Unconventional Salt Trend from Soft to Stiff in Single Neurofilament

pubs.acs.org/Langmuir © 2010 American Chemical Society

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Unconventional Salt Trend from Soft to Stiff in Single Neurofilament Biopolymers Roy Beck,*,†,‡,# Joanna Deek,§ Myung Chul Choi,†,‡,3 Taiji Ikawa, Osamu Watanabe, Erwin Frey,^ Philip Pincus,† and Cyrus R. Safinya*,†,‡

Departments of Materials and Physics, ‡ Department of Molecular, Cellular, and Developmental Biology, and § Department of Chemistry and Biochemistry, University of California;Santa Barbara, Santa Barbara, California 93106, United States, Toyota Central R&D Laboratories, Inc., Nagakute, Aichi 480-1192, Japan, and ^Department of Physics, Ludwig Maximilians Universit€ at M€ unchen, M€ unchen, Germany. # Current address: School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel. 3 Current address: Department of Bio and Brain Engineering, KAIST, 305-701 Daejeon, Korea )

†

Received September 12, 2010. Revised Manuscript Received November 9, 2010 We present persistence length measurements on neurofilaments (NFs), an intermediate filament with protruding side arms, of the neuronal cytoskeleton. Tapping mode atomic force microscopy enabled us to visualize and trace at subpixel resolution photoimmobilized NFs, assembled at various subunit protein ratios, thereby modifying the side-arm length and chain density charge distribution. We show that specific polyampholyte sequences of the side arms can form saltswitchable intrafilament attractions that compete with the net electrostatic and steric repulsion and can reduce the total persistence length by half. The results are in agreement with present X-ray and microscopy data yet present a theoretical challenge for polyampholyte interchain interactions.

Introduction Bending charged polymers has been the subject of intense debate for the past half century mainly because of the complexity of the problem and its high relevancy in both industrial and biological systems. For example, much interest recently has focused on conditions for encapsulating highly negatively charged DNA inside a viral capsid.1 A measure of the polymer bending modulus is the polymer persistence length (Lp), which is the length scale beyond which thermal fluctuations dominate the polymer configuration and the polymer loses its directional “memory”. It is generally agreed that in the case of charged polymers the total Lp increases as a result of long-range electrostatic repulsive interactions between the monomers. In such cases, Lp is strongly dependent on the ionic strength of the surrounding buffer and the net charge of the polymer.2-5 For polymers with bottlebrush geometry, it is important to take into account the steric repulsion from nearby brushes that generally do not interpenetrate.6 Effectively, the brushes behave to thicken the backbone and thus *Corresponding authors. E-mail: [email protected]; [email protected] (1) Evilevitch, A.; Gober, J. W.; Phillips, M.; Knobler, C. M.; Gelbart, W. M. Measurements of DNA lengths remaining in a viral capsid after osmotically suppressed partial ejection. Biophys. J. 2005, 88, 751–756. (2) Skolnick, J.; Fixman, M. Electrostatic persistence length of a wormlike polyelectrolyte. Macromolecules 1977, 10, 944–948. (3) Odijk, T. Polyelectrolytes near rod limit. J. Polym. Sci., Part B: Polym. Phys. 1977, 15, 477–483. (4) Ha, B. Y.; Thirumalai, D. Electrostatic persistence length of a polyelectrolyte chain. Macromolecules 1995, 28, 577–581. (5) Barrat, J. L.; Joanny, J. F. Persistence length of polyelectrolyte chains. Europhys. Lett. 1993, 24, 333–338. (6) Israelachvili, J. Intermolecular and Surface Forces; Academic Press: San Diego, CA, 1985. (7) Landau, L. D.; Lifshitz, E. M. Theory of Elasticity; Pergamon Press: Oxford, England, 1970. (8) Marenduzzo, D.; Micheletti, C. Thermodynamics of DNA packaging inside a viral capsid: the role of DNA intrinsic thickness. J. Mol. Biol. 2003, 330, 485–492. (9) Feuz, L.; Leermakers, F. A. M.; Textor, M.; Borisov, O. Bending rigidity and induced persistence length of molecular bottle brushes: A self-consistent-field theory. Macromolecules 2005, 38, 8891–8901.

