Values Of Persistence Length Research Articles

Quantitative Elasticity of Flexible Polymer Chains Using Interferometer-Based AFM.

We estimate the elasticity of single polymer chains using atomic force microscope (AFM)-based oscillatory experiments. An accurate estimate of elasticity using AFM is limited by assumptions in describing the dynamics of an oscillating cantilever. Here, we use a home-built fiber-interferometry-based detection system that allows a simple and universal point-mass description of cantilever oscillations. By oscillating the cantilever base and detecting changes in cantilever oscillations with an interferometer, we extracted stiffness versus extension profiles for polymers. For polyethylene glycol (PEG) in a good solvent, stiffness–extension data showed significant deviation from conventional force–extension curves (FECs) measured in constant velocity pulling experiments. Furthermore, modeling stiffness data with an entropic worm-like chain (WLC) model yielded a persistence length of (0.5 ± 0.2 nm) compared to anomaly low value (0.12 nm ± 0.01) in conventional pulling experiments. This value also matched well with equilibrium measurements performed using magnetic tweezers. In contrast, polystyrene (PS) in a poor solvent, like water, showed no deviation between the two experiments. However, the stiffness profile for PS in good solvent (8M Urea) showed significant deviation from conventional force–extension curves. We obtained a persistence length of (0.8 ± 0.2 nm) compared to (0.22 nm ± 0.01) in pulling experiments. Our unambiguous measurements using interferometer yield physically acceptable values of persistence length. It validates the WLC model in good solvents but suggests caution for its use in poor solvents.

Elasticity of single flexible polymer chains in good and poor solvents

Force versus extension curves measure entropic elasticity of single polymer chain in force spectroscopy experiments. A Worm-like Chain model is used to describe force extension experiments with an intrinsic chain parameter called persistence length, which is a measure of local bending flexibility. For flexible polymers, there is a discrepancy in estimates of persistence length in various force regimes. For instance, Atomic Force Microscopy (AFM) based pulling experiments report anomaly low values which are also inconsistent with magnetic tweezers experiments. To understand this, we investigate the role of coupling between microscopic force probe and intrinsic elasticity of polyethylene glycol chain in AFM-based experiments. We perform experiments using oscillatory rheology by providing an external excitation of fixed frequency to the probe. We show that a proper quantification of elastic response measured directly by oscillatory technique deviates significantly from conventional force-extension curves. The persistence length obtained by fitting WLC to stiffness extension data matches well with equilibrium tweezers experiments. In addition, for polystyrene chain in poor solvent no deviation in elastic response is observed between oscillatory and constant velocity pulling experiments. However, such deviation is seen for polystyrene in good solvent. We attribute this to hydrophobic interaction between monomers of polystyrene in water. Our results suggest that oscillatory rheology on single polymer chains provide quantitative estimate of its elastic response. The consistency in values of persistence length using magnetic tweezers experiments in low force regime and the AFM experiments in high force regime suggests that WLC is successful in describing the polymer elasticity in the force range typically probed in AFM experiments.

Size-exclusion chromatography of xylan derivatives-the critical evaluation of macromolecular data.

Hydroxypropyl xylans with varying degrees of substitution were characterized by size-exclusion chromatography. Molar masses of the samples were determined using two approaches: by conventional calibration with molar mass standards and by a multi-detection method that utilizes the combination of static light scattering, viscometry, and differential refractive index detection. The molar mass results obtained by the multi-detection method were accurate, but required the determination of separate refractive index increments for each structurally different sample. The column calibration approach with standard pullulan samples gave biased results due to the differences in hydrodynamic volumes between pullulans and hydroxypropyl xylans with similar molar masses. The degree of hydroxypropylation affected the chain conformation and compactness of the polymer chains. Mark-Houwink parameters and persistence length values suggested that the hydroxypropyl substituents reduced the flexibility of the xylan chain and made the polymer chain more extended.

