# Semi-Flexible dense polymer brushes in flow – Simulation & Theory (Update)

A talk given at the Institute of Physical Chemistry in Cologne on June 1st 2015.

This talk includes an updated version of the theoretical part to become consistent with our final theoretical model published in EPL 109, 68001 (2015)!

#### Abstract

The response of dense brushes of semi-flexible polymers to flow is of great interest in both technological and biological contexts. Examples include the glycocalyx on the endothelial surface layer in blood vessels [S. Weinbaum et al., Annu. Rev. Biomed. Eng. 9, 121–167, 2007] and mucus-like layers in lungs or the interior of nuclear pores. We employ smoothed dissipative particle dynamics (SDPD) [P. Espanol, M. Revenga, Phys. Rev. E 67, 026705, 2003] simulations to study semi-flxible polymer brushes for a wide range of conditions including grafting density, polymer elasticity, and shear stress due to flow. Our simulation results are in good agreement with previous studies [Y.W. Kim et al., Macromolecules 42, 3650–3655, 2009], which focused on brushes with low grafting densities. We also propose a theoretical model which describes the deformation of dense semi-flexible polymer brushes in shear flow for a wide parameter range. The model allows us to predict effective deformation (height), inner density profile and hydrodynamic penetration depth (solvent velocity proﬁle). Therefore, it is suitable to predict the effect of grafted surfaces on the flow profile in a slit or tube. The work was recently published [F. Römer, D.A. Fedosov, EPL 109, 68001 ,2015].

#### Cited publications

• K. Binder, T. Kreer, and A. Milchev, “Polymer brushes under flow and in other out-of-equilibrium conditions” Soft Matter 7, 7159-7172 (2011). doi:10.1039/C1SM05212H
[BibTeX] [Abstract]

Polymer brushes are formed from flexible linear macromolecules tethered at one chain end to a solid substrate{,} forming a dense polymeric layer of polymer chains which are more or less stretched in the direction perpendicular to the substrate surface. These systems find interest also due to numerous applications (colloid stabilization{,} improvement of lubrication properties when the surfaces are exposed to shear{,} protection of the surface against adsorption of nanoparticles or proteins{,} etc.){,} for which often the dynamic non-equilibrium response of these brushes to external perturbation is important. The present review summarizes recent computer simulation studies pertinent to these questions. Polymer brushes exposed to shear due to flow of the solvent or a polymer melt the brush interacts with are discussed{,} and the friction between two brushes is discussed. Another topic that is emphasized is the interaction of polymer brushes with {“}nanoinclusions{“} (i.e.{,} small colloidal particles or linear macromolecules down to oligomers){,} discussing the absorption or expulsion of these objects{,} and again the response to shear. The simulations are interpreted in terms of scaling concepts and other phenomenological theories wherever possible{,} and an outlook to related experiments is given.

@Article{Binder2011,
Title = {Polymer brushes under flow and in other out-of-equilibrium conditions},
Author = {Binder, Kurt and Kreer, Torsten and Milchev, Andrey},
Journal = {Soft Matter},
Year = {2011},
Pages = {7159-7172},
Volume = {7},
Abstract = {Polymer brushes are formed from flexible linear macromolecules tethered at one chain end to a solid substrate{,} forming a dense polymeric layer of polymer chains which are more or less stretched in the direction perpendicular to the substrate surface. These systems find interest also due to numerous applications (colloid stabilization{,} improvement of lubrication properties when the surfaces are exposed to shear{,} protection of the surface against adsorption of nanoparticles or proteins{,} etc.){,} for which often the dynamic non-equilibrium response of these brushes to external perturbation is important. The present review summarizes recent computer simulation studies pertinent to these questions. Polymer brushes exposed to shear due to flow of the solvent or a polymer melt the brush interacts with are discussed{,} and the friction between two brushes is discussed. Another topic that is emphasized is the interaction of polymer brushes with {"}nanoinclusions{"} (i.e.{,} small colloidal particles or linear macromolecules down to oligomers){,} discussing the absorption or expulsion of these objects{,} and again the response to shear. The simulations are interpreted in terms of scaling concepts and other phenomenological theories wherever possible{,} and an outlook to related experiments is given.},
Doi = {10.1039/C1SM05212H},
Issue = {16},
Publisher = {The Royal Society of Chemistry}
}

• H. C. Brinkman, “A Calculation of the Viscous Force Excerted by a Flowing Fluid on a Dens Swarm of Particles” Appl. Sci. Res. A1 A1, 27 (1947).

A calculation is given of the viscous force, exerted by a flowing fluid on a dense swarm of particles. The model underlying these calculations is that of a spherical particle embedded in a porous mass. The flow through this porous mass is decribed by a modification of Darcy’s equation. Such a modification was necessa’ry in order to obtain consistent boundary conditions. A relation between permeability and particle size and density is obtained. Our results are compared with an experimental relation due to Carman.

@Article{Brinkman,
Title = {A Calculation of the Viscous Force Excerted by a Flowing Fluid on a Dens Swarm of Particles},
Author = {Brinkman, H. C.},
Journal = {Appl. Sci. Res. A1},
Year = {1947},
Pages = {27},
Volume = {A1},
Abstract = {A calculation is given of the viscous force, exerted by a flowing fluid on a dense swarm of particles. The model underlying these calculations is that of a spherical particle embedded in a porous mass. The flow through this porous mass is decribed by a modification of Darcy's equation. Such a modification was necessa'ry in order to obtain consistent boundary conditions. A relation between permeability and particle size and density is obtained. Our results are compared with an experimental relation due to Carman.},
Url = {http://dns2.asia.edu.tw/~ysho/YSHO-English/1000%20CE/PDF/App%20Sci%20Res%20Sec%20A1,%2027.pdf}
}

• B. Button, L. Cai, C. Ehre, M. Kesimer, D. B. Hill, J. K. Sheehan, R. C. Boucher, and M. Rubinstein, “A Periciliary Brush Promotes the Lung Health by Separating the Mucus Layer from Airway Epithelia” Science 337, 937-941 (2012). doi:10.1126/science.1223012
[BibTeX] [Abstract]

Mucus clearance is the primary defense mechanism that protects airways from inhaled infectious and toxic agents. In the current gel-on-liquid mucus clearance model, a mucus gel is propelled on top of a “watery” periciliary layer surrounding the cilia. However, this model fails to explain the formation of a distinct mucus layer in health or why mucus clearance fails in disease. We propose a gel-on-brush model in which the periciliary layer is occupied by membrane-spanning mucins and mucopolysaccharides densely tethered to the airway surface. This brush prevents mucus penetration into the periciliary space and causes mucus to form a distinct layer. The relative osmotic moduli of the mucus and periciliary brush layers explain both the stability of mucus clearance in health and its failure in airway disease.