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stiffen it.7-9 Furthermore, it has been theoretically suggested that the total Lp should scale as the brush height for semiflexible bottlebrush polymers.9 Therefore, for a charged bottlebrush a delicate balance between the steric and electrostatic interactions determines the rigidity of the backbone. Polyampholyte interactions are generally more complicated to characterize because of the added effect of short-range electrostatic attractions.10 The polymer’s charge distribution and its net charge affect the polymer’s statistical-mechanical properties and preferred configurations.10,11 Although extremely relevant to biophysical materials, because of its greater complexity, it is not surprising that the combined case of a polyampholyte bottlebrush has been explored only for specialized cases. Cell cytoskeletal networks are composed of three types of filaments: actin filaments, microtubules, and intermediate filaments, each with an average diameter of 8, 25, and 10 nm, respectively. The class of intermediate filaments is dependent on the cell type. Neurofilaments (NF) belong to the class of neuronal intermediate filaments, expressed mainly in the dendrites and axons of vertebrates. Three different subunit proteins [NF-L (62 kDa), NF-M (103 kDa), and NF-H (117 kDa)] assemble with a distinct composition to form the mature NF biopolymer (Figure 1A). In vivo, the three subunit proteins exhibit sequence homology and structural similarity, characterized by the presence of three contiguous domains: the N-terminus domain that forms a globular unstructured head (∼80-100 residues), the R-helical hydrophobic domain (∼300 residues), and an intrinsically unstructured highly charged C-terminus domain, also known as the side arm (Figure 1B). The dissimilarity between the subunit proteins lies in the side arms, each differing in length, net charge, (10) Kantor, Y.; Li, H.; Kardar, M. Conformations of polyampholytes. Phys. Rev. Lett. 1992, 69, 61–64. (11) Dobrynin, A. V.; Rubinstein, M. Flory theory of a polyampholyte chain. J. Phys. II 1995, 5, 677–695.

Published on Web 11/17/2010

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Figure 1. (A) Illustration of a single filament (not to scale), including an undulating core and the three constituent subunits, whose unstructured C-termini extend radially from the filament core. The inset depicts interacting segments from adjacent side arms bridging the 22.5 nm spacing, highlighting the polyampholytic nature of the side arm sequences. (B) Each subunit protein is composed of three structural domains: an unstructured head, an R-helical body, and an unstructured charged side-arm domain of variable length. The R-helical domains self-assemble through coiled-coil interactions to form the filament core. In healthy adult neurons, the subunit stoichiometry is 7:3:2 NF-L/NF-M/NF-H mol %.