Deinococcus radiodurans RecA nucleoprotein filaments characterized at the single-molecule level with optical tweezers

Deinococcus radiodurans can survive extreme doses of ionizing radiation due to the very efficient DNA repair mechanisms that are able to cope even with hundreds of double-strand breaks. RecA, the critical protein of homologous recombination in bacteria, is one of the key components of the DNA-repair system. Repair of double-strand breaks requires RecA binding to DNA and assembly of the RecA nucleoprotein helical filaments. The Escherichia coli RecA protein (EcRecA) and its interactions with DNA have been extensively studied using various approaches including single-molecule techniques, while the D. radiodurans RecA (DrRecA) remains much less characterized. However, DrRecA shows some remarkable differences from E. coli homolog. Here we combine microfluidics and single-molecule DNA manipulation with optical tweezers to follow the binding of DrRecA to long double-stranded DNA molecules and probe the mechanical properties of DrRecA nucleoprotein filaments at physiological pH. Our data provide a direct comparison of DrRecA and EcRecA binding to double-stranded DNA under identical conditions. We report a significantly faster filaments assembly as well as lower values of persistence length and contour length for DrRecA nucleoprotein filaments compared to EcRecA. Our results support the existing model of DrRecA forming more frequent and less continuous filaments relative to those of EcRecA.

80 A new approach in determining the rigidity of nucleic acids and polymers

In polymer physics, persistence length of the chain molecules varying in degrees of stiffness is usually evaluated from hydrodynamic data for a set of polymers of different molecular mass М. It is known that from the extrapolation of translational diffusion coefficient to infinite molecular mass, one can calculate persistence length and hydrodynamic radius for rigid and semi-rigid molecules. If the persistence length of the molecule is much greater than its contour length, then the hydrodynamic parameters of the chain are independent of its size and such extrapolation is not applicable. In this case we proposed to plot the dependence M/s 0 2 (s 0 – sedimentation coefficient) or MD 2 (D – translational diffusion coefficient) vs. M (in the absence of volume effects) or n (number of monomers). In these coordinates the appearance of a plateau will correspond to the complete impermeability of the molecule and from plateau height the persistence length can be calculated. We analyzed literature data for a few synthetic polymers by our approach and determined their persistence lengths, the values of which were very close to those in the literature. Usually, the synthesis of polymer molecules with very high molecular mass is a very difficult task. But at the same time, natural polymers with high molecular mass are common in biology. A typical example is a DNA molecule. With increasing contour length of DNA, its conformation passes the next stages: (1) a rigid rod-like particle, (2) a semi-rigid permeable coil, and (3) an impermeable Gaussian coil (Serdyuk, Zaccai, & Zaccai, 2007). We analyzed by our approach sedimentation data of DNA molecules from the literature. It was shown that the plateau starts from 40,000 base pairs of the DNA molecule and the estimated value of persistence length was about 50 nm. This value is close to that from literature data (Lu, Weers, & Stellwagen, 2002). Thus, the proposed approach can be applied for flexibility analysis of biological macromolecules of different natures – from nucleic acids to proteins in strong denaturants.

Persistence Length of Human Cardiac α-Tropomyosin Measured by Single Molecule Direct Probe Microscopy

α-Tropomyosin (αTm) is the predominant tropomyosin isoform in adult human heart and constitutes a major component in Ca2+-regulated systolic contraction of cardiac muscle. We present here the first direct probe images of WT human cardiac αTm by atomic force microscopy, and quantify its mechanical flexibility with three independent analysis methods. Single molecules of bacterially-expressed human cardiac αTm were imaged on poly-lysine coated mica and their contours were analyzed. Analysis of tangent-angle (θ(s)) correlation along molecular contours, second moment of tangent angles (<θ2(s)>), and end-to-end length (Le-e) distributions respectively yielded values of persistence length (Lp) of 41–46 nm, 40–45 nm, and 42–52 nm, corresponding to 1–1.3 molecular contour lengths (Lc). We also demonstrate that a sufficiently large population, with at least 100 molecules, is required for a reliable Lp measurement of αTm in single molecule studies. Our estimate that Lp for αTm is only slightly longer than Lc is consistent with a previous study showing there is little spread of cooperative activation into near-neighbor regulatory units of cardiac thin filaments. The Lp determined here for human cardiac αTm perhaps represents an evolutionarily tuned optimum between Ca2+ sensitivity and cooperativity in cardiac thin filaments and likely constitutes an essential parameter for normal function in the human heart.