@Article{Button2012,
Title = {A Periciliary Brush Promotes the Lung Health by Separating the Mucus Layer from Airway Epithelia},
Author = {Button, Brian and Cai, Li-Heng and Ehre, Camille and Kesimer, Mehmet and Hill, David B. and Sheehan, John K. and Boucher, Richard C. and Rubinstein, Michael},
Journal = {Science},
Year = {2012},
Number = {6097},
Pages = {937-941},
Volume = {337},
Abstract = {Mucus clearance is the primary defense mechanism that protects airways from inhaled infectious and toxic agents. In the current gel-on-liquid mucus clearance model, a mucus gel is propelled on top of a “watery” periciliary layer surrounding the cilia. However, this model fails to explain the formation of a distinct mucus layer in health or why mucus clearance fails in disease. We propose a gel-on-brush model in which the periciliary layer is occupied by membrane-spanning mucins and mucopolysaccharides densely tethered to the airway surface. This brush prevents mucus penetration into the periciliary space and causes mucus to form a distinct layer. The relative osmotic moduli of the mucus and periciliary brush layers explain both the stability of mucus clearance in health and its failure in airway disease.},
Doi = {10.1126/science.1223012},
Eprint = {http://www.sciencemag.org/content/337/6097/937.full.pdf}
}

• C. -M. Chen and Y. -A. Fwu, “Monte Carlo simulations of polymer brushes” Phys. Rev. E 63, 11506 (2000). doi:10.1103/PhysRevE.63.011506
[BibTeX]
@Article{Chen2000,
Title = {Monte Carlo simulations of polymer brushes},
Author = {Chen, C.-M. and Fwu, Y.-A.},
Journal = {Phys. Rev. E},
Year = {2000},
Pages = {011506},
Volume = {63},
Doi = {10.1103/PhysRevE.63.011506},
Issue = {1},
Numpages = {10},
Publisher = {American Physical Society}
}

• R. G. Cox, “The motion of long slender bodies in a viscous fluid Part 1. General theory” J. Fluid Mech. 44, 791–810 (1970). doi:10.1017/S002211207000215X
[BibTeX] [Abstract]

ABSTRACT A solid long slender body is considered placed in a fluid undergoing a given undisturbed flow. Under conditions in which fluid inertia is negligible, the force per unit length on the body is obtained as an asymptotic expansion in terms of the ratio of the cross-sectional radius to body length. Specific examples are given for the resistance to translation of long slender bodies for cases in which the body centre-line is curved as well as for those for which the centre-line is straight.

@Article{Cox70,
Title = {The motion of long slender bodies in a viscous fluid Part 1. General theory},
Author = {Cox,R. G.},
Journal = {J. Fluid Mech.},
Year = {1970},
Month = {12},
Pages = {791--810},
Volume = {44},
Abstract = { ABSTRACT A solid long slender body is considered placed in a fluid undergoing a given undisturbed flow. Under conditions in which fluid inertia is negligible, the force per unit length on the body is obtained as an asymptotic expansion in terms of the ratio of the cross-sectional radius to body length. Specific examples are given for the resistance to translation of long slender bodies for cases in which the body centre-line is curved as well as for those for which the centre-line is straight. },
Doi = {10.1017/S002211207000215X},
ISSN = {1469-7645},
Issue = {04},
Numpages = {20}
}

• M. Deng, X. Li, H. Liang, B. Caswell, and G. E. Karniadakis, “Simulation and modelling of slip flow over surfaces grafted with polymer brushes and glycocalyx fibres” J. Fluid Mech. 711, 192–211 (2012). doi:10.1017/jfm.2012.387
[BibTeX] [Abstract]

ABSTRACT Fabrication of functionalized surfaces using polymer brushes is a relatively simple process and parallels the presence of glycocalyx filaments coating the luminal surface of our vasculature. In this paper, we perform atomistic-like simulations based on dissipative particle dynamics (DPD) to study both polymer brushes and glycocalyx filaments subject to shear flow, and we apply mean-field theory to extract useful scaling arguments on their response. For polymer brushes, a weak shear flow has no effect on the brush density profile or its height, while the slip length is independent of the shear rate and is of the order of the brush mesh size as a result of screening by hydrodynamic interactions. However, for strong shear flow, the polymer brush is penetrated deeper and is deformed, with a corresponding decrease of the brush height and an increase of the slip length. The transition from the weak to the strong shear regime can be described by a simple ‘blob’ argument, leading to the scaling ${\dot {\gamma } }_{0} \propto {\sigma }^{3/ 2}$ , where ${\dot {\gamma } }_{0}$ is the critical transition shear rate and $\sigma$ is the grafting density. Furthermore, in the strong shear regime, we observe a cyclic dynamic motion of individual polymers, causing a reversal in the direction of surface flow. To study the glycocalyx layer, we first assume a homogeneous flow that ignores the discrete effects of blood cells, and we simulate microchannel flows at different flow rates. Surprisingly, we find that, at low Reynolds number, the slip length decreases with the mean flow velocity, unlike the behaviour of polymer brushes, for which the slip length remains constant under similar conditions. (The slip length and brush height are measured with respect to polymer mesh size and polymer contour length, respectively.) We also performed additional DPD simulations of blood flow in a tube with walls having a glycocalyx layer and with the deformable red blood cells modelled accurately at the spectrin level. In this case, a plasma cell-free layer is formed, with thickness more than three times the glycocalyx layer. We then find our scaling arguments based on the homogeneous flow assumption to be valid for this physiologically correct case as well. Taken together, our findings point to the opposing roles of conformational entropy and bending rigidity – dominant effects for the brush and glycocalyx, respectively – which, in turn, lead to different flow characteristics, despite the apparent similarity of the two systems.

