Daniel Havelka

Electric field generated by axial longitudinal vibration modes of microtubule.

Microtubules are electrically polar structures fulfilling prerequisites for generation of oscillatory electric field in the kHz to GHz region. Energy supply for excitation of elasto-electrical vibrations in microtubules may be provided from GTP-hydrolysis; motor protein-microtubule interactions; and energy efflux from mitochondria. We calculated electric field generated by axial longitudinal vibration modes of microtubules for random, and coherent excitation. In case of coherent excitation of vibrations, the electric field intensity is highest at the end of microtubule. The dielectrophoretic force exerted by electric field on the surrounding molecules will influence the kinetics of microtubule polymerization via change in the probability of the transport of charge and mass particles. The electric field generated by vibrations of electrically polar cellular structures is expected to play an important role in biological self-organization.

High-frequency electric field and radiation characteristics of cellular microtubule network

Microtubules are important structures in the cytoskeleton, which organizes the cell. Since microtubules are electrically polar, certain microtubule normal vibration modes efficiently generate oscillating electric field. This oscillating field may be important for the intracellular organization and intercellular interaction. There are experiments which indicate electrodynamic activity of variety of cells in the frequency region from kHz to GHz, expecting the microtubules to be the source of this activity. In this paper, results from the calculation of intensity of electric field and of radiated electromagnetic power from the whole cellular microtubule network are presented. The subunits of microtubule (tubulin heterodimers) are approximated by elementary electric dipoles. Mechanical oscillation of microtubule is represented by the spatial function which modulates the dipole moment of subunits. The field around oscillating microtubules is calculated as a vector superposition of contributions from all modulated elementary electric dipoles which comprise the cellular microtubule network. The electromagnetic radiation and field characteristics of the whole cellular microtubule network have not been theoretically analyzed before. For the perspective experimental studies, the results indicate that macroscopic detection system (antenna) is not suitable for measurement of cellular electrodynamic activity in the radiofrequency region since the radiation rate from single cells is very low (lower than 10⁻²⁰ W). Low noise nanoscopic detection methods with high spatial resolution which enable measurement in the cell vicinity are desirable in order to measure cellular electrodynamic activity reliably.

Mechano-electrical vibrations of microtubules--link to subcellular morphology.

Spontaneous mechanical oscillations were predicted and experimentally proven on almost every level of cellular structure. Besides morphogenetic potential of oscillatory mechanical force, oscillations may drive vibrations of electrically polar structures or these structures themselves may oscillate on their own natural frequencies. Vibrations of electric charge will generate oscillating electric field, role of which in morphogenesis is discussed in this paper. This idea is demonstrated in silico on the conformation of two growing microtubules.

Electro-acoustic behavior of the mitotic spindle: a semi-classical coarse-grained model.

The regulation of chromosome separation during mitosis is not fully understood yet. Microtubules forming mitotic spindles are targets of treatment strategies which are aimed at (i) the triggering of the apoptosis or (ii) the interruption of uncontrolled cell division. Despite these facts, only few physical models relating to the dynamics of mitotic spindles exist up to now. In this paper, we present the first electromechanical model which enables calculation of the electromagnetic field coupled to acoustic vibrations of the mitotic spindle. This electromagnetic field originates from the electrical polarity of microtubules which form the mitotic spindle. The model is based on the approximation of resonantly vibrating microtubules by a network of oscillating electric dipoles. Our computational results predict the existence of a rapidly changing electric field which is generated by either driven or endogenous vibrations of the mitotic spindle. For certain values of parameters, the intensity of the electric field and its gradient reach values which may exert a not-inconsiderable force on chromosomes which are aligned in the spindle midzone. Our model may describe possible mechanisms of the effects of ultra-short electrical and mechanical pulses on dividing cells—a strategy used in novel methods for cancer treatment.