Spontaneous Dimerization of Titin Protein Z1Z2 Domains Induces Strong Nanomechanical Anchoring

Muscle elasticity strongly relies on the mechanical anchoring of the giant protein titin to both the sarcomere M-band and the Z-disk. Such strong attachment ensures the reversible dynamics of the stretching-relaxing cycles determining the muscle passive elasticity. Similarly, the design of biomaterials with enhanced elastic function requires experimental strategies able to secure the constituent molecules to avoid mechanical failure. Here we show that an engineered titin-mimicking protein is able to spontaneously dimerize in solution. Our observations reveal that the titin Z1Z2 domains are key to induce dimerization over a long-range distance in proteins that would otherwise remain in their monomeric form. Using single molecule force spectroscopy, we measure the threshold force that triggers the noncovalent transition from protein dimer to monomer, occurring at ∼700 piconewtons. Such extremely high mechanical stability is likely to be a natural protective mechanism that guarantees muscle integrity. We propose a simple molecular model to understand the force-induced dimer-to-monomer transition based on the geometric distribution of forces occurring within a dimeric protein under mechanical tension.

Flexibility Change in Human Cardiac α-Tropomyosin E180G Mutant: Possible Link to Cardiac Hypertrophy

α-Tropomyosin (αTm) is the predominant tropomyosin isoform in adult human heart and constitutes a major component in Ca2+-regulated systolic contraction of cardiac muscle. The familial hypertrophic cardiomyopathy (FHC)-related αTm E180G mutant is associated with decreased thermal stability and enhanced Ca2+-sensitivity in functional assays. A mechanistic relationship between the E180G missense mutation and functional changes has not been established. We present here the first direct probe images of WT human cardiac and E180G mutant αTm by atomic force microscopy, and demonstrate that the mutant is more flexible than WT. Single molecules of bacterially-expressed human cardiac αTm were imaged on poly-lysine coated mica and their contours were analyzed. Analysis of tangent correlation along molecular contours yielded values of persistence length (Lp), which showed 27% increase in flexibility of the E180G mutant. Increased flexibility of the mutant was confirmed by shorter mean end-to-end length and fitting end-to-end length distributions to the worm-like chain model. Corresponding to increased flexibility, it is expected that less mechanical moment, and hence a lesser extent of Ca2+-induced conformational change of troponin, are required to perturb αTm to initiate thin filament activation during systole, thus explaining enhanced Ca2+-sensitivity of function. Hypersensitivity to Ca2+ could overwork cardiac muscle resulting in hypertrophy in FHC. Support: NIH and American Heart Association.

Conformational analysis and estimation of the persistence length of DNA using atomic force microscopy in solution

The worm-like chain model describes the mechanical properties of semi-flexible polymers by introducing a certain correlation length along the contour. This correlation length is called the persistence length. Using atomic force microscopy in solution, we performed measurements of the persistence length of DNA molecules. We found good agreement between the theoretical model and experimental data. However, the measured persistence length values in solution differ from those found by several authors using the same technique but in dry air. In order to determine the contribution of the electrostatic persistence length to the total persistence length, we varied the salt concentration. We found a large discrepancy between the Odijk, Skolnick and Fixman theory and our measurements. The effect of divalent ions and the omission in the theory of the dependence of non-electrostatic persistence length on salt concentration are qualitatively invoked.

Electron Microscopy and Persistence Length Analysis of Semi-Rigid Smooth Muscle Tropomyosin Strands

The structural mechanics of tropomyosin are essential determinants of its affinity and positioning on F-actin. Thus, tissue-specific differences among tropomyosin isoforms may influence both access of actin-binding proteins along the actin filaments and the cooperativity of actin-myosin interactions. Here, 40 nm long smooth and striated muscle tropomyosin molecules were rotary-shadowed and compared by means of electron microscopy. Electron microscopy shows that striated muscle tropomyosin primarily consists of single molecules or paired molecules linked end-to-end. In contrast, smooth muscle tropomyosin is more a mixture of varying-length chains of end-to-end polymers. Both isoforms are characterized by gradually bending molecular contours that lack obvious signs of kinking. The flexural stiffness of the tropomyosins was quantified and evaluated. The persistence lengths along the shaft of rotary-shadowed smooth and striated muscle tropomyosin molecules are equivalent to each other (approximately 100 nm) and to values obtained from molecular-dynamics simulations of the tropomyosins; however, the persistence length surrounding the end-to-end linkage is almost twofold higher for smooth compared to cardiac muscle tropomyosin. The tendency of smooth muscle tropomyosin to form semi-rigid polymers with continuous and undampened rigidity may compensate for the lack of troponin-based structural support in smooth muscles and ensure positional fidelity on smooth muscle thin filaments.