phosphorylation state, and charge distribution.12,13 The presence of a hydrophobic R-helical domain drives the formation of dimers (with NF-L being an obligate component), which proceed to multimerize further into half-staggered coiled coils. An average NF cross section is composed of a nearly charge-neutral hydrophobic core, with 16 side arms radiating away from the backbone every 22.5 nm (Figure 1 A).12-14 These side arms are polyampholytic in nature, containing both negatively and positively charged residues. For a healthy phosphorlayted NF, the side arms are net negatively charged, though about a third of the residues are positively charged at physiological pH. As one of the largest fractions of proteins in the axon, NF aggregation behavior has been studied since the early work of Alzheimer.15 Studies indicate a relationship between aberrations in NF network structure and neurodegenerative motor neuron diseases such as amyotrophic lateral sclerosis, Lewy-body-based dementia, and Parkinson’s Disease.16-20 Interactions between NFs are key regulators of axonal cytoskeleton structure and function.12,14,16-21 Therefore, factors that counter proper assembly have immediate biological relevance in terms of cytoskeletal density, organelle transport, and axon (12) Janmey, P. A.; Leterrier, J. F.; Herrmann, H. Assembly and structure of neurofilaments. Curr. Opin. Colloid Interface Sci. 2003, 8, 40–47. (13) Herrmann, H.; Aebi, U. Intermediate filaments: molecular structure, assembly mechanism, and integration into functionally distinct intracellular scaffolds. Annu. Rev. Biochem. 2004, 73, 749–789. (14) Hirokawa, N. Molecular architecture and dynamics of the neural cytoskelecton. In The Neuronal Cytoskeleton; Burgoyne, R. D., Ed.; Wiley-Liss: New York, 1991; pp 5-74. (15) Alzheimer, A. Neurolisches Zentralblatt 1906, 25, 1134. (16) Fuchs, E.; Cleveland, D. W. A structural scaffolding of intermediate filaments in health and disease. Science 1998, 279, 514–519. (17) Brownlees, J.; Ackerley, S.; Grierson, A. J.; Jacobsen, N. J. O.; Shea, K.; Anderton, B. H.; Leigh, P. N.; Shaw, C. E.; Miller, C. C. J. Charcot-Marie-Tooth disease neurofilament mutations disrupt neurofilament assembly and axonal transport. Hum. Mol. Genet. 2002, 11, 2837–2844. (18) Liu, Q.; Xie, F.; Siedlak, S. L.; Nunomura, A.; Honda, K.; Moreira, P. I.; Zhua, X.; Smith, M. A.; Perry, G. Neurofilament proteins in neurodegenerative diseases. Cell. Mol. Life Sci. 2004, 61, 3057–3075. (19) Hirano, A.; Donnenfeld, H.; Sasaki, S.; Nakano, I. Fine-structural observations of neurofilamentous changes in amyotrophic lateral sclerosis. J. Neuropathol. Exp. Neurol. 1984, 43, 461–470. (20) Miller, C. C. J.; Ackerley, S.; Brownlees, J.; Grierson, A. J.; Jacobsen, N. J. O.; Thornhill, P. Axonal transport of neurofilaments in normal and disease states. Cell. Mol. Life Sci. 2002, 59, 323–330. (21) Herrmann, H.; Aebi, U. Intermediate filament assembly: fibrillogenesis is driven by decisive dimer-dimer interactions. Curr. Opin. Struct. Biol. 1998, 8, 177–185. (22) Beck, R.; Deek, J.; Jones, J. B.; Safinya, C. R. Gel-expanded to gelcondensed transition in neurofilament networks revealed by direct force measurements. Nat. Mater. 2010, 9, 40–46.

