Semiflexible Chains at Surfaces: Worm-Like Chains and beyond
Abstract
:1. Introduction
2. The WLC Model: Some Results in 3D and 2D
2.1. Single Chain Properties
2.2. Melt of Worm-Like Chains
2.2.1. Simulations of WLC Melts and Lattice Artifacts
Generalities
Caveats
2.2.2. Two-Dimensional Polymer Melts: Isotropic-Nematic Phase Transition
Flexible Chains
Weak Persistence Length Effects
Strong Persistence Length Effects
2.2.3. Three-Dimensional Polymer Melts: Corrections to Chain Ideality
3. Adsorption of WLC
3.1. Loop and Tail Partition Function
3.2. Reversible Adsorption of an Ideal WLC from Dilute Solution
3.3. Irreversible Chemisorption of a WLC from Dilute Solution
4. Filaments in 2D beyond WLC
4.1. The Helical Filament Squeezed in 2D
4.1.1. A Bit of Mechanics
4.1.2. Thermally-Injected Twist-Kinks and Hyper Flexibility: The Arc/Arc Toy Model
4.1.3. The Free Energy Map
4.2. Emergence of Bistability
4.2.1. Long Range Elasticity and Switchability
4.2.2. Bistability and Cooperativity
4.3. Polymorphic Model of Microtubules
5. Miscellaneous Topics and Outlook
- We restricted our study to adsorption from dilute solution and mentioned that nematic order is expected in very dense solutions or melts. Even if the nematic order is not thermodynamically stable in the bulk, there may be a thin layer of thickness ℓ closest to the wall where orientational order prevails as described in work by Milner [144]. Strong adsorption of WLC in the melt has been simulated recently [145] with a focus on the distribution of loops and tails, layering effects closest to the wall and local mobility.
- We only considered adsorption on undeformable planar surfaces. Biofilaments can deform soft surfaces like membranes to optimize their surface binding [146]; for example, when the orientation for adsorption is not compatible with the in-plane orientation of the preferred curvature. WLCs have to adapt to the curvature of undeformable shells to adsorb, and this can lead to special arrangements as found in [147]. Surfaces bearing fixed obstacles alter the 2D dynamics of a WLC [148,149].
- Another way to fix polymers on a surface is end-grafting, earlier mentioned in the latest stage of irreversible adsorption. One recent simulation work compares single end graft and middle graft WLC in great detail [153], which is related to the distributions of loops and tails discussed above (Section 3.1). The role of stiffness in densely-grafted brushes was considered early by Pickett and Witten [154]. More recently, simulations in the Binder group discuss grafted WLC in the brush regime and the crossover to the dilute surface regime (so-called mushrooms) [155].
- Anisotropic filaments (tapes) with two flexural moduli [156,157] do occur; examples are synthetic ladder polymers or short (rigid) associated polypeptides. Helical polypeptide tapes [158] can reassemble in a hierarchy of structures. Similar associations play a role in amyloid diseases [158]. Mesini and coworkers studied a family of organogelators and report various self-assembled structures, including microtubes [159]. Recently, the adsorption of helical tapes on rigid surfaces was considered by Quint [160].
- It is sometimes argued that the reptation tube can be represented by some transverse (in a first approximation harmonic) potential [161]. The motion of a WLC confined to an effective tube by a transverse harmonic potential was considered by several authors [21,162]. The loosely-related topic of polymers in random media was considered in [163].
- Some larger scale man-made chains can be considered as semiflexible. The mechanics of semiflexible chains formed by poly(ethylene glycol)-linked paramagnetic particles was studied by Gast and coworkers [164] as a function of the length of the poly(ethylene glycol) spacer.
- Concerning the helical filaments squeezed in 2D discussed in Section 4.1, many open questions remain in the specific biological contexts. Open questions pertain also to the nonequilibrium behavior of squeelices: e.g., when they are transported along molecular motor-covered substrates, where they display circular, spiraling or wavy trajectories [165] that are also observed experimentally [112,166].
- The investigation of cooperativity and switchability discussed in Section 4.2 and Section 4.3 has only just began. For instance, there are indications for cooperative binding of molecular motors on microtubules [167], for which cooperative conformational changes in the tubulins may be responsible [131]. The polymorphic switching model discussed in Section 4.3 has so far only been employed to taxol-stabilized microtubules, for which there is the most experimental evidence (as taxol is the main microtubule stabilizer preventing further polymerization/depolymerization). In fact, many other molecules, especially microtubule-associated proteins, may also induce conformational changes of tubulin upon binding with different associated energy gains . This subject deserves further study as a new route for microtubule regulation that goes beyond the regulation of spatial distribution and length (as typically discussed in biology) towards a regulation of their mechanical behavior and response.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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ℓ (nm) | b (nm) | ||
---|---|---|---|
PE (Dodecanol1) | 0.59 | 0.13 | 4.5 |
PIB (Benzene) | 0.59 | 0.26 | 2.3 |
PS (Cyclohexane) | 0.86 | 0.26 | 3.3 |
PDMS (Hexane) | 0.57 | 0.29 | 2 |
NaPSS (high salt) | 1.0 | 0.25 | 4 |
PDADMAC (high salt) | 3.0 | 0.47 | 5.3 |
HA (high salt) | 4–5; 7–10 | 1.0 | 4–5; 7–10 |
d-DNA | 50 | 0.34 | 150 |
IF | 10 | ∼10 | ∼100 |
F-actin | 17 × 10 | 5 | 3400 |
ℓ (nm) | b (nm) | (nm) | (nm) | |
---|---|---|---|---|
PE (dodecanol1) | 0.59 | 0.13 | 0.21 | 1.6 |
PIB (benzene) | 0.59 | 0.26 | 0.34 | 1 |
PS (cyclohexane) | 0.86 | 0.26 | 0.38 | 1.9 |
PDMS (hexane) | 0.57 | 0.29 | 0.36 | 0.90 |
NAPSS (high salt) | 1.0 | 0.25 | 0.39 | 2.5 |
PDADMAC (high salt) | 3.0 | 0.47 | 0.80 | 7.6 |
HA (high salt) | 4–5; 7–10 | 1.0 | 1.6–2 | 12–35 |
d-DNA | 50 | 0.34 | ∼1.8 | ∼ 1.4 × 10 |
IF | 10 | ∼ 10 | ∼46 | ∼ 2 × 10 |
F-actin | 17 × 10 | 5 | ∼75 | 3 × 10 |
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Baschnagel, J.; Meyer, H.; Wittmer, J.; Kulić, I.; Mohrbach, H.; Ziebert, F.; Nam, G.-M.; Lee, N.-K.; Johner, A. Semiflexible Chains at Surfaces: Worm-Like Chains and beyond. Polymers 2016, 8, 286. https://doi.org/10.3390/polym8080286
Baschnagel J, Meyer H, Wittmer J, Kulić I, Mohrbach H, Ziebert F, Nam G-M, Lee N-K, Johner A. Semiflexible Chains at Surfaces: Worm-Like Chains and beyond. Polymers. 2016; 8(8):286. https://doi.org/10.3390/polym8080286
Chicago/Turabian StyleBaschnagel, Jörg, Hendrik Meyer, Joachim Wittmer, Igor Kulić, Hervé Mohrbach, Falko Ziebert, Gi-Moon Nam, Nam-Kyung Lee, and Albert Johner. 2016. "Semiflexible Chains at Surfaces: Worm-Like Chains and beyond" Polymers 8, no. 8: 286. https://doi.org/10.3390/polym8080286