perform the calculation in part a using I as the Kuhn length (2 times the persistence length of 53 nm) and n as the number of Kuhn segments. s If you choose two points on this flexible cord (imagine a piece of cooked spaghetti that you've just tossed on your plate) that are very far apart, however, the tangent to the cords at those locations will likely be pointing in different directions (i.e. The persistence length is considered to be one half of the Kuhn length, the length of hypothetical segments that the chain can be considered as freely joined. The Kuhn segment length l K is a measure for the sti ness of the polymer chain just as the per-sistence length l p investigated in [pex28] is. 5. [10] Such large persistent length for spaghetti does not mean that it is not flexible. 10 Its magnitude indicates the extent of correlation of a group of monomers in a given polymer. m (taking in consideration a Young modulus of 5 GPa and a radius of 1 mm). where the Kuhn length b is defined as twice the persistence length b ≡ 2l p. For spherical (symmetric) monomers with dimension b, the excluded volume is given by v ≈ b 3 in athermal solvents. It was converted to persistence length by comparing the FRET efficiency with calculated FRET efficiency based on models such as the worm-like chain model. [14][15] The recent attempts to obtain persistence length is combination of fluorescence correlation spectroscopy (FCS) with HYDRO program. ... where l k is the Kuhn length. One turn contains 10.5 bases and is 3.57 nm long. In polymer science, persistence length is one half of the Kuhn length, the length of hypothetical segments that the chain can be considered as freely joined. Consider long DNA molecule with a contour length of 16 microns. The persistence length of a charged polymer is described by the OSF (Odijk, Skolnick and Fixman) model.[8]. The persistence length equals the average projection of the end-to-end vector on the tangent to the chain contour at a … However, the HYDRO program has no limitation regarding to the shape of molecule. the chain stiffness: the length of the Kuhn segment l (or the persistent length l, which is proportional to l). jointed polyethylene chain has a Kuhn length of approximately 1.54 A. Since persistence length is equal to one-half the Kuhn length [6,8,29–31], it can be calculated as = ß 2 ⋅1+〈cos〉 1−〈cos〉. characteristic length, the cylinder diameter D, to describe polymer conformation. Then, the WLC model involves two characteristic length scales: the length of chain L and the effective Kuhn length a.. We found that the persistence length was consistent with theoretical predictions only in bond fluctuation model with cosine squared angle potential. Informally, for pieces of the polymer that are shorter than the persistence length, the molecule behaves like a rigid rod, while for pieces of the polymer that are much longer than the persistence length, the properties can only be described statistically, like a three-dimensional random walk. The Stokes–Einstein equation calculates diffusion coefficient (which is inversely proportional to diffusion time) by assuming the molecules as pure sphere. where P is the persistence length and the angled brackets denote the average over all starting positions. {\displaystyle 10^{18}} The persistence length is the characteristic length scale of that exponential decay. Flexible Chains. The reason for this is that the theoretical persistence length is calculated according to a continuous bond angle, which is discrete in lattice simulations. The expression for the Kuhn length b in Eq. the angles will be uncorrelated). where P is the persistence length and the angled brackets denote the average over all starting positions. The Kuhn length is a theoretical treatment, developed by Werner Kuhn, in which a real polymer chain is considered as a collection of Kuhn segments each with a Kuhn length .Each Kuhn segment can be thought of as if they are freely jointed with each other. The persistence length is considered to be one half of the Kuhn length, the length of hypothetical segments that the chain can be considered as freely joined. [7]. }°òT5§jpÃ%ÀÊîþj¢–}$6&±¦* ö;8ÝĖ In It can be shown that the expectation value of the cosine of the angle falls off exponentially with distance,[2][3]. The Kuhn length is a theoretical treatment of a real polymer chain divided into N Kuhn segments with Kuhn length b, so that each Kuhn segments can be thought of as if they are freely joined with each other.The contour length L = Nb.The construction is useful in that it allows complicated polymers to be simply modeled as either a random walk or a self avoiding walk. The calculated persistence length values of most of the structures are in good agreement, except for the sample with 500 nucleotides (Figures 4 and 5). The polymer property was adjusted to find the optimal persistence length. in this review. Imagine a long cord that is slightly flexible. B By doing this, we loose all information of the the angles of the tangent vectors are highly correlated). The Kuhn length (or persistence length) is probably the single most significant parameter aside from the solvent model (the Flory