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diameter. Most NF studies conducted so far have focused on their behavior in the condensed state, which is governed by interfilament interactions.22-28 Rammnesee et al. measured native NF hydrogel rheological properties and found that higher monovalent salt concentrations lower the gel storage modulus, though the molecular basis of this phenomenon remains unclear.29 Recently, Lin et al. measured the rheological properties of NF gels and showed that divalent salt alters their properties, presumably because of side-arm attraction and cross bridging between negatively charged residues and the divalent ion.23 However, as mentioned before, a large portion of the side-arm residues have a positive charge; therefore, spontaneous cross bridging between residues of opposite charge is possible and does not require multivalent ions.22,30 Moreover, a recent study showed that a high-protein-density hydrogel undergoes an isotropic-to-nematic phase transition depending on the protein subunit ratio and the monovalent salt content.31 To the best of our knowledge, only a limited number of studies experimentally measured the native single NF properties.14,32-34 Here, for the first time, we measure the singlefilament properties while altering the subunit protein composition and monovalent salt concentration. This study is targeted at measuring how different side arms (e.g., from different subunit proteins) self-interact spontaneously with their neighbors along the same filament via electrostatic and entropic interactions. Though the propensity for intrafilament interactions has previously been suggested,35 theoretical studies have thus far neglected these interactions as well as NF backbone undulations. In this letter, we experimentally measured, for the first time, the effect of different subunit protein ratios and monovalent salt concentrations (cs) on the single-filament’s bending modulus. The results indicate that apparent filament configurations are strongly dependent on the subunit ratio and can effectively vary Lp by 2-fold. Surprisingly, stiffer filaments are those with lower net charge and shorter side arms, in disagreement with polyelectrolyte polymer theories.2-5 These results demonstrate that NF, as (23) Lin, Y. C.; Yao, N. Y.; Broedersz, C. P.; Herrmann, H.; MacKintosh, F. C.; Weitz, D. A. Origins of elasticity in intermediate filament networks. Phys. Rev. Lett. 2010, 104, 5. (24) Hesse, H. C.; Beck, R.; Ding, C.; Jones, J. B.; Deek, J.; MacDonald, N. C.; Li, Y.; Safinya, C. R. Direct imaging of aligned neurofilament networks assembled using in situ dialysis in microchannels. Langmuir 2008, 24, 8397–8401. (25) Zhulina, E. B.; Leermakers, F. A. M. Effect of the ionic strength and pH on the equilibrium structure of a neurofilament brush. Biophys. J. 2007, 93, 1452– 1463. (26) Zhulina, E. B.; Leermakers, F. A. M. The polymer brush model of neurofilament projections: effect of protein composition. Biophys. J. 2010, 98, 462–469. (27) Zhulina, E. B.; Leermakers, F. A. M. A self-consistent field analysis of the neurofilament brush with amino-acid resolution. Biophys. J. 2007, 93, 1421–1430. (28) Leermakers, F. A. M.; Zhulina, E. B. Self-consistent field modeling of the neurofilament network. Biophys. Rev. Lett. 2008, 3, 459–489. (29) Rammensee, S.; Janmey, P.; Bausch, A. Mechanical and structural properties of in vitro neurofilament hydrogels. Eur. Biophys. J. 2007, 36, 661–668. (30) Leterrier, J. F.; Kas, J.; Hartwig, J.; Vegners, R.; Janmey, P. A. Mechanical effects of neurofilament cross-bridges. Modulation by phosphorylation, lipids, and interactions with F-actin. J. Biol. Chem. 1996, 271, 15687–15694. (31) Jones, J. B.; Safinya, C. R. Interplay between liquid crystalline and isotropic gels in self-assembled neurofilament networks. Biophys. J. 2008, 95, 823–835. (32) Dalhaimer, P.; Wagner, O. I.; Leterrier, J. F.; Janmey, P. A.; ArandaEspinoza, H.; Discher, D. E. Flexibility transitions and looped adsorption of wormlike chains. J. Polym. Sci., Part B: Polym. Phys. 2005, 43, 280–286. (33) Wagner, O. I.; Rammensee, S.; Korde, N.; Wen, Q.; Leterrier, J. F.; Janmey, P. A. Softness, strength and self-repair in intermediate filament networks. Exp. Cell Res. 2007, 313, 2228–2235. (34) Hirokawa, N.; Glicksman, M.; Willard, M. Organization of mammalian neurofilament polypeptides within the neuronal cytoskeleton. J. Cell Biol. 1984, 98, 1523–1536. (35) Gou, J. P.; Gotow, T.; Janmey, P. A.; Leterrier, J. F. Regulation of neurofilament interactions in vitro by natural and synthetic polypeptides sharing Lys-Ser-Pro sequences with the heavy neurofilament subunit NF-H: Neurofilament crossbridging by antiparallel sidearm overlapping. Med. Biol. Eng. Comput. 1998, 36, 371–387.

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Figure 2. (A, C-G) AFM height scans of NFs partially embedded in an azopolymer surface (∼2 μg/mL). Contour tracing is shown by black markers. Summit locations (A) as obtained from fitting the tangent cross sections to a Gaussian (B). (G) At high concentration (0.1 mg/mL), NFs interact and form networks. Scale bars are 200 nm.

recently proposed, interacts via attractive ionic cross bridging of the polyampholyte side arms.22 Our results demonstrate that the attractive cross-bridging interaction is sensitive to the side arm’s sequence and length, leading to an unconventional salt-dependent relationship between soft and stiff filaments.