@Article{Deng12,
Title = {Simulation and modelling of slip flow over surfaces grafted with polymer brushes and glycocalyx fibres},
Author = {Deng,Mingge and Li,Xuejin and Liang,Haojun and Caswell,Bruce and Karniadakis,George Em},
Journal = {J. Fluid Mech.},
Year = {2012},
Month = {11},
Pages = {192--211},
Volume = {711},
Abstract = {ABSTRACT Fabrication of functionalized surfaces using polymer brushes is a relatively simple process and parallels the presence of glycocalyx filaments coating the luminal surface of our vasculature. In this paper, we perform atomistic-like simulations based on dissipative particle dynamics (DPD) to study both polymer brushes and glycocalyx filaments subject to shear flow, and we apply mean-field theory to extract useful scaling arguments on their response. For polymer brushes, a weak shear flow has no effect on the brush density profile or its height, while the slip length is independent of the shear rate and is of the order of the brush mesh size as a result of screening by hydrodynamic interactions. However, for strong shear flow, the polymer brush is penetrated deeper and is deformed, with a corresponding decrease of the brush height and an increase of the slip length. The transition from the weak to the strong shear regime can be described by a simple ‘blob’ argument, leading to the scaling ${\dot {\gamma } }_{0} \propto {\sigma }^{3/ 2}$ , where ${\dot {\gamma } }_{0}$ is the critical transition shear rate and $\sigma$ is the grafting density. Furthermore, in the strong shear regime, we observe a cyclic dynamic motion of individual polymers, causing a reversal in the direction of surface flow. To study the glycocalyx layer, we first assume a homogeneous flow that ignores the discrete effects of blood cells, and we simulate microchannel flows at different flow rates. Surprisingly, we find that, at low Reynolds number, the slip length decreases with the mean flow velocity, unlike the behaviour of polymer brushes, for which the slip length remains constant under similar conditions. (The slip length and brush height are measured with respect to polymer mesh size and polymer contour length, respectively.) We also performed additional DPD simulations of blood flow in a tube with walls having a glycocalyx layer and with the deformable red blood cells modelled accurately at the spectrin level. In this case, a plasma cell-free layer is formed, with thickness more than three times the glycocalyx layer. We then find our scaling arguments based on the homogeneous flow assumption to be valid for this physiologically correct case as well. Taken together, our findings point to the opposing roles of conformational entropy and bending rigidity – dominant effects for the brush and glycocalyx, respectively – which, in turn, lead to different flow characteristics, despite the apparent similarity of the two systems.},
Doi = {10.1017/jfm.2012.387},
ISSN = {1469-7645},
Numpages = {20}
}

• E. C. Du Fort and S. P. Frankel, “Stability conditions in the numerical treatment of parabolic differential equations” Math. Comp. 7, 135-152 (1953).
[BibTeX]
@Article{DuFort_SCT_1953,
Title = {Stability conditions in the numerical treatment of parabolic differential equations},
Author = {Du Fort, E. C. and Frankel, S. P.},
Journal = {Math. Comp.},
Year = {1953},
Pages = {135-152},
Volume = {7}
}

• P. Español and M. Revenga, “Smoothed dissipative particle dynamics” Phys. Rev. E 67, 26705 (2003). doi:10.1103/PhysRevE.67.026705
[BibTeX] [Abstract]

We present a fluid particle model that is both a thermodynamically consistent version of smoothed particle hydrodynamics (SPH) and a version of dissipative particle dynamics (DPD), capturing the best of both methods. The model is a discrete version of Navier-Stokes equations, like SPH, and includes thermal fluctuations, like DPD. This model solves some problems with the physical interpretation of the original DPD model.

@Article{SDPD,
Title = {Smoothed dissipative particle dynamics},
Author = {Espa\~nol, Pep and Revenga, Mariano},
Journal = {Phys. Rev. E},
Year = {2003},
Pages = {026705},
Volume = {67},
Abstract = {We present a fluid particle model that is both a thermodynamically consistent version of smoothed particle hydrodynamics (SPH) and a version of dissipative particle dynamics (DPD), capturing the best of both methods. The model is a discrete version of Navier-Stokes equations, like SPH, and includes thermal fluctuations, like DPD. This model solves some problems with the physical interpretation of the original DPD model.},
Doi = {10.1103/PhysRevE.67.026705},
Issue = {2},
Numpages = {12},
Publisher = {American Physical Society}
}

• R. A. Gingold and J. J. Monaghan, “Smoothed particle hydrodynamics: theory and application to non-spherical stars” Mon. Not. R. Astron. Soc. 181, 375 (1977).
@Article{SPH,
Title = {Smoothed particle hydrodynamics: theory and application to non-spherical stars},
Author = {R.A. Gingold and J.J. Monaghan},
Journal = {Mon. Not. R. Astron. Soc.},
Year = {1977},
Pages = {375},
Volume = {181},
}

• E. Guyon, J. -P. Hulin, L. Petit, and C. D. Mitescu, Physical Hydrodynamics, Oxford University Press, 2001.
[BibTeX]
@Book{PhysHydro,
Title = {Physical Hydrodynamics},
Author = {Guyon, E. and Hulin, J.-P. and Petit, L. and Mitescu, C.D.},
Publisher = {Oxford University Press},
Year = {2001}
}

• P. J. Hoogerbrugge and J. M. V. A. Koelman, “Simulating Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics” Europhys. Lett. 19, 155 (1992). doi:10.1209/0295-5075/19/3/001
[BibTeX] [Abstract]

We present a novel method for simulating hydrodynamic phenomena. This particle-based method combines features from molecular dynamics and lattice-gas automata. It is shown theoretically as well as in simulations that a quantitative description of isothermal Navier-Stokes flow is obtained with relatively few particles. Computationally, the method is much faster than molecular dynamics, and the at same time it is much more flexible than lattice-gas automata schemes.