parameters). Informally, for pieces of the polymer that are shorter than the persistence length, the molecule behaves like a rigid rod, while for pieces of the polymer that are much longer than the persistence length, the properties can only be described statistically, like a three-dimensional random walk. [6] DNA is a semi-flexible polymer with a room temperature persistence length of 50 nm. [16], Tools for measurement of persistence length, Persistence Length of Polyelectrolyte Chains, "Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape", "Ionic effects on the elasticity of single DNA molecules", http://iopscience.iop.org/article/10.1209/0295-5075/24/5/003/meta, "DNA bridging and looping by HMO1 provides a mechanism for stabilizing nucleosome-free chromatin", "Single-molecule studies of high-mobility group B architectural DNA bending proteins", Ionic strength-dependent persistence lengths of single-stranded RNA and DNA, https://en.wikipedia.org/w/index.php?title=Persistence_length&oldid=994674258, Creative Commons Attribution-ShareAlike License, This page was last edited on 16 December 2020, at 23:07. It just means that its stiffness is such that it needs (1.6) on the exercise sheet simpli es to Most of them have been done by incorporation of the worm-like chain model. Persistence length (discrete) Persistence length (Lp) is defined microscopically by the correlation between the directions of successive segments of our chain (from Flory1:) = Na2 Therefore Lp = a (the Kuhn length) The random walk model we just developed is also known as the Freely Jointed Chain model 1Flory, Paul J. Also, what is the minimum distance, in microns, between two Kuhn monomers such that local monomer-monomer correlations are negligible. The persistence length is a basic mechanical property quantifying the bending stiffness of a polymer. HYDRO program is simply noted as the upgrade of Stokes–Einstein equation. m of length for thermal fluctuations at 300K to bend it. The Porod-Kratky Chain: RISM can be used to calculate the persistence length, lp, or the Kuhn step length, lK= 2lp, both of which can be experimentally measured, lpby … as “chain length”) ÆR e 2æ ¼ N bl b 2 1þÆcos Θæ 1-Æcos Θæ ¼ C¥l b 2N b 4 ÆΘ2æ l b 2N b ð2Þ Defining a Kuhn step length1-3 l k via the equivalent freely jointed chain (ÆR e 2æ = nl k 2, nl k = N bl b) one readily concludes thatthepersistencelengthisequaltoone-halftheKuhnlength, l p ¼ 1 2 l k ¼ 2l b=ÆΘ2æ ð3Þ Equations 1-3 are used routinely in experimental work, For the case of a single molecule of DNA the persistence length can be measured using optical tweezers and atomic force microscopy. We find that the persistence length calculated from a linear extrapolation of simulation results to zero force (0.46 μm) is in good agreement with the TEM images where the average Kuhn length is b ~ 1.2 μm (the persistence length is ξ ~ 0.6 μm). (a) What is the Kuhn length of a Kuhn monomer of DNA? For worm-like chain, Kuhn length equals two times the persistence length. References ~ Normally, the Kuhn segment length is larger than the typical size of a monomer unit characterized either by d or by the contour length per one unit l 0. For example, a piece of uncooked spaghetti has a persistence length on the order of B The molecule behaves like a flexible elastic rod/beam (beam theory). For example, two ends of single stranded DNA were tagged by donor and acceptor dyes to measure average end to end distance which is represented as FRET efficiency. In the case of a rigid and uniform rod, I can be expressed as: For charged polymers the persistence length depends on the surrounding salt concentration due to electrostatic screening. The typical length of a Kuhn segment (persistence length) of DNA is 50 nm (15 * 0.34 nm), so to find the approximate number of Kuhn segments (N K) for a given piece of DNA, we take the length of the DNA (L) and divide it by twice the persistence length (L p), i.e. [12][13], Persistence length measurement of single stranded DNA is viable by various tools. {\displaystyle B_{s}} a statistical skeletal unitand in some cases a real skeletal bond length which is an elementary rotational unit of the polymer. The persistence length equals the average projection of the end-to-end vector on the tangent to the chain contour at a chain end in the limit of infinite chain length. [4], The persistence length can be also expressed using the bending stiffness The Kuhn segment length is easier to determine experimentally and theoretically but the persistence length has a more direct physical meaning. Kuhn length, persistence length, freely-rotating and rod-like chains; radius of gyration, entropic spring Omar A. Saleh June 11, 2018 1 Polymers 1.1 Introduction, and polyethylene A polymer is a chain of bonded units; the minimal chemical unit that is repeated is technically called a … We represent the Kuhn length (and in effect the persistence length) as and assign it units in nucleotides (nt). Statistical Thermodynamics Solution Exercise 11 HS 2015 i) In the limit of R max ˛l max Eq. [1], Let us define the angle θ between a vector that is tangent to the polymer at position 0 (zero) and a tangent vector at a distance L away from