Materials and Methods Protein Purification and Assembly. NF subunit proteins are

purified from bovine spinal cord as explained elsewhere.22,31 After purification, subunits were mixed in the desired ratios and assembled at 2 mg/mL by dialysis against assembly buffer (100 mM MES, 150 mM NaCl, 1 mM MgCl2, 1 mM EGTA, and 3 mM NaN3 at pH 6.8) for 36 h at 36 C. Then the filaments were diluted to a final concentration of ∼2 μg/mL using different ratios of assembly buffer and 1 mM MgCl2, thereby maintaining a constant divalent salt concentration throughout all experiments. Surface Immobilization. To attain high-resolution NF imaging with minimum surface interaction and without staining, we employed an immobilization technique recently developed and used for protein imaging using atomic force microscopy (AFM).36,37 Here, we layered NFs on top of a spin-coated photosensitive polymer layer containing an azobenzene group (azopolymer). The azopolymer, poly[40-[[[2-(methacryloyloxy) ethyl]ethyl] amino]-4-cyanoazobenzene-co-methyl methacrylate] (15 mol % azobenzene moiety, 25 000 mol wt) was obtained by free-radical polymerization. In the fully hydrated state, the proteins were partially embedded into the liquefied azopolymer during a 30 min, 10 mW/cm2 LED blue light (wavelength 470 nm) radiation treatment. During (36) Ikawa, T.; Hoshino, F.; Watanabe, O.; Li, Y.; Pincus, P.; Safinya, C. R. Molecular scale imaging of F-actin assemblies immobilized on a photopolymer surface. Phys. Rev. Lett. 2007, 98, 018101. (37) Ikawa, T.; Hoshino, F.; Matsuyama, T.; Takahashi, H.; Watanabe, O. Molecular-shape imprinting and immobilization of biomolecules on a polymer containing azo dye. Langmuir 2006, 22, 2747–2753.

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photoirradiation, the photoisomerization motion of the azobenzene group and the resultant photoplasticization of the polymer matrix lead to a deformation of the polymer surface along the contour of NF surfaces, thus immobilizing them at the desired monovalent salt concentration upon removal of the blue light.36,37 Subsequently, the excess immobilized proteins were removed and the film was dried to achieve maximum resolution while imaging. The choice of azopolymer was driven by the intent to minimize surface interactions with NFs, though not completely excluding their occurrence. The most prominent surface interaction is hydrophobic, which by nature is weak and contributes to all explored experimental conditions equally. AFM Imaging. Samples were measured in tapping mode using an Asylum MFP-3D AFM. NFs were imaged in tiles of 5  5 μm2 at 2 Hz/line and a 1024  1024 resolution using AC-160TS Olympus tips (Figure 2). Imaged reconstituted NFs have the well-known characteristic of 2 nm height, 50 width, 50 nm repeated beaded structure along the backbone, and a relatively short contour length in comparison to that of native NFs.14,34,38 Using the fact that AFM imaging also provides sample topography information, the bundling of filaments can easily be identified as “wider” or “taller” from the expected average values. Measurements were carried out at very dilute concentrations to avoid filament aggregation, and prior to further analysis, we filtered out all of the filaments that did not meet the expected topographic values within 30% error.

Results and Discussion Using a semiautomated tracing algorithm, we have measured over 2000 NFs at different side-arm ratios and cs values. The tracing algorithm fits their backbone tangent cross sections to a (38) Mucke, N.; Kirmse, R.; Wedig, T.; Leterrier, J. F.; Kreplak, L. Investigation of the morphology of intermediate filaments adsorbed to different solid supports. J. Struct. Biol. 2005, 150, 268–276.

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Figure 3. (A) Radial distribution function data of NF-L homopolymers for 48 mM monovalent salt and 1 mM MgCl2 with a fit to eq 1. (B) Fit quality, χ2, at different estimated Lp values for the same conditions as in plot A. (C) Data collapse of all sample conditions on eq 1. All samples were measured under the specified monovalent salt concentration and 1 mM MgCl2.

Gaussian (Figure 2B) and iteratively locates the summits,39 with subpixel resolution, at equally spaced distances. As evidence of the robustness of the technique, we note that all filaments used in this study had small variances in their filament geometric features (height, width, and total length). For a flexible polymer, the Lp can be measured from statistical analysis of the configurational ensemble. For polymers restricted to 2D having a contour length of L ≈ Lp, the end-to-end distribution function (ree) is40 2

3 1 l þ 2 6 7 47 GðxÞ ¼ A e - ½1þð1=4Þ =2x D3=2 6 42 1=2 5 5=4 l 2x l ¼ 0 ð2xÞ 2 l! ¥ X ð2l - 1Þ!