The influence of discoidin domain receptor 2 on the persistence length of collagen type I fibers

Collagen fibers in the vertebrate tissue are responsible for its tensile strength. A disruption in the morphological or mechanical properties of collagen fibers is bound to impact tensile strength and contractility of tissues and affect several cellular processes. We had recently established that binding of discoidin domain receptor (DDR2) with collagen type I results in disruption of the native structure and morphology of collagen fibers. In this study we investigate if DDR2 affects the mechanical properties of collagen fibers. We used an analytical approach to determine the persistence length (PL) of collagen fibers from transmission electron microscope images of immobilized collagen. Fluctuations in the curvature of collagen fibers formed in-vitro (with or without recombinant DDR2) were analyzed to ascertain their PL. The PL values and fiber-diameter measurements were utilized to estimate Young's Modulus (E) of collagen fibers. Our results show that DDR2 significantly reduced PL and E of collagen fibers. We further found that PL for native collagen fibers increases as a function of collagen concentration with little dependence on fiber diameter. These results signify a physiological role of DDR2 in modulating extracellular matrix stiffness, which may be of relevance for tissue engineering and medical implants especially in diseases where DDR2 is upregulated.

Effect of Counterion Binding Efficiency on Structure and Dynamics of Wormlike Micelles

We have studied the effect of counterion binding efficiency on the linear viscoelastic properties of wormlike micelles formed from hexadecyltrimethylammonium bromide (CTAB) in the presence of different nonpenetrating inorganic salts: potassium bromide (KBr), sodium nitrate (NaNO(3)), and sodium chlorate (NaClO(3)). We have varied the salt/surfactant ratio R at fixed surfactant concentration of 350 mM. Results are compared to data for the system cetylpyridinium chloride (CPyCl) and the penetrating counterion sodium salicylate (NaSal) (Oelschlaeger, C.; Schopferer, M.; Scheffold, F.; Willenbacher, N. Langmuir 2009, 25, 716-723). Mechanical high-frequency rheology and diffusing wave spectroscopy (DWS) based tracer microrheology are used to determine the shear moduli G' and G'' in the frequency range from 0.1 Hz up to 1 MHz (Willenbacher, N.; Oelschlaeger, C.; Schopferer, M.; Fischer, P.; Cardinaux, F.; Scheffold, F. Phys. Rev. Lett. 2007, 99, 068302, 1-4). This enables us to determine the plateau modulus G(0), which is related to the cross-link density or mesh size of the entanglement network, the bending stiffness kappa (also expressed as persistence length l(p) = kappa/k(B)T) corresponding to the semiflexible nature of the micelles, and the scission energy E(sciss), which is related to their contour length. The viscosity maximum shifts to higher R values, and the variation of viscosity with R is less pronounced as the binding strength decreases. The plateau modulus increases with R at low ionic strength and is constant around the viscosity maximum; the increase in G(0) at high R, which is presumably due to branching, is weak compared to the system with penetrating counterion. The scission energy E(sciss) approximately = 20 k(B)T is independent of counterion binding efficiency irrespective of R and is slightly higher compared to the system CPyCl/NaSal, indicating that branching may be significant already at the viscosity maximum in this latter case. The micellar flexibility increases with increasing binding efficiency of counterions according to the Hofmeister series. The persistence length values for systems CTAB/KBr, CTAB/NaNO(3), and CTAB/NaClO(3) are 40, 34, and 29 nm, respectively, independent of R, and are significantly higher than in the case of CPyCl/NaSal.

Is DNA a worm-like chain in Couette flow? In search of persistence length, a critical review.

Persistence length is the foremost measure of DNA flexibility. Its origins lie in polymer theory which was adapted for DNA following the determination of BDNA structure in 1953. There is no single definition of persistence length used, and the links between published definitions are based on assumptions which may, or may not be, clearly stated. DNA flexibility is affected by local ionic strength, solvent environment, bound ligands and intrinsic sequence-dependent flexibility. This article is a review of persistence length providing a mathematical treatment of the relationships between four definitions of persistence length, including: correlation, Kuhn length, bending, and curvature. Persistence length has been measured using various microscopy, force extension and solution methods such as linear dichroism and transient electric birefringence. For each experimental method a model of DNA is required to interpret the data. The importance of understanding the underlying models, along with the assumptions required by each definition to determine a value of persistence length, is highlighted for linear dichroism data, where it transpires that no model is currently available for long DNA or medium to high shear rate experiments.