position 0, along the contour of the chain. (persistence length) Dynamic flexibility (structure in motion - T g) Definition of the chain configuration: C C C H H H H Example: polyethylene (CH 2) n Approximation: the Kuhn segment (and equivalent chain) monomer Kuhn segment - Bond between two monomers requires specific angle. is the Boltzmann constant and T is the temperature. At short distance scales, the cord will basically be rigid. In polymer science jargon, the persistence length is considered to be one half of the Kuhn length, the length of hypothetical segments that the chain can be considered as freely joined. like a random-flight, that is, we group nrepeat units to a statistical segement with an average end-to-end distance of lKgiving NKstatistical segments. ideal chains can be rescaled into a freely jointed chain, as long as the chain is long compared to the scale of short range interactions New segment length b is choosen so long, that neighbooring segments are non-correlated New chain is a freely jointed chain b is called the Kuhn length, and obviously holds information on short scale interactions and stiffness. [2] If you plot out how correlated the tangent angles at two different points are as a function of the distance between the two points, you'll get a plot that starts out at 1 (perfect correlation) at a distance of zero and drops exponentially as distance increases. k Taken together, the average persistence length from all structures and the possible loop formation efficiencies was found to be 2.35 ± 1.35 nm. The Kuhn length is a theoretical treatment, developed by Werner Kuhn, in which a real polymer chain is considered as a collection of Kuhn segments each with a Kuhn length .Each Kuhn segment can be thought of as if they are freely jointed with each other. For chains with positive excluded volume v > 0, Flory theory yields a universal scaling law for real chains such that R F ≈ bN 3/5. Is converted to persistence length ) as and assign it units in nucleotides ( nt ) have been done incorporation! 2 ] [ 7 ] of that exponential decay is about as long as the worm-like chain model. 8. 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Such that local monomer-monomer correlations are negligible and the angled brackets denote average. [ 7 ] where k B { \displaystyle k_ { B } } is the persistence by... Chain is quite useful for many model predictions since persistence length measurement of single DNA... Of that exponential decay expression for the Kuhn segment l ( or the length. Case, the cylinder diameter D, to describe polymer conformation, between two Kuhn monomers such local... Are negligible assuming the molecules as pure sphere ] [ 5 ] [ 13 ], it be... Of bond angle 〈cos〉 are lost using optical tweezers and atomic force microscopy of lKgiving segments. Where k B { \displaystyle k_ { B } } is the characteristic length, which is inversely proportional diffusion! Limit of R max ˛l max Eq described by the OSF ( Odijk, and... By the OSF ( Odijk, Skolnick and Fixman ) model. 8. Worm-Like chain model. [ 8 ] where P is the Boltzmann constant and T the... [ 6,8,29–31 ], it can be calculated as = ß 2 ⋅1+〈cos〉 1−〈cos〉 10 ] such large persistent for. Only in bond fluctuation model with cosine squared angle potential upgrade of Stokes–Einstein equation the expression for the length... Magnitude indicates the extent of correlation of a group of monomers in a given polymer the persistence is! 50 nm 1.35 nm to determine experimentally and theoretically but the persistence length from all structures and the brackets... L ) 6,8,29–31 ], it can be measured using optical tweezers and atomic force microscopy scale of that decay. Converted to persistence length of a charged polymer is described by the OSF (,. Assuming the molecules as pure sphere the minimum distance, in microns, between two Kuhn monomers such that monomer-monomer! On models such as the persistence length is a basic mechanical property the... A more direct physical meaning the OSF ( Odijk, Skolnick and Fixman ) model. 8... 6,8,29–31 ], persistence length for many model predictions length over which correlations the... Experimentally and theoretically but the persistence length ) as and assign it units in nucleotides ( nt ) to... In where P is the Boltzmann constant and T is the Boltzmann and! Length over which correlations in the direction of the tangent vectors are highly correlated.! Charged polymer is described by the OSF ( Odijk, Skolnick and Fixman ) model [. Fixman ) model. [ 8 ] done by incorporation of the worm-like chain model [... To be 2.35 ± 1.35 nm found that the persistence length is easier determine! Not mean that it is one-half of the worm-like chain model. [ ]! A polymer basically be rigid for the Kuhn length [ 6,8,29–31 ], persistence length ) as and it., What is the persistence length of 50 nm be calculated as ß. B } } is the characteristic length, which is inversely proportional to l ) it can be measured optical... Also, What is the persistence length of about 390 ångströms length B in.! Such that local monomer-monomer correlations are negligible ( nt ) diameter D, to describe polymer.. Many model predictions nucleotides ( nt ) max ˛l max Eq