Vladimir Grubelnik

Mitochondria regulate the amplitude of simple and complex calcium oscillations

In a mathematical model for simple calcium oscillations [Biophys. Chem. 71 (1998) 125], it has been shown that mitochondria play an important role in the maintenance of constant amplitudes of cytosolic Ca(2+) oscillations. Simple plausible rate laws for Ca(2+) fluxes across the inner mitochondrial membrane have been used in this model. Here we show that it is possible to use the same rate laws as a plug-in element in other existing mathematical models and obtain the same effect on amplitude regulation. This result appears to be universal, independent of the type of model and the type of Ca(2+) oscillations. We demonstrate this on two models for spiking Ca(2+) oscillations [J. Biol. Chem. 266 (1991) 11068; Cell Calcium 14 (1993) 311] and on two recent models for bursting Ca(2+) oscillations; one of them being a receptor-operated model [Biophys. J. 79 (2000) 1188] and the other one being a store-operated model [BioSystems 57 (2000) 75].

Signal amplification in biological and electrical engineering systems: universal role of cascades.

In this paper we compare the cascade mechanisms of signal amplification in biological and electrical engineering systems, and show that they share the capacity to considerably amplify signals, and respond to signal changes both quickly and completely, which effectively preserves the form of the input signal. For biological systems, these characteristics are crucial for efficient and reliable cellular signaling. We show that this highly-efficient biological mechanism of signal amplification that has naturally evolved is mathematically fully equivalent with some man-developed amplifiers, which indicates parallels between biological evolution and successful technology development.

Role of cascades in converting oscillatory signals into stationary step-like responses

In biological signal transduction pathways intermediates are often oscillatory and need to be converted into smooth output signals at the end. We show by mathematical modelling that protein kinase cascades enable converting oscillatory signals into sharp stationary step-like outputs. The importance of this result is demonstrated for the switch-like protein activation by calcium oscillations, which is of biological importance for regulating different cellular processes. In addition, we found that protein kinase cascades cause memory effects in the protein activation, which might be of a physiological advantage since a smaller amount of calcium transported in the cell is required for an effective activation of cellular processes.

Mathematical modelling of the electrostatic pendulum in school and undergraduate education

The electrostatic pendulum, also known as the electrostatic ping-pong, is an exciting experiment in school as well as in undergraduate education. We can easily demonstrate how the frequency of the electrostatic pendulum depends on the voltage across the capacitor. In this paper, we develop a simple mathematical model describing the dynamics of this experiment. In a step-wise manner, we introduce the external forces influencing the dynamics of the electrostatic pendulum. First, we take into account the electric force only. Then, we add air resistance and the non-elasticity of ball collisions with the capacitor plates. The model predictions show that the non-elastic collisions have greater effect on the pendulum dynamics than air resistance; in particular, this is true for higher frequencies of the pendulum. For lower frequencies, however, gravity is of crucial importance. The mathematical model is implemented in a graphic-oriented computer program, which gives the possibility of using this theoretical analysis also at the secondary school level.

Drop formation in a falling stream of liquid

The narrowing of a falling stream of liquid is a well-known demonstration of the equation of continuity. We consider the behavior of the bottom of a falling liquid stream where the stream ceases to narrow, and swells and forms droplets. Drop formation is demonstrated by detailed photos of experiments. A simple mathematical description of the observations is given, including the key processes responsible for drop formation.

Quantum Fermi acceleration in the resonant gaps of a periodically driven one-dimensional potential box

We study numerically the quantum mechanics of a point particle in the one-dimensional potential box, whose boundary oscillates periodically according to the sawtooth driving law. We perform very accurate numerical calculations over up to about 500 periods. Unlike in smooth driving, this system admits classical Fermi acceleration, because the Kolmogorov–Arnold–Moser theorem does not apply, and surprisingly also admits quantum Fermi acceleration, but only in the extremely narrow resonant gaps located at the values of the driving parameter that corresponds to either one-photon transitions or multi-photon transitions. In the gaps the energy of the particle increases indefinitely, quadratically with time, as predicted by our quite general two-level theory derived for general periodic quantum systems, whilst outside the gaps it oscillates and displays beatings with long or very long periods which are theoretically unexplained, but very well and clearly manifested.

E-Learning Materials for 3rd Grade of Primary School - Physics

It is very important for the development of natural science competences of children to choose the right approach to teaching the physics. E-learning materials developed so far are a useful addition to the learning process. Their function is to assist in explaining the real world around us. Among other goals, this means the explanation of experiments and preparation to conduct them. In the frame of our national project we have prepared the e-learning materials which cover the basics of physics for primary school pupils. Children are encouraged to study the materials and conduct their own experiments. Teachers who have used our materials are giving us very encouraging responses and would like to use other learning materials prepared in this way.

Applying network theory to fables: complexity in Slovene belles-lettres for different age groups

Words are the building blocks of human communication. They are arranged in sentences in a non-trivial and universal way, which implies the existence of fundamental organizational principles that have shaped language development. One of the fundamental examples is the Zipf’s law, which says that the frequency of word occurrence is roughly an inverse power-law function of its rank. In our article, we study the structure and complexity of texts in Slovene belles-lettres, with an emphasis on evaluating the differences in the texts for different age groups. We show that the co-occurrence connectivity of words forms a complex and heterogeneous network that is characterized by an efficient transfer of information. Moreover, we show