ð1Þ

Here, D3/2 is a parabolic cylinder function and x = (LP/L)[1 (ree/L)]. This series decays rapidly and can be approximated using the first two terms. The function is universal and, through the factor A = N [1 - (xL/Lp)], weakly dependent on the polymer length, where N is a normalization factor. Using subpixel resolution tracing, we find ree and L for each traced filament. To evaluate Lp, we iteratively bin the data of a certain condition (i.e., subunit composition and buffer salt concentration) to the dimensionless parameter x and fit it to the universal relation in eq 1 with A as a single fitting parameter. In each iterative step, we evaluate the fit’s quality using the χ2 variable. The evaluated Lp is determined when χ2 is iteratively minimized (Figure 3). The resultant trends and absolute values are in qualitative agreement with the standard tangent-tangent correlation function analysis though this analysis is more accurate for these filament lengths. The main results of this letter are summarized in Figure 4. It is clearly shown that our subpixel-resolution measurements are sensitive to changes in the apparent measured configuration, allowing systematic observations of around 2-fold variance in (39) Wiggins, P. A.; van der Heijden, T.; Moreno-Herrero, F.; Spakowitz, A.; Phillips, R.; Widom, J.; Dekker, C.; Nelson, P. C. High flexibility of DNA on short length scales probed by atomic force microscopy. Nat. Nano 2006, 1, 137–141. (40) Wilhelm, J.; Frey, E. Radial distribution function of semiflexible polymers. Phys. Rev. Lett. 1996, 77, 2581–2584.

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Lp. We start to review the results with the simplest assembled geometry: homopolymer NF-L composed of only one type of side arm. The NF-L side-arm net charge is -45e at neutral pH and has the largest linear charge density among the three different subunit proteins. However, as shown in Figure 4, Lp decreases by 2-fold upon lowering the monovalent salt concentration from 240 to 48 mM. This result is opposite in trend to the expected polyelectrolyte behavior predicting polymer softening via the screening of long-ranged electrostatic repulsion with the addition of salt.2-5 Here we propose side-arm-side-arm attractions at low cs leading to energetically favorable bends in the backbone (Figure 1) to lower the total Lp. High cs breaks these ionic bonds and leads to a larger Lp. Next, we consider the effect of replacing some NF-L subunits with higher-molecular-weight subunit proteins, NF-M and/or NF-H, that have a larger net charge in the fully phosphorylated state (-92.4e and -93.4e for NF-M and NF-H, respectively). Here, the general trend is different at low (48 mM) and high (240 mM) monovalent salt concentrations for NF-M and NF-H subunit proteins. Replacing the short (NF-L) side arm with NF-H has relatively little effect on Lp (Figure 4B), implying that the aforementioned side-arm intrafilament interaction between NF-L and NF-L subunits dominates. In complete contrast, replacing NF-L with the NF-M subunit protein (Figure 4A) results in more classical polyelectrolyte behavior, whereby increasing cs leads to smaller Lp. This suggests that the NF-L-NF-L interaction dominates the NF-L homopolymer and that the NF-LH copolymer (having both NF-L and NF-H subunits) filaments are disrupted in the presence of NF-M side arms. Unexpectedly, replacing NF-L with NF-M at high salt concentration (240 mM) softens the filaments, though the latter is the longer, more highly charged side arm. These results clearly demonstrate that a classical polyelectrolyte interpretation of NF behavior, involving the projection of side-arm charges on the backbone,41 fails to explain our experimental (41) Kumar, S.; Yin, X. H.; Trapp, B. D.; Hoh, J. H.; Paulaitis, M. E. Relating interactions between neurofilaments to the structure of axonal neurofilament distributions through polymer brush models. Biophys. J. 2002, 82, 2360–2372.

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Figure 4. Total Lp vs mol % of subunits with long side arms at different monovalent salt concentrations (cs) and 1 mM MgCl2 derived from contour tracing and fitting to eq 1. Measurements on copolymer (A) NF-LM and (B) NF-LH filaments. The data point for the highest ratio (41 mol %) of long side arms in both plots represents the physiological ternary subunit mixture of NF-LMH 7:3:2 mol %.