@Article{DPD,
Title = {Simulating Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics},
Author = {Hoogerbrugge, P.J. and Koelman, J.M.V.A.},
Journal = {Europhys. Lett.},
Year = {1992},
Number = {3},
Pages = {155},
Volume = {19},
Abstract = {We present a novel method for simulating hydrodynamic phenomena. This particle-based method combines features from molecular dynamics and lattice-gas automata. It is shown theoretically as well as in simulations that a quantitative description of isothermal Navier-Stokes flow is obtained with relatively few particles. Computationally, the method is much faster than molecular dynamics, and the at same time it is much more flexible than lattice-gas automata schemes.},
Doi = {10.1209/0295-5075/19/3/001}
}

• G. G. Kim and K. Char, “Semiflexible Polymer Brushes: Most Probable Configuration Approach Based on Cotinuous Chain Model” Bull. Korean Chem. Soc. 20, 1026-1030 (1999).
@Article{Kim1999,
Title = {Semiflexible Polymer Brushes: Most Probable Configuration Approach Based on Cotinuous Chain Model},
Author = {Gwang Gyu Kim and Kookheon Char},
Journal = {Bull. Korean Chem. Soc.},
Year = {1999},
Pages = {1026-1030},
Volume = {20},
}

• Y. W. Kim, V. Lobaskin, C. Gutsche, F. Kremer, P. Pincus, and R. R. Netz, “Nonlinear Response of Grafted Semiflexible Polymers in Shear Flow” Macromolecules 42, 3650-3655 (2009). doi:10.1021/ma900184e
[BibTeX] [Abstract]

Using Brownian-hydrodynamic and lattice-Boltzmann simulations, we study the nonlinear response of grafted semiflexible polymers to shear flow as a function of shear rate, grafting density, and chain stiffness. Simulation results for brush height and flow stagnation layer height agree well with a mean-field theory that incorporates the interplay of hydrodynamic screening and drag-induced polymer deformation. Our predictions for the stagnation height show excellent agreement with recent experiments on the nonlinear hydrodynamic drag of DNA-grafted colloids held in a laser trap.

@Article{Kim2009,
Title = {Nonlinear Response of Grafted Semiflexible Polymers in Shear Flow},
Author = {Kim, Yong Woon and Lobaskin, V. and Gutsche, C. and Kremer, F. and Pincus, Philip and Netz, Roland R.},
Journal = {Macromolecules},
Year = {2009},
Number = {10},
Pages = {3650-3655},
Volume = {42},
Abstract = { Using Brownian-hydrodynamic and lattice-Boltzmann simulations, we study the nonlinear response of grafted semiflexible polymers to shear flow as a function of shear rate, grafting density, and chain stiffness. Simulation results for brush height and flow stagnation layer height agree well with a mean-field theory that incorporates the interplay of hydrodynamic screening and drag-induced polymer deformation. Our predictions for the stagnation height show excellent agreement with recent experiments on the nonlinear hydrodynamic drag of DNA-grafted colloids held in a laser trap. },
Doi = {10.1021/ma900184e},
Eprint = {http://pubs.acs.org/doi/pdf/10.1021/ma900184e}
}

• D. V. Kuznetsov and Z. Y. Chen, “Semiflexible polymer brushes: A scaling theory” J. Chem. Phys. 109, 7017-7027 (1998). doi:10.1063/1.477338
[BibTeX] [Abstract]

We present a simple scaling theory to describe the conformational properties of semiflexible polymers grafted on a flat surface. For orientation-dependent interactions between polymer segments, we analyzed the physical properties of a polymer brush from the collapsed to strongly stretched regimes. Our analysis predicts first-order isotropic–nematic phase transitions between isotropically and nematically collapsed brushes, and between stretched and nematically collapsed brushes. It is also found that the orientational interactions would raise the effective θ temperature as compared with the isotropic counterparts.

@Article{Kuznetsov98,
Title = {Semiflexible polymer brushes: A scaling theory},
Author = {Dmitri V. Kuznetsov and Zheng Yu Chen},
Journal = {J. Chem. Phys.},
Year = {1998},
Pages = {7017-7027},
Volume = {109},
Abstract = {We present a simple scaling theory to describe the conformational properties of semiflexible polymers grafted on a flat surface. For orientation-dependent interactions between polymer segments, we analyzed the physical properties of a polymer brush from the collapsed to strongly stretched regimes. Our analysis predicts first-order isotropic–nematic phase transitions between isotropically and nematically collapsed brushes, and between stretched and nematically collapsed brushes. It is also found that the orientational interactions would raise the effective θ temperature as compared with the isotropic counterparts.},
Doi = {10.1063/1.477338}
}

• K. Legendre, S. Safieddine, P. Küssel-Andermann, C. Petit, and A. El-Amraou, “$\alpha$II-$\beta$V spectrin bridges the plasma membrane and cortical lattice in the lateral wall of the auditory outer hair cells” J. Cell Sci. 121, 3347–3356 (2008). doi:10.1242/​jcs.028134
[BibTeX]
@Article{Legendre08,
Title = {$\alpha$II-$\beta$V spectrin bridges the plasma membrane and cortical lattice in the lateral wall of the auditory outer hair cells},
Author = {Kirian Legendre and Saaid Safieddine and Polonca Küssel-Andermann and Christine Petit and Aziz El-Amraou},
Journal = {J. Cell Sci.},
Year = {2008},
Pages = {3347--3356},
Volume = {121},
Doi = {10.1242/​jcs.028134}
}

• H. Matsui, V. E. Wagner, D. B. Hill, U. E. Schwab, T. D. Rogers, B. Button, R. M. Taylor, R. Superfine, M. Rubinstein, B. H. Iglewski, and R. C. Boucher, “A physical linkage between cystic fibrosis airway surface dehydration and Pseudomonas aeruginosa biofilms” PNAS 103, 18131-18136 (2006). doi:10.1073/pnas.0606428103
[BibTeX] [Abstract]

A vexing problem in cystic fibrosis (CF) pathogenesis has been to explain the high prevalence of Pseudomonas aeruginosa biofilms in CF airways. We speculated that airway surface liquid (ASL) hyperabsorption generates a concentrated airway mucus that interacts with P. aeruginosa to promote biofilms. To model CF vs. normal airway infections, normal (2.5% solids) and CF-like concentrated (8% solids) mucus were prepared, placed in flat chambers, and infected with an ≈5 × 103 strain PAO1 P. aeruginosa. Although bacteria grew to 1010 cfu/ml in both mucus concentrations, macrocolony formation was detected only in the CF-like (8% solids) mucus. Biophysical and functional measurements revealed that concentrated mucus exhibited properties that restrict bacterial motility and small molecule diffusion, resulting in high local bacterial densities with high autoinducer concentrations. These properties also rendered secondary forms of antimicrobial defense, e.g., lactoferrin, ineffective in preventing biofilm formation in a CF-like mucus environment. These data link airway surface liquid hyperabsorption to the high incidence of P. aeruginosa biofilms in CF via changes in the hydration-dependent physical–chemical properties of mucus and suggest that the thickened mucus gel model will be useful to develop therapies of P. aeruginosa biofilms in CF airways.

