Finite element analysis of microelectrotension of cell membranes

Multiscale modelling of the extracellular matrix

The extracellular matrix is a complex three-dimensional network of molecules that provides cells with a complex microenvironment. The major constituents of the extracellular matrix such as collagen, elastin and associated proteins form supramolecular assemblies contributing to its physicochemical properties and organization. The structure of proteins and their supramolecular assemblies such as fibrils have been studied at the atomic level (e.g., by X-ray crystallography, Nuclear Magnetic Resonance and cryo-Electron Microscopy) or at the microscopic scale. However, many protein complexes are too large to be studied at the atomic level and too small to be studied by microscopy. Most extracellular matrix components fall into this intermediate scale, so-called the mesoscopic scale, preventing their detailed characterization. Simulation and modelling are some of the few powerful and promising approaches that can deepen our understanding of mesoscale systems. We have developed a set of modelling tools to study the self-organization of the extracellular matrix and large motion of macromolecules at the mesoscale level by taking advantage of the dynamics of articulated rigid bodies as a mean to study a larger range of motions at the cost of atomic resolution.

Comparative Study of Pore Formation Energy by High Intensity, Nanosecond Electrical Pulse

Nanosecond, high intensity electric pulses create nanopores in the cell membrane. Pore formation energy is probed by taking account of the strain energy based on the continuum model. Maxwell stress acting on the cell membrane is included in the 3D model calculation as well as the effect of membrane curvature. In addition, comparison between cylindrical and toroidal pores were made to explore the difference of strain energy and force over the pores at a range of radii. Through the analyses the transmembrane potential were kept constant in order to obtain a transient response in that the electric pulse has a ultrashort duration and pore-evolving process is rapid as well. Our results demonstrate that under the same circumstances toroidal pores have higher strain energy than cylindrical pores due to the surface area and volume of the pore shape.

Mechanic stress generated by a time-varying electromagnetic field on bone surface

Bone cells sense mechanical load, which is essential for bone growth and remodeling. In a fracture, this mechanism is compromised. Electromagnetic stimulation has been widely used to assist in bone healing, but the underlying mechanisms are largely unknown. A recent hypothesis suggests that electromagnetic stimulation could influence tissue biomechanics; however, a detailed quantitative understanding of EM-induced biomechanical changes in the bone is unavailable. This paper used a muscle/bone model to study the biomechanics of the bone under EM exposure. Due to the dielectric properties of the muscle/bone interface, a time-varying magnetic field can generate both compressing and shear stresses on the bone surface, where many mechanical sensing cells are available for cellular mechanotransduction. I calculated these stresses and found that the shear stress is significantly greater than the compressing stress. Detailed parametric analysis suggests that both the compressing and shear stresses are dependent on the geometrical and electrical properties of the muscle and the bone. These stresses are also functions of the orientation of the coil and the frequency of the magnetic field. It is speculated that the EM field could apply biomechanical influence to fractured bone, through the fine-tuning of the controllable field parameters. Graphical abstract Mechanic stress on bone surface in a time-varying magnetic field.

Quantification of cell membrane permeability induced by monopolar and high-frequency bipolar bursts of electrical pulses

High-frequency bipolar electric pulses have been shown to mitigate undesirable muscle contraction during irreversible electroporation (IRE) therapy. Here, we evaluate the potential applicability of such pulses for introducing exogenous molecules into cells, such as in electrochemotherapy (ECT). For this purpose we develop a method for calculating the time course of the effective permeability of an electroporated cell membrane based on real-time imaging of propidium transport into single cells that allows a quantitative comparison between different pulsing schemes. We calculate the effective permeability for several pulsed electric field treatments including trains of 100μs monopolar pulses, conventionally used in IRE and ECT, and pulse trains containing bursts or evenly-spaced 1μs bipolar pulses. We show that shorter bipolar pulses induce lower effective membrane permeability than longer monopolar pulses with equivalent treatment times. This lower efficiency can be attributed to incomplete membrane charging. Nevertheless, bipolar pulses could be used for increasing the uptake of small molecules into cells more symmetrically, but at the expense of higher applied voltages. These data indicate that high-frequency bipolar bursts of electrical pulses may be designed to electroporate cells as effectively as and more homogeneously than conventional monopolar pulses.