Investigation of Structural Transition of dsDNA on Various Substrates Studied by Atomic Force Microscopy

Structural transition of single dsDNA molecule which is immobilized on 3-aminopropyltriethoxysilane (APTES) treated substrate (APTES/substrate) or alkylthiol treated substrate (alkylthiol/substrate) has been investigated by atomic force microscopy (AFM). The obtained force versus distance (F-D) curves are used to dissect the transition from B-form to S-form, the melting from double stranded (ds) to single stranded (ss) DNA, and its Young's modulus as well as persistence length. The melt from dsDNA to ssDNA is evidenced by fitting with freely jointed chain (FJC) model. FJC fit and Young's modulus or persistence length values when the molecules are fixed on alkylthiol/substrate are more agreeable with other studies than those on APTES. We have clarified the different results of those experiments by analyzing the binding force between DNA molecules and APTES or alkylthiol linkers on the substrate. The DNA binding to APTES linker is much stronger than that on alkylthiol/substrate.

Bending rigidity of type I collagen homotrimer fibrils

Normal type I collagen is an α1(I)2α2(I) heterotrimeric triple helix, but α1(I)3 homotrimers are also found in fetal tissues and various pathological conditions, e.g., causing bone fragility and reducing tendon tensile strength. It remains unclear whether α1(I)3 homotrimers alter mechanical properties of individual fibrils or affect tissues by altering their organization at a higher level. To address this question, we investigated how homotrimers affect fibril bending rigidity. Homotrimer fibrils have been shown to be more loosely packed so that we expected them to be more susceptible to bending. However, confocal imaging of in vitro fibrillogenesis revealed straight, spear-like homotrimer fibrils and curved heterotrimer fibrils. Surprisingly, homotrimer fibrils were more rigid despite being thinner and more hydrated. To quantify fibril rigidity, we analyzed their shape by Fourier decomposition, determined the correlation function for the direction along each fibril, and calculated the distribution of local fibril curvature. The fibril persistence length of homotrimers was 3 ∼ 10 times longer than for homotrimers. These persistence length values indicated much higher bending rigidity of homotrimer helices. We conjectured that the increased rigidity might be related to stabilization of the region surrounding the mammalian collagenase cleavage site. In heterotrimers, this region is known to be the most flexible along the helix. We corroborated this hypothesis by probing the susceptibility of the collagenase cleavage site to MMP-1. Dissection of the observed effects revealed an increased stability of the homotrimer helix at this site. We argue that the loss of the α2(I) chain reduces type I collagen flexibility within the region most vulnerable to bending, thereby increasing the overall bending rigidity of the helix and fibrils. Higher fibril rigidity may alter tissue mechanics not only directly but also by changing the tissue scaffold architecture.

Conformation of comb‐like liquid crystal polymers in isotropic solution probed by small‐angle neutron scattering

AbstractThe conformational characteristics of a comb‐like side‐chain liquid crystal polysiloxane (SCLCP), dissolved in deuterated chloroform, were evaluated by small‐angle neutron scattering (SANS) measurements over a wide q range. SANS studies were carried out on specimens with constant backbone length (DP = 198) and variable spacer length (n = 3, 5, and 11), and with constant spacer length (n = 5) and variable DP (45, 72, 127, and 198). The form factor P(q) at high q was analyzed using the wormlike chain model with finite cross‐sectional thickness (Rc) and taking into account the molecular weight polydispersity. The analysis generated values of persistence length in the range lp = 28–32 Å, considerably larger than that of the unsubstituted polysiloxane chain (lp = 5.8 Å), with contour lengths per monomer comparable to the fully‐extended polysiloxane backbone (lm = 2.9 Å). This indicates a relatively rigid SCLCP chain due to the influence of the densely attached mesogenic groups. The SCLCP with n = 11 is more flexible (lp = 28 Å) than those with n = 3 and n = 5 (lp = 32 Å). The cross‐sectional thickness increases with spacer length, Rc ∼ n0.21±0.02 (3 ≤ n ≤ 11), and the contour length per monomer decreases with increasing spacer length, lm ∼ n−0.35±0.01. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2412–2424, 2006

Coarse-Grained Modeling of the Actin Filament Derived from Atomistic-Scale Simulations