@Article{Matsui28112006,
Title = {A physical linkage between cystic fibrosis airway surface dehydration and Pseudomonas aeruginosa biofilms},
Author = {Matsui, Hirotoshi and Wagner, Victoria E. and Hill, David B. and Schwab, Ute E. and Rogers, Troy D. and Button, Brian and Taylor, Russell M. and Superfine, Richard and Rubinstein, Michael and Iglewski, Barbara H. and Boucher, Richard C.},
Journal = {PNAS},
Year = {2006},
Number = {48},
Pages = {18131-18136},
Volume = {103},
Abstract = {A vexing problem in cystic fibrosis (CF) pathogenesis has been to explain the high prevalence of Pseudomonas aeruginosa biofilms in CF airways. We speculated that airway surface liquid (ASL) hyperabsorption generates a concentrated airway mucus that interacts with P. aeruginosa to promote biofilms. To model CF vs. normal airway infections, normal (2.5% solids) and CF-like concentrated (8% solids) mucus were prepared, placed in flat chambers, and infected with an ≈5 × 103 strain PAO1 P. aeruginosa. Although bacteria grew to 1010 cfu/ml in both mucus concentrations, macrocolony formation was detected only in the CF-like (8% solids) mucus. Biophysical and functional measurements revealed that concentrated mucus exhibited properties that restrict bacterial motility and small molecule diffusion, resulting in high local bacterial densities with high autoinducer concentrations. These properties also rendered secondary forms of antimicrobial defense, e.g., lactoferrin, ineffective in preventing biofilm formation in a CF-like mucus environment. These data link airway surface liquid hyperabsorption to the high incidence of P. aeruginosa biofilms in CF via changes in the hydration-dependent physical–chemical properties of mucus and suggest that the thickened mucus gel model will be useful to develop therapies of P. aeruginosa biofilms in CF airways.},
Doi = {10.1073/pnas.0606428103},
Eprint = {http://www.pnas.org/content/103/48/18131.full.pdf+html}
}

• A. Milchev and K. Binder, “Unconventional ordering behavior of semi-flexible polymers in dense brushes under compression” Soft Matter 10, 3783-3797 (2014). doi:10.1039/C3SM53133C
[BibTeX] [Abstract]

Using a coarse-grained bead-spring model for semi-flexible macromolecules which form a polymer brush{,} the structure and dynamics of the polymers were investigated{,} varying the chain stiffness and the grafting density. The anchoring conditions for the grafted chains were chosen such that their first bonds were oriented along the normal to the substrate plane. The compression of such a semi-flexible brush by a planar piston was observed to be a two-stage process: for a small compression the chains were shown to contract by {“}buckling{“} deformation whereas for a larger compression the chains exhibited a collective (almost uniform) bending deformation. Thus{,} the stiff polymer brush underwent a 2nd order phase transition of collective bond reorientation. The pressure{,} required to keep the stiff brush at a given degree of compression{,} was thereby significantly smaller than for an otherwise identical brush made of entirely flexible polymer chains! While both the brush height and the chain linear dimensions in the z-direction perpendicular to the substrate increased monotonically with an increase in the chain stiffness{,} the lateral (xy) chain linear dimensions exhibited a maximum at an intermediate chain stiffness. Increasing the grafting density led to a strong decrease of these lateral dimensions which is compatible with an exponential decay. Also the recovery kinetics after removal of the compressing piston were studied{,} and were found to follow a power-law/exponential decay with time. A simple mean-field theoretical consideration{,} accounting for the buckling/bending behavior of semi-flexible polymer brushes under compression was suggested.

@Article{Milchev2014,
Title = {Unconventional ordering behavior of semi-flexible polymers in dense brushes under compression},
Author = {Milchev, Andrey and Binder, Kurt},
Journal = {Soft Matter},
Year = {2014},
Pages = {3783-3797},
Volume = {10},
Abstract = {Using a coarse-grained bead-spring model for semi-flexible macromolecules which form a polymer brush{,} the structure and dynamics of the polymers were investigated{,} varying the chain stiffness and the grafting density. The anchoring conditions for the grafted chains were chosen such that their first bonds were oriented along the normal to the substrate plane. The compression of such a semi-flexible brush by a planar piston was observed to be a two-stage process: for a small compression the chains were shown to contract by {"}buckling{"} deformation whereas for a larger compression the chains exhibited a collective (almost uniform) bending deformation. Thus{,} the stiff polymer brush underwent a 2nd order phase transition of collective bond reorientation. The pressure{,} required to keep the stiff brush at a given degree of compression{,} was thereby significantly smaller than for an otherwise identical brush made of entirely flexible polymer chains! While both the brush height and the chain linear dimensions in the z-direction perpendicular to the substrate increased monotonically with an increase in the chain stiffness{,} the lateral (xy) chain linear dimensions exhibited a maximum at an intermediate chain stiffness. Increasing the grafting density led to a strong decrease of these lateral dimensions which is compatible with an exponential decay. Also the recovery kinetics after removal of the compressing piston were studied{,} and were found to follow a power-law/exponential decay with time. A simple mean-field theoretical consideration{,} accounting for the buckling/bending behavior of semi-flexible polymer brushes under compression was suggested.},
Doi = {10.1039/C3SM53133C},
Issue = {21}
}

• S. T. Milner, “Hydrodynamic penetration into parabolic brushes” Macromolecules 24, 3704-3705 (1991). doi:10.1021/ma00012a036
[BibTeX]
@Article{Milner91,
Title = {Hydrodynamic penetration into parabolic brushes},
Author = {Milner, S. T.},
Journal = {Macromolecules},
Year = {1991},
Number = {12},
Pages = {3704-3705},
Volume = {24},
Doi = {10.1021/ma00012a036},
Eprint = {http://pubs.acs.org/doi/pdf/10.1021/ma00012a036}
}