Vesicle biomechanics in a time-varying magnetic field

Background

Cells exhibit distortion when exposed to a strong electric field, suggesting that the field imposes control over cellular biomechanics. Closed pure lipid bilayer membranes (vesicles) have been widely used for the experimental and theoretical studies of cellular biomechanics under this electrodeformation. An alternative method used to generate an electric field is by electromagnetic induction with a time-varying magnetic field. References reporting the magnetic control of cellular mechanics have recently emerged. However, theoretical analysis of the cellular mechanics under a time-varying magnetic field is inadequate.

We developed an analytical theory to investigate the biomechanics of a modeled vesicle under a time-varying magnetic field. Following previous publications and to simplify the calculation, this model treated the inner and suspending media as lossy dielectrics, the membrane thickness set at zero, and the electric resistance of the membrane assumed to be negligible. This work provided the first analytical solutions for the surface charges, electric field, radial pressure, overall translational forces, and rotational torques introduced on a vesicle by the time-varying magnetic field. Frequency responses of these measures were analyzed, particularly the frequency used clinically by transcranial magnetic stimulation (TMS).

Results

The induced surface charges interacted with the electric field to produce a biomechanical impact upon the vesicle. The distribution of the induced surface charges depended on the orientation of the coil and field frequency. The densities of these charges were trivial at low frequency ranges, but significant at high frequency ranges. The direction of the radial force on the vesicle was dependent on the conductivity ratio between the vesicle and the medium. At relatively low frequencies (<200 KHz), including the frequency used in TMS, the computed radial pressure and translational forces on the vesicle were both negligible.

Conclusions

This work provides an analytical framework and insight into factors affecting cellular biomechanics under a time-varying magnetic field. Biological effects of clinical TMS are not likely to occur via alteration of the biomechanics of brain cells.

Contact-free scanning and imaging with the scanning ion conductance microscope

Scanning ion conductance microscopy (SICM) offers the ability to obtain very high-resolution topographical images of living cells. One of the great advantages of SICM lies in its ability to perform contact-free scanning. However, it is not yet clear when the requirements for this scan mode are met. We have used finite element modeling (FEM) to examine the conditions for contact-free scanning. Our findings provide a framework for understanding the contact-free mode of SICM and also extend previous findings with regard to SICM resolution. Finally, we demonstrate the importance of our findings for accurate biological imaging.

NONLINEAR DYNAMICS OF CELL CYCLES WITH STOCHASTIC MATHEMATICAL MODELS

Cell cycles are fundamental components of all living organisms and their systematic studies extend our knowledge about the interconnection between regulatory, metabolic, and signaling networks, and therefore open new opportunities for our ultimate efficient control of cellular processes for disease treatments, as well as for a wide variety of biomedical and biotechnological applications. In the study of cell cycles, nonlinear phenomena play a paramount role, in particular in those cases where the cellular dynamics is in the focus of attention. Quantification of this dynamics is a challenging task due to a wide range of parameters that require estimations and the presence of many stochastic effects. Based on the originally deterministic model, in this paper we develop a hierarchy of models that allow us to describe the nonlinear dynamics accounting for special events of cell cycles. First, we develop a model that takes into account fluctuations of relative concentrations of proteins during special events of cell cycles. Such fluctuations are induced by varying rates of relative concentrations of proteins and/or by relative concentrations of proteins themselves. As such fluctuations may be responsible for qualitative changes in the cell, we develop a new model that accounts for the effect of cellular dynamics on the cell cycle. Finally, we analyze numerically nonlinear effects in the cell cycle by constructing phase portraits based on the newly developed model and carry out a parametric sensitivity analysis in order to identify parameters for an efficient cell cycle control. The results of computational experiments demonstrate that the metabolic events in gene regulatory networks can qualitatively influence the dynamics of the cell cycle.