A coarse-grained (CG) procedure that incorporates the information obtained from all-atom molecular dynamics (MD) simulations is presented and applied to actin filaments (F-actin). This procedure matches the averaged values and fluctuations of the effective internal coordinates that are used to define a CG model to the values extracted from atomistic MD simulations. The fluctuations of effective internal coordinates in a CG model are computed via normal-mode analysis (NMA), and the computed fluctuations are matched with the atomistic MD results in a self-consistent manner. Each actin monomer (G-actin) is coarse-grained into four sites, and each site corresponds to one of the subdomains of G-actin. The potential energy of a CG G-actin contains three bonds, two angles, and one dihedral angle; effective harmonic bonds are used to describe the intermonomer interactions in a CG F-actin. The persistence length of a CG F-actin was found to be sensitive to the cut-off distance of assigning intermonomer bonds. Effective harmonic bonds for a monomer with its third nearest neighboring monomers are found to be necessary to reproduce the values of persistence length obtained from all-atom MD simulations. Compared to the elastic network model, incorporating the information of internal coordinate fluctuations enhances the accuracy and robustness for a CG model to describe the shapes of low-frequency vibrational modes. Combining the fluctuation-matching CG procedure and NMA, the achievable time- and length scales of modeling actin filaments can be greatly enhanced. In particular, a method is described to compute the force-extension curve using the CG model developed in this work and NMA. It was found that F-actin is easily buckled under compressive deformation, and a writhing mode is developed as a result. In addition to the bending and twisting modes, this novel writhing mode of F-actin could also play important roles in the interactions of F-actin with actin-binding proteins and in the force-generation process via polymerization.

Persistence Length of Titin from Rabbit Skeletal Muscles Measured with Scattering and Microrheology Techniques

The persistence length of titin from rabbit skeletal muscles was measured using a combination of static and dynamic light scattering, and neutron small angle scattering. Values of persistence length in the range 9-16 nm were found for titin-II, which corresponds to mainly physiologically inelastic A-band part of the protein, and for a proteolytic fragment with 100-nm contour length from the physiologically elastic I-band part. The ratio of the hydrodynamic radius to the static radius of gyration indicates that the proteins obey Gaussian statistics typical of a flexible polymer in a -solvent. Furthermore, measurements of the flexibility as a function of temperature demonstrate that titin-II and the I-band titin fragment experience a similar denaturation process; unfolding begins at 318 K and proceeds in two stages: an initial gradual 50% change in persistence length is followed by a sharp unwinding transition at 338 K. Complementary microrheology (video particle tracking) measurements indicate that the viscoelasticity in dilute solution behaves according to the Flory/Fox model, providing a value of the radius of gyration for titin-II (63 +/- 1 nm) in agreement with static light scattering and small angle neutron scattering results.

The Elasticity of Individual Titin PEVK Exons Measured by Single Molecule Atomic Force Microscopy

The I-band region of the giant muscle protein titin contains a large domain enriched for the amino acids proline, glutamate, valine, and lysine and is denoted the PEVK domain. The PEVK domain of titin encodes a random coil shown to be an important factor in the passive elasticity of titin. Muscle-specific splicing of 116 PEVK exons encodes this domain. It has been proposed that proline contents determine the elasticity of the PEVK polypeptide, where the individual exons code for "flexibility cassettes." To test this hypothesis, we have measured the elasticity of three distinct polypeptides encoded by individual PEVK exons (161, 120 and 184) that varied greatly in their proline contents (7, 14, and 37% respectively) and total PEVK contents (55, 70, and 87%). We used single molecule atomic force microscopy techniques to measure the persistence length, p, of the engineered PEVK proteins. Surprisingly, all three exons 161, 120, and 184 coded for proteins with similar values of persistence length, p = 0.92 +/- 0.38, 0.89 +/- 0.42, and 0.98 +/- 0.4 nm, respectively. We conclude that the PEVK exons encode polypeptides of similar elastic properties, unrelated to their total PEVK contents. Hence, alternative splicing solely adjusts the length of the PEVK domain of titin.

Calculated phase diagrams for cellulose/ammonia/ammonium thiocyanate solutions in comparison to experimental results

Flory's lattice theory for rigid rod molecules and Kuhn chains is used to calculate phase diagrams for cellulose/ammonia/ammonium thiocyanate solutions. Persistence length values measured by light scattering and reported previously are used as rod length values. Variations in the phase diagram based on varying rod length/solvent composition and cellulose molecular weight are explored. Spinodal curves are calculated in a region of the phase diagram predicting phase separation between two anisotropic solutions. Finally, calculated phase diagrams are compared to published data for the system. Discrepancies between theory and data may be accounted for by soft interactions between cellulose molecules and solvent which are not incorporated into the lattice theory.