• J. T. Padding and A. A. Louis, “Hydrodynamic interactions and Brownian forces in colloidal suspensions: Coarse-graining over time and length scales” Phys. Rev. E 74, 31402 (2006). doi:10.1103/PhysRevE.74.031402
[BibTeX] [Abstract]

We describe in detail how to implement a coarse-grained hybrid molecular dynamics and stochastic rotation dynamics simulation technique that captures the combined effects of Brownian and hydrodynamic forces in colloidal suspensions. The importance of carefully tuning the simulation parameters to correctly resolve the multiple time and length scales of this problem is emphasized. We systematically analyze how our coarse-graining scheme resolves dimensionless hydrodynamic numbers such as the Reynolds number Re, which indicates the importance of inertial effects, the Schmidt number Sc, which indicates whether momentum transport is liquidlike or gaslike, the Mach number, which measures compressibility effects, the Knudsen number, which describes the importance of noncontinuum molecular effects, and the Peclet number, which describes the relative effects of convective and diffusive transport. With these dimensionless numbers in the correct regime the many Brownian and hydrodynamic time scales can be telescoped together to maximize computational efficiency while still correctly resolving the physically relevant processes. We also show how to control a number of numerical artifacts, such as finite-size effects and solvent-induced attractive depletion interactions. When all these considerations are properly taken into account, the measured colloidal velocity autocorrelation functions and related self-diffusion and friction coefficients compare quantitatively with theoretical calculations. By contrast, these calculations demonstrate that, notwithstanding its seductive simplicity, the basic Langevin equation does a remarkably poor job of capturing the decay rate of the velocity autocorrelation function in the colloidal regime, strongly underestimating it at short times and strongly overestimating it at long times. Finally, we discuss in detail how to map the parameters of our method onto physical systems and from this extract more general lessons—keeping in mind that there is no such thing as a free lunch—that may be relevant for other coarse-graining schemes such as lattice Boltzmann or dissipative particle dynamics.

@Article{Padding06,
Title = {Hydrodynamic interactions and Brownian forces in colloidal suspensions: Coarse-graining over time and length scales},
Author = {Padding, J. T. and Louis, A. A.},
Journal = {Phys. Rev. E},
Year = {2006},
Month = {Sep},
Pages = {031402},
Volume = {74},
Abstract = {We describe in detail how to implement a coarse-grained hybrid molecular dynamics and stochastic rotation dynamics simulation technique that captures the combined effects of Brownian and hydrodynamic forces in colloidal suspensions. The importance of carefully tuning the simulation parameters to correctly resolve the multiple time and length scales of this problem is emphasized. We systematically analyze how our coarse-graining scheme resolves dimensionless hydrodynamic numbers such as the Reynolds number Re, which indicates the importance of inertial effects, the Schmidt number Sc, which indicates whether momentum transport is liquidlike or gaslike, the Mach number, which measures compressibility effects, the Knudsen number, which describes the importance of noncontinuum molecular effects, and the Peclet number, which describes the relative effects of convective and diffusive transport. With these dimensionless numbers in the correct regime the many Brownian and hydrodynamic time scales can be telescoped together to maximize computational efficiency while still correctly resolving the physically relevant processes. We also show how to control a number of numerical artifacts, such as finite-size effects and solvent-induced attractive depletion interactions. When all these considerations are properly taken into account, the measured colloidal velocity autocorrelation functions and related self-diffusion and friction coefficients compare quantitatively with theoretical calculations. By contrast, these calculations demonstrate that, notwithstanding its seductive simplicity, the basic Langevin equation does a remarkably poor job of capturing the decay rate of the velocity autocorrelation function in the colloidal regime, strongly underestimating it at short times and strongly overestimating it at long times. Finally, we discuss in detail how to map the parameters of our method onto physical systems and from this extract more general lessons—keeping in mind that there is no such thing as a free lunch—that may be relevant for other coarse-graining schemes such as lattice Boltzmann or dissipative particle dynamics.},
Doi = {10.1103/PhysRevE.74.031402},
Issue = {3},
Numpages = {29},
Publisher = {American Physical Society}
}

• M. A. Powers and D. J. Forbes, “Nuclear Transport: Beginning to Gel?” Curr. Biol. 22, R1006–R109 (2012). doi:10.1016/j.cub.2012.10.037
[BibTeX]
@Article{Powers2012,
Title = {Nuclear Transport: Beginning to Gel?},
Author = {Maureen A. Powers and Douglass J. Forbes},
Journal = {Curr. Biol.},
Year = {2012},
Pages = {R1006--R109},
Volume = {22},
Doi = {10.1016/j.cub.2012.10.037}
}

• F. Römer and D. A. Fedosov, “Dense brushes of stiff polymers or filaments in fluid flow” Europhysics Letters 109, 68001 (2015). doi:10.1209/0295-5075/109/68001
@Article{EPL-2015,
Title = {Dense brushes of stiff polymers or filaments in fluid flow},
Author = {F. R\"omer and D. A. Fedosov},
Journal = {Europhysics Letters},
Year = {2015},
Number = {6},
Pages = {68001},
Volume = {109},
Doi = {10.1209/0295-5075/109/68001},
Url = {http://wgserve.de/fr/wp-content/papercite-data/pdf/EPL_109_68001_(2015).pdf}
}

• X. Schlagberger and R. R. Netz, “Orientation of elastic rods in homogeneous Stokes flow” Europhys. Lett. 70, 129 (2005).
[BibTeX] [Abstract]

Using hydrodynamic simulation methods and scaling arguments, we consider an elastic rod which is moving in a gravitational or electric field through a quiescent fluid in the low-Reynolds-number limit. Hydrodynamic effects lead to rod bending and orientation perpendicular to the direction of motion, similar to what is seen in anomalous electric birefringence experiments on TM and FD viruses or polyelectrolytes. Static and dynamic scaling relations for the mean orientation as a function of rod length and elasticity are established.

