Membrane Biophysics

Ashrafuzzaman, Mohammad; Tuszyński, Jack A.

doi:10.1007/978-3-642-16105-6

Cited by 39 publications

(59 citation statements)

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“…Consider, for example, the local charge density [Eq. (6)]. This function has a pole at s = 0, corresponding to the long-time limit of q(x, t) [cf.…”

Section: Padé Approximation Before Inverse Laplace Transformationmentioning

confidence: 99%

“…Ultimately, this x dependence arises because, in determining the coefficients α 0 , .., α p , β 0 , .., β q of the Padé approximation, a linear system of p + q + 2 equations has to be solved, which acquire x dependence from the numerator in Eq. (6). Consequently, analogous approximations to the the ionic current density and electric field exhibit decay times τ I and τ E with τ q = τ I = τ E [41].…”

Section: Padé Approximation Before Inverse Laplace Transformationmentioning

confidence: 99%

“…We report expressions for the inverse Laplace transforms of the ionic charge density [Eq. (6)], the ionic current density [Eq. (9)], and the electric field [Eq.…”

Section: Exact Inverse Laplace Transformationmentioning

confidence: 99%

“…Understanding the time-dependent formation of electric double layers (EDLs) in response to varying external influences is a fundamental problem of relevance to diverse fields including electrochemistry [1,2], colloid science [3,4], biophysics [5,6], and microfluidics [7]. Moreover, the speed with which EDLs can form in so-called electric double-layer capacitors (EDLCs) crucially determines the feasibility of these devices for energy storage [8] and conversion of energy [9,10].…”

Section: Introductionmentioning

confidence: 99%

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Transient dynamics of electric double-layer capacitors: Exact expressions within the Debye-Falkenhagen approximation

Janssen

Bier

2018

Phys. Rev. E

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We revisit a classical problem of theoretical electrochemistry: the response of an electric double-layer capacitor (EDLC) subject to a small, suddenly applied external potential. We solve the Debye-Falkenhagen equation to obtain exact expressions for key EDLC quantities: the ionic charge density, the ionic current density, and the electric field. In contrast to earlier works, our results are not restricted to the long-time asymptotics of those quantities. The solutions take the form of infinite sums whose successive terms all decay exponentially with increasingly short relaxation times. Importantly, this set of relaxation times is the same among all aforementioned EDLC quantities; this property is demanded on physical grounds but not generally achieved within approximation schemes. The scaling of the largest relaxation timescale τ_{1}, that determines the long-time decay, is in accordance with earlier results: Depending on the Debye length, λ_{D}, and the electrode separation, 2L, it amounts to τ_{1}≃λ_{D}L/D for L≫λ_{D} and τ_{1}≃4L^{2}/(π^{2}D) for L≪λ_{D}, respectively (with D being the ionic diffusivity).

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“…Consider, for example, the local charge density [Eq. (6)]. This function has a pole at s = 0, corresponding to the long-time limit of q(x, t) [cf.…”

Section: Padé Approximation Before Inverse Laplace Transformationmentioning

confidence: 99%

Section: Padé Approximation Before Inverse Laplace Transformationmentioning

confidence: 99%

“…We report expressions for the inverse Laplace transforms of the ionic charge density [Eq. (6)], the ionic current density [Eq. (9)], and the electric field [Eq.…”

Section: Exact Inverse Laplace Transformationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Transient dynamics of electric double-layer capacitors: Exact expressions within the Debye-Falkenhagen approximation

Janssen

Bier

2018

Phys. Rev. E

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“…Many processes in biology and engineering can be described by systems separated by a membrane. 1,2 Lenzi et al 3 studied anomalous diffusion of particles in a heterogeneous system separated by a semipermeable membrane, where the particle dynamics was governed by fractional diffusion equations in the bulk and by kinetic equations on the membrane, which characterizes an interface between two different media. For 0 < < 1, the mathematical model that was offered in Lenzi et al 3 is…”

Section: Introductionmentioning

confidence: 99%

Anomalous diffusion phenomena with conservation law for the fractional kinetic process

Tokmagambetov

Torebek

2018

Math Methods in App Sciences

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Engineering Lipid Membranes with Programmable DNA Nanostructures

et al. 2019

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Lipid and DNA are abundant biomolecules with critical functions in cells. The water-insoluble, amphipathic lipid molecules are best known for their roles in energy storage (e.g. as triglyceride), signaling (e.g. as sphingolipid), and compartmentalization (e.g. by forming membrane-enclosed bodies). The soluble, highly negatively charged DNA, which stores cells' genetic information, has proven to be an excellent material for constructing programmable nanostructures in vitro thanks to its self-assembling capabilities. These two seemingly distant molecules make contact within cell nuclei, often via lipidated proteins, with proposed functions of modulating chromatin structures. Carefully formulated lipid/DNA complexes are promising reagents for gene therapy. The past few years saw an emerging research field of interfacing DNA nanostructures with lipid membranes, with an overarching goal of generating DNA/lipid hybrid materials that possess novel and controllable structure, dynamics, and function. An arsenal of DNA-based tools has been created to coat, mold, deform, and penetrate lipid bilayers, affording us the ability to manipulate membranes with nanoscopic precision. These membrane engineering methods not only enable quantitative biophysical studies, but also open new opportunities in synthetic biology (e.g. artificial cells) and therapeutics (e.g. drug delivery).

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Membrane Biophysics

Cited by 39 publications

References 0 publications

Transient dynamics of electric double-layer capacitors: Exact expressions within the Debye-Falkenhagen approximation

Transient dynamics of electric double-layer capacitors: Exact expressions within the Debye-Falkenhagen approximation

Anomalous diffusion phenomena with conservation law for the fractional kinetic process

Engineering Lipid Membranes with Programmable DNA Nanostructures

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