Multi-mode electro-mechanical vibrations of a microtubule: In silico demonstration of electric pulse moving along a microtubule

Microtubules are known to be involved in intracellular signaling. Here, we show in silico that electrically polar collective vibration modes of microtubules form electric oscillating potential which is quasi-periodic both in space and in time. While single mode microtubule vibration excites an electric field with spatially stationary local minima and maxima of the electric field, the multimode excitation causes the formation of an electric pulse and many transient local electric field minima. The biophysical mechanism we describe lends support to the view that microtubules may comprise a substrate for ultra-fast electrical signaling in neurons or other living cells.

Electric field generated by longitudinal axial microtubule vibration modes with high spatial resolution microtubule model

Microtubules are electrically polar structures fulfilling prerequisites for generation of oscillatory electric field in the kHz to GHz region. Energy supply for excitation of elasto-electrical vibrations in microtubules may be provided from GTP-hydrolysis; motor protein-microtubule interactions; and energy efflux from mitochondria. It recently was determined from anisotropic elastic network modeling of entire microtubules that the frequencies of microtubule longitudinal axial eigenmodes lie in the region of tens of GHz for the physiologically common microtubule lengths. We calculated electric field generated by axial longitudinal vibration modes of microtubule, which model is based on subnanometer precision of charge distribution. Due to elastoelectric nature of the vibrations, the vibration wavelength is million-fold shorter than that of the electromagnetic field in free space and the electric field around the microtubule manifests rich spatial structure with multiple minima. The dielectrophoretic force exerted by electric field on the surrounding molecules will influence the kinetics of reactions via change in the probability of the transport of charge and mass particles. The electric field generated by vibrations of electrically polar cellular structures is expected to play a role in biological self-organization.

Electric oscillations generated by collective vibration modes of microtubule

Microtubules are important organizing structures of eukaroytic cells. They are electrically polar and have collective vibration modes from kHz to low THz region. In approximation of microtubule subunits (tubulin molecules) as rigid particles, we calculate electric field generated by optical branch of axial longitudinal vibration modes of microtubule. This oscillatory electric field, due to its complex spatial distribution, may play an important role in cellular temporal and spatial organization.

Deformation pattern in vibrating microtubule: Structural mechanics study based on an atomistic approach

The mechanical properties of microtubules are of great importance for understanding their biological function and for applications in artificial devices. Although microtubule mechanics has been extensively studied both theoretically and experimentally, the relation to its molecular structure is understood only partially. Here, we report on the structural analysis of microtubule vibration modes calculated by an atomistic approach. Molecular dynamics was applied to refine the atomic structure of a microtubule and a Cα elastic network model was analyzed for its normal modes. We mapped fluctuations and local deformations up to the level of individual aminoacid residues. The deformation is mode-shape dependent and principally different in α-tubulins and β-tubulins. Parts of the tubulin dimer sequence responding specifically to longitudinal and radial stress are identified. We show that substantial strain within a microtubule is located both in the regions of contact between adjacent dimers and in the body of tubulins. Our results provide supportive evidence for the generally accepted assumption that the mechanics of microtubules, including its anisotropy, is determined by the bonds between tubulins.

Electric field generated by higher vibration modes of microtubule

Certain structures in a living cell may generate electric oscillations. Microtubules, which form a part of a cellular skeleton, belong to this class of structures and fulfill all conditions for generation of electric oscillations in kHz÷GHz band. We present selected results from calculations of the oscillatory electric field generated by higher vibration modes of microtubules. We propose that the electric field of certain modes may play specific function in cellular organization.

Post Processing of Results of EM Field Simulators

In this chapter we shall focus on the needs that many researchers, scientists and even students have very often. When using commercial simulation software for numerical simulation of electromagnetic field we frequently encounter many insufficiencies which those software products have. Usually, main aim of computational software developers is to optimize and refine so called core of these programmes – EM field solver. After that CAD (Computer Assisted Design) and post processing parts of EM simulators are dealt with. Mainly this can be an issue with newer, short-time in development products but one’s own post processing using Matlab can be greatly beneficial even when using well established simulators of EM field. This is largely due to its flexibility which cannot be overcome by any EM field simulator.