@Article{Netz05,
Title = {Orientation of elastic rods in homogeneous Stokes flow},
Author = {X. Schlagberger and R. R. Netz},
Journal = {Europhys. Lett.},
Year = {2005},
Number = {1},
Pages = {129},
Volume = {70},
Abstract = {Using hydrodynamic simulation methods and scaling arguments, we consider an elastic rod which is moving in a gravitational or electric field through a quiescent fluid in the low-Reynolds-number limit. Hydrodynamic effects lead to rod bending and orientation perpendicular to the direction of motion, similar to what is seen in anomalous electric birefringence experiments on TM and FD viruses or polyelectrolytes. Static and dynamic scaling relations for the mean orientation as a function of rod length and elasticity are established.}
}

• J. A. Tolomeo and M. C. Holley, “Mechanics of microtubule bundles in pillar cells from the inner ear” Biophys. J. 73, 2241–2247 (1997). doi:10.1016/S0006-3495(97)78255-9
[BibTeX] [Abstract]

@Article{Tolomeo1997,
Title = {Mechanics of microtubule bundles in pillar cells from the inner ear},
Author = {Tolomeo, J.A. and Holley, M.C.},
Journal = {Biophys. J.},
Year = {1997},
Number = {4},
Pages = {2241--2247},
Volume = {73},
Booktitle = {Biophysical Journal},
Doi = {10.1016/S0006-3495(97)78255-9},
Owner = {roemer},
Publisher = {Elsevier},
Timestamp = {2014.06.04}
}

• A. Vázquez-Quesada, M. Ellero, and P. Español, “Consistent scaling of thermal fluctuations in smoothed dissipative particle dynamics” J. Chem. Phys. 130, 34901 (2009). doi:10.1063/1.3050100
[BibTeX]
@Article{SDPDscaling,
Title = {Consistent scaling of thermal fluctuations in smoothed dissipative particle dynamics},
Journal = {J. Chem. Phys.},
Year = {2009},
Number = {3},
Pages = {034901},
Volume = {130},
Doi = {10.1063/1.3050100}
}

• J. D. Weeks, D. Chandler, and H. C. Andersen, “Role of repulsive forces in determining the equilibrium structure of simple liquids” J. Chem. Phys. 54, 5237-5247 (1971).
[BibTeX]
@Article{Weeks_WCA_1971,
Title = {Role of repulsive forces in determining the equilibrium structure of simple liquids},
Author = {Weeks, J. D. and Chandler, D. and Andersen, H. C.},
Journal = {J. Chem. Phys.},
Year = {1971},
Pages = {5237-5247},
Volume = {54},
Timestamp = {2015.06.01}
}

• S. Weinbaum, J. M. Tarbell, and E. R. Damiano, “The Structure and Function of the Endothelial Glycocalyx Layer” Annu. Rev. Biomed. Eng. 9, 121-167 (2007). doi:10.1146/annurev.bioeng.9.060906.151959
[BibTeX] [Abstract]

Abstract Over the past decade, since it was first observed in vivo, there has been an explosion in interest in the thin (∼500 nm), gel-like endothelial glycocalyx layer (EGL) that coats the luminal surface of blood vessels. In this review, we examine the mechanical and biochemical properties of the EGL and the latest studies on the interactions of this layer with red and white blood cells. This includes its deformation owing to fluid shear stress, its penetration by leukocyte microvilli, and its restorative response after the passage of a white cell in a tightly fitting capillary. We also examine recently discovered functions of the EGL in modulating the oncotic forces that regulate the exchange of water in microvessels and the role of the EGL in transducing fluid shear stress into the intracellular cytoskeleton of endothelial cells, in the initiation of intracellular signaling, and in the inflammatory response.

@Article{Weinbaum2007,
Title = {The Structure and Function of the Endothelial Glycocalyx Layer},
Author = {Weinbaum, Sheldon and Tarbell, John M. and Damiano, Edward R.},
Journal = {Annu. Rev. Biomed. Eng.},
Year = {2007},
Number = {1},
Pages = {121-167},
Volume = {9},
Abstract = { Abstract Over the past decade, since it was first observed in vivo, there has been an explosion in interest in the thin (∼500 nm), gel-like endothelial glycocalyx layer (EGL) that coats the luminal surface of blood vessels. In this review, we examine the mechanical and biochemical properties of the EGL and the latest studies on the interactions of this layer with red and white blood cells. This includes its deformation owing to fluid shear stress, its penetration by leukocyte microvilli, and its restorative response after the passage of a white cell in a tightly fitting capillary. We also examine recently discovered functions of the EGL in modulating the oncotic forces that regulate the exchange of water in microvessels and the role of the EGL in transducing fluid shear stress into the intracellular cytoskeleton of endothelial cells, in the initiation of intracellular signaling, and in the inflammatory response. },
Doi = {10.1146/annurev.bioeng.9.060906.151959},
Eprint = {http://www.annualreviews.org/doi/pdf/10.1146/annurev.bioeng.9.060906.151959}
}

• S. Weinbaum, X. Zhang, Y. Han, H. Vink, and S. C. Cowin, “Mechanotransduction and flow across the endothelial glycocalyx” PNAS 100, 7988-7995 (2003). doi:10.1073/pnas.1332808100
[BibTeX] [Abstract]

In this inaugural paper, we shall provide an overview of the endothelial surface layer or glycocalyx in several roles: as a transport barrier, as a porous hydrodynamic interface in the motion of red and white cells in microvessels, and as a mechanotransducer of fluid shearing stresses to the actin cortical cytoskeleton of the endothelial cell. These functions will be examined from a new perspective, the quasiperiodic ultrastructural model proposed in Squire et al. [Squire, J. M., Chew, M., Nneji, G., Neal, C., Barry, J. & Michel, C. (2001) J. Struct. Biol. 136, 239–255] for the 3D organization of the endothelial surface layer and its linkage to the submembranous scaffold. We shall show that the core proteins in the bush-like structures comprising the matrix have a flexural rigidity, EI, that is sufficiently stiff to serve as a molecular filter for plasma proteins and as an exquisitely designed transducer of fluid shearing stresses. However, EI is inadequate to prevent the buckling of these protein structures during the intermittent motion of red cells or the penetration of white cell microvilli. In these cellular interactions, the viscous draining resistance of the matrix is essential for preventing adhesive molecular interactions between proteins in the endothelial membrane and circulating cellular components.