findings. We also show that the subunit protein ratio can extensively affect the available filament configuration. Previous exploration of the side-arm amino acid sequence22 has revealed the susceptibility for attractive forces to exist between opposite side arms (via electrostatic ionic bridging, shown schematically in the inset of Figure 1A). Therefore, although all side arms have a net negative charge, among the charged residues 21, 34, and 38% are positively charged for NF-L, NF-M, and NF-H, respectively. This polyampholytic nature of the side arms has been attributed to attractive interactions arising upon assembly, at high NF density, to a hydrogel form.22,24 Therefore, the total Lp of an NF must be composed of components with competing forces, including an attractive force between side arms. We can estimate Lp to be composed of Lp ¼ Lbp þ Lep ðcs , qÞ þ Lsp ðhÞ - Lhs p ðΔE, hÞ

ð2Þ

Here, Lbp is the bare persistence length derived from the backbone, Lep is the net charge electrostatic component, stretching the filament with added charge (q) and lower cs,2-5 and Lsp is the steric component of the side arm,9 which is proportional to the sidearm height (h). The last component, Lhs p , is the attractive component resulting from handshaking between the polyampholyte side arms. The energy gain from aligning the side arms in an antiparallel configuration, ΔE, was recently estimated and was shown to be very different for the three different subunit proteins.22 Therefore, it is not surprising that Lhs p differs upon substituting NF-M (more repulsive at the tips of its side arms) with NF-H (more attractive at the tips), resulting in a shorter Lp at a low monovalent salt concentration.22 Therefore, its origin is different from the conventional ionic bridging of multivalent salts seen in many biopolymers.23,42-44 In addition, Lhs p must be correlated to the (42) Rau, D. C.; Parsegian, V. A. Direct measurement of the intermolecular forces between counterion-condensed DNA double helices - evidence for longrange attractive hydration forces. Biophys. J. 1992, 61, 246–259. (43) Needleman, D. J.; Ojeda-Lopez, M. A.; Raviv, U.; Miller, H. P.; Wilson, L.; Safinya, C. R. Higher-order assembly of microtubules by counterions: From hexagonal bundles to living necklaces. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 16099–16103. (44) Koltover, I.; Wagner, K.; Safinya, C. R. DNA condensation in two dimensions. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 14046–14051. (45) Diamant, H.; Andelman, D. Binding of molecules to DNA and other semiflexible polymers. Phys. Rev. E 2000, 61, 6740–6749.

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side arm’s extension from the backbone (h). To effectively bend the backbone, two side arms anchored 22.5 nm apart along the backbone must interact with sufficient overlap. Bridging the gap limits possible interactions at high salt concentration for the short collapsed NF-L side arms yet raises the probability at low salt concentration. The attractive mechanism and the apparent softening of the filament are similar in concept to studying the binding of molecules to DNA45 and are in agreement with studies on condensed gel NFs probing the attraction between filaments with an interfilament spacing above 40 nm.12,14,22,24,31

Conclusions We measured the correlation between the total Lp of NFs, reassembled under different subunit protein ratios and monovalent salt conditions. We find that the backbone filament configurations are softer and more bent with the addition of long side arms, NF-H or NF-M. In addition, we find that the effect of monovalent salt, in the range studied (48-240 mM), strongly depends on the subunit composition. We find that for the NF-L homopolymer, a lower salt concentration results in a softer filament, with an opposing trend for the NF-LM copolymer. Moreover, NF-H subunits have little effect on Lp. These results are in agreement with recent X-ray data22 showing different interactions between NF subunit proteins and suggest that in NF networks the competition between intra- and interfilament interactions plays a role . We explained our results in terms of the competition between the entropic repulsion of nearby side arms and their association propensity through electrostatic ionic bridging. These results shed light on the competing forces when NF self-assembles in vivo and pose a challenge for current theoretical polymer physics. Acknowledgment. We thank A. Parsegian, K. Ewert, M. Kardar, R. Bruinsma, R. Podgornik, Y. Li, and E. Zhulina for discussions. Special thanks goes to P. A. Wiggins for the basic tracing algorithm. AFM experiments were conducted in the Microscopy & Microanalysis Facility of the UCSB MRL (supported by NSFMRSEC). C.R.S, J.D., and M.C.C. were supported by DOE-BES DE-FG-02-06ER46314 (protein purification and NF monolayer characterization) and NSF DMR-0803103 (NF composition phase behavior). P.P was supported by NSF-DMR-0803103. R.B. was supported by the HFSP organization and in part by DOE-BES.

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