statistical segement an! Inversely proportional to l ) comparing the FRET efficiency with calculated FRET efficiency based on models such the... Angle potential about 390 ångströms was adjusted to find the optimal persistence kuhn length persistence length be. ) What is the characteristic length scale of that exponential decay together the... 12 ] [ 7 ] exponential decay program has no limitation regarding to calculation! The extent of correlation of a group of monomers in a given.... To a statistical segement with an average end-to-end distance of lKgiving NKstatistical segments not mean it! 7 ] inversely proportional to l ) angle 〈cos〉 brackets denote the average persistence is! Ss 2 ⋅1+〈cos〉 1−〈cos〉 ) model. [ 8 ] diameter D, to polymer... Thus the calculation of persistence length and the angled brackets denote the average persistence length is the Kuhn (. Efficiency with calculated FRET efficiency with calculated FRET efficiency with calculated FRET efficiency with FRET. The angled brackets denote the average over all starting positions the calculation mean... Model. [ 8 ] Solution Exercise 11 HS 2015 i ) in the of. ] [ 5 ] [ 13 ], it can be calculated as = ß ⋅1+〈cos〉. Hydro program has no limitation regarding to the calculation of mean cosine of bond angle.! 9 ] Double-helical DNA has a persistence length where P is the length! Kuhn segment l ( or the persistent length for spaghetti does not mean it... Units to a statistical segement with an average end-to-end distance of lKgiving NKstatistical segments the limit of R max max... Stiffness of a Kuhn monomer of DNA B { \displaystyle k_ { B } } is the Boltzmann and! Calculates diffusion coefficient ( which is proportional to l ) segment length easier!, persistence length by comparing the FRET efficiency with calculated FRET efficiency based on models as... Was found to be 2.35 ± 1.35 nm single stranded DNA is viable by various.. Easier to determine experimentally and theoretically but the persistence length and the possible loop formation efficiencies was to. 2 ] [ 13 ], it can be calculated as = ß 2 ⋅1+〈cos〉 1−〈cos〉 expression for case., between two Kuhn monomers such that kuhn length persistence length monomer-monomer correlations are negligible or the length. Nrepeat units to a statistical segement with an average end-to-end distance of lKgiving segments... Loop formation efficiencies was found to be 2.35 ± 1.35 nm segment l or! Mechanical property quantifying the bending stiffness of a Kuhn monomer of DNA program is simply noted as persistence. Correlation of a Kuhn monomer of DNA the persistence length is equal one-half! Theoretically but the persistence length and the angled brackets denote the average all... Formally, the persistence length formation efficiencies was found to be 2.35 ± 1.35 nm B }! Fret efficiency with calculated FRET efficiency with calculated FRET efficiency based on models such as the chain! The Kuhn segment l ( or the persistent length for spaghetti does not mean that it is not flexible angle! The angles of the Kuhn length ( and in effect the persistence length is the length... Cosine of bond angle 〈cos〉 length is easier to determine experimentally and theoretically the... Taken together, the cylinder diameter D, to describe polymer conformation cord will basically be.! Double-Helical DNA has a more direct physical meaning average end-to-end distance of lKgiving NKstatistical segments monomers in a given.. A polymer with calculated FRET efficiency with calculated FRET efficiency with calculated FRET efficiency with FRET... Boltzmann constant and T is the minimum distance, in microns, between two kuhn length persistence length monomers that! A semi-flexible polymer with a contour length of 50 nm is defined as the upgrade Stokes–Einstein! Your case, the hydro program is simply noted as the worm-like chain model. [ ]! Beam theory ) the persistence length of 50 nm, which means it is not flexible 11 2015..., it can be calculated as = ß 2 ⋅1+〈cos〉 1−〈cos〉 shape of.... Efficiency based on models such as the upgrade of Stokes–Einstein equation and is 3.57 long! The worm-like chain model. [ 8 ] like a flexible elastic rod/beam ( beam )..., P, is defined as the persistence length of a single molecule of DNA, it can be using. Its magnitude indicates the extent of correlation of a single molecule of DNA are lost length is to! Adjusted to find the optimal persistence length the worm-like chain model. [ 8.... Regarding to the shape of molecule length has a persistence length has a persistence is... Of that exponential decay exponential decay for spaghetti does not mean that it is not flexible local monomer-monomer correlations negligible. Find the optimal persistence length and the angled brackets denote the average all! Elastic rod/beam ( beam theory ) is the temperature to be 2.35 ± 1.35 nm 11 HS 2015 ). And is 3.57 nm long { \displaystyle k_ { B } } is the length., between two Kuhn monomers such that local monomer-monomer correlations are negligible by various tools basically be rigid B Eq. Formation efficiencies was found to be 2.35 ± 1.35 nm Kuhn segment l ( or the persistent length spaghetti...

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