@Article{Weinbaum2003,
Title = {Mechanotransduction and flow across the endothelial glycocalyx},
Author = {Weinbaum, Sheldon and Zhang, Xiaobing and Han, Yuefeng and Vink, Hans and Cowin, Stephen C.},
Journal = {PNAS},
Year = {2003},
Number = {13},
Pages = {7988-7995},
Volume = {100},
Abstract = {In this inaugural paper, we shall provide an overview of the endothelial surface layer or glycocalyx in several roles: as a transport barrier, as a porous hydrodynamic interface in the motion of red and white cells in microvessels, and as a mechanotransducer of fluid shearing stresses to the actin cortical cytoskeleton of the endothelial cell. These functions will be examined from a new perspective, the quasiperiodic ultrastructural model proposed in Squire et al. [Squire, J. M., Chew, M., Nneji, G., Neal, C., Barry, J. & Michel, C. (2001) J. Struct. Biol. 136, 239–255] for the 3D organization of the endothelial surface layer and its linkage to the submembranous scaffold. We shall show that the core proteins in the bush-like structures comprising the matrix have a flexural rigidity, EI, that is sufficiently stiff to serve as a molecular filter for plasma proteins and as an exquisitely designed transducer of fluid shearing stresses. However, EI is inadequate to prevent the buckling of these protein structures during the intermittent motion of red cells or the penetration of white cell microvilli. In these cellular interactions, the viscous draining resistance of the matrix is essential for preventing adhesive molecular interactions between proteins in the endothelial membrane and circulating cellular components.},
Doi = {10.1073/pnas.1332808100},
Eprint = {http://www.pnas.org/content/100/13/7988.full.pdf+html}
}

• C. H. Wiggins, D. Riveline, A. Ott, and R. E. Goldstein, “Trapping and Wiggling: Elastohydrodynamics of Driven Microfilaments” Biophys. J. 74, 1043-1060 (1998). doi:10.1016/S0006-3495(98)74029-9
[BibTeX] [Abstract]

We present an analysis of the planar motion of single semiflexible filaments subject to viscous drag or point forcing. These are the relevant forces in dynamic experiments designed to measure biopolymer bending moduli. By analogy with the Stokes problems in hydrodynamics (motion of a viscous fluid induced by that of a wall bounding the fluid), we consider the motion of a polymer, one end of which is moved in an impulsive or oscillatory way. Analytical solutions for the time-dependent shapes of such moving polymers are obtained within an analysis applicable to small-amplitude deformations. In the case of oscillatory driving, particular attention is paid to a characteristic length determined by the frequency of oscillation, the polymer persistence length, and the viscous drag coefficient. Experiments on actin filaments manipulated with optical traps confirm the scaling law predicted by the analysis and provide a new technique for measuring the elastic bending modulus. Exploiting this model, we also present a reanalysis of several published experiments on microtubules.

@Article{Wiggins98,
Title = {Trapping and Wiggling: Elastohydrodynamics of Driven Microfilaments},
Author = {Wiggins, Chris H. and Riveline, D. and Ott, A. and Goldstein, Raymond E.},
Journal = {Biophys. J.},
Year = {1998},
Pages = {1043-1060},
Volume = {74},
Abstract = {We present an analysis of the planar motion of single semiflexible filaments subject to viscous drag or point forcing. These are the relevant forces in dynamic experiments designed to measure biopolymer bending moduli. By analogy with the Stokes problems in hydrodynamics (motion of a viscous fluid induced by that of a wall bounding the fluid), we consider the motion of a polymer, one end of which is moved in an impulsive or oscillatory way. Analytical solutions for the time-dependent shapes of such moving polymers are obtained within an analysis applicable to small-amplitude deformations. In the case of oscillatory driving, particular attention is paid to a characteristic length determined by the frequency of oscillation, the polymer persistence length, and the viscous drag coefficient. Experiments on actin filaments manipulated with optical traps confirm the scaling law predicted by the analysis and provide a new technique for measuring the elastic bending modulus. Exploiting this model, we also present a reanalysis of several published experiments on microtubules.},
Doi = {10.1016/S0006-3495(98)74029-9}
}

• C. M. Wijmans and B. Smit, “Simulating Tethered Polymer Layers in Shear Flow with the Dissipative Particle Dynamics Technique” Macromolecules 35, 7138-7148 (2002). doi:10.1021/ma020086b
[BibTeX] [Abstract]

The dissipative particle dynamics (DPD) method is used to simulate shear flow between two flat plates. To test this technique, simulations were conducted of both constant and oscillatory shear of a simple fluid. The results of these simulations agree well with theoretical predictions. We subsequently applied our model to study the effect of shear flow on end-tethered polymer layers (“brushes”). When exposed to a constant shear flow, chains in a polymer brush are stretched in the direction of the flow, and the overall layer thickness decreases. This result is similar to what was found in previous simulation studies. However, in the present simulations solvent particles are taken into account explicitly. At low frequencies, the response of a brush to oscillatory shear is qualitatively similar to its response to constant shear. As the flow velocity changes during an oscillation cycle, the polymer chains are able to relax their configurations with respect to the shear rate. At higher frequencies the interpretation of the brush behavior becomes more difficult due to conflicting time scales of the polymer and solvent dynamics in the present DPD model.

@Article{Wijmans02,
Title = {Simulating Tethered Polymer Layers in Shear Flow with the Dissipative Particle Dynamics Technique},
Author = {Wijmans, C. M. and Smit, B.},
Journal = {Macromolecules},
Year = {2002},
Number = {18},
Pages = {7138-7148},
Volume = {35},
Abstract = { The dissipative particle dynamics (DPD) method is used to simulate shear flow between two flat plates. To test this technique, simulations were conducted of both constant and oscillatory shear of a simple fluid. The results of these simulations agree well with theoretical predictions. We subsequently applied our model to study the effect of shear flow on end-tethered polymer layers (“brushes”). When exposed to a constant shear flow, chains in a polymer brush are stretched in the direction of the flow, and the overall layer thickness decreases. This result is similar to what was found in previous simulation studies. However, in the present simulations solvent particles are taken into account explicitly. At low frequencies, the response of a brush to oscillatory shear is qualitatively similar to its response to constant shear. As the flow velocity changes during an oscillation cycle, the polymer chains are able to relax their configurations with respect to the shear rate. At higher frequencies the interpretation of the brush behavior becomes more difficult due to conflicting time scales of the polymer and solvent dynamics in the present DPD model. },
Doi = {10.1021/ma020086b},
Eprint = {http://pubs.acs.org/doi/pdf/10.1021/ma020086b}
}