1. Extended Lindstedt-Poincare method for non-stationary resonances of dynamical systems with cubic nonlinearitRudi Pušenjak, 2008, izvirni znanstveni članek Opis: This paper presents the extended Lindstedt-Poincare (EL-P) method, which applies multiple time variables to treat non-stationary oscillations arising in dynamical systems with cubic nonlinearities due to the slowly varied excitation parameters. The method is applied extensively in research of non-stationary vibrations of clamped-hinged beams. Recognizing the aperiodic nature of non-stationary oscillations, the new formulation is presented by adding an additional, slow time scale beside time scales of the nonlinear system, which generally correspond to the incommensurate nonlinear frequencies of the response. Using this concept, a generalized approach of the study to the passage through fundamental, superharmonic and subharmonic resonances is presented in the paper. Effects of slowly varying excitation frequency and slowly varying excitation amplitude on the non-stationary oscillations are studied with the computation of deviations from the stationary response. Although the method is formulated for N-dof dynamical systems having weak cubic nonlinearities, it is applied for non-stationary vibrations, where two-mode shape approximation of damped and undamped clamped-hinged beam, respectively, is used and the simultaneous appearance of internal resonance is taken into account. Stability analysis of stationary solutions is performed and comparisons of stationary resonance curves by results obtained with the incremental harmonic balance (IHB) method show good agreement. The passage through the fundamental resonance of damped and undamped clamped-hinged beam, respectively, is investigated in detail. Ključne besede: dynamical systems with cubic nonlinearities, nonlinear oscillations, nonstationary nonlinear oscillations, time scales, excitation frequency, resonance, Lindstedt-Poincare method Objavljeno: 01.06.2012; Ogledov: 1123; Prenosov: 18 Povezava na celotno besedilo |
2. Cellular diversity promotes intercellular Ca[sup]2+ wave propagationMarko Gosak, 2009, izvirni znanstveni članek Opis: Calcium ions are an important second messenger in living cells. Calcium signals in form of waves serve as a means of intercellular communication and thus represent a vibrant subject for experimental and theoretical investigations. Here we study the role of cellular variability on the occurrence of ▫$Ca^{2+}$▫ wave propagation in a net of diffusively coupled cells. Dynamics of individual cells is simulated by a mathematical model for ▫$Ca^{2+}$▫ oscillations. Structural diversity of cells is introduced via variations of the bifurcation parameters, which signify cell sensitivity for external stimulation. Remarkably, for sufficient values of variability ▫$Ca^{2+}$▫ waves emerge, which are mostly ordered for intermediate variability strength. We analyze the spatial profile via the autocorrelation function, which confirms aresonance-like response due to the cellular variability. Thus, the reported phenomenon is a novel observation of diversity-induced spatial coherence resonance in a tissue-like media. Ključne besede: dynamic systems, waves, calcium oscillations, resonance, diversity-induced resonance, cellular variability, coupled cells, intracellular processes Objavljeno: 07.06.2012; Ogledov: 950; Prenosov: 10 Povezava na celotno besedilo |
3. Establishing the stochastic nature of intracellular calcium oscillations from experimental dataMatjaž Perc, Anne K. Green, C. Jane Dixon, Marko Marhl, 2008, izvirni znanstveni članek Opis: Calcium has been established as a key messenger in both intra- and intercellular signaling. Experimentally observed intracellular calcium responses to different agonists show a variety of behaviors from simple spiking to complex oscillatory regimes. Here we study typical experimental traces of calcium oscillations in hepatocytes obtained in response to phenylephrine and ATP. The traces were analyzed with methods of nonlinear time series analysis in order to determine the stochastic/deterministic nature of the intracellular calcium oscillations. Despite the fact that the oscillations appear, visually, to be deterministic yet perturbed by noise, our analyses provide strong evidence that the measured calcium traces in hepatocytes are prevalently of stochastic nature. In particular, bursting calcium oscillations are temporally correlated Gaussian series distorted by a monotonic, instantaneous, time-independent function, whilst the spiking behavior appears to have a dynamical nonlinear component whereby the overall determinism level is still low. The biological importance of this finding is discussed in relation to the mechanisms incorporated in mathematical models as well as the role of stochasticity and determinism at cellular and tissue levels which resemble typical statistical and thermodynamic effects in physics. Ključne besede: dynamic systems, stochastic processes, cellular signaling, calcium oscillations, time series analyses, noise, temporal correlation Objavljeno: 07.06.2012; Ogledov: 1009; Prenosov: 70 Povezava na celotno besedilo |
4. MLC-kinase/phosphatase control of Ca[sup]2+ signal transduction in airway smooth musclesAleš Fajmut, Milan Brumen, 2008, izvirni znanstveni članek Opis: In airway smooth muscles, kinase/phosphatase-dependent phosphorylation and dephosphorylation of the myosin light chain (MLC) have been revealed by many authors as important steps in calcium ▫$(Ca^{2+})$▫ signalling pathway from the variation of ▫$Ca^{2+}$▫ concentration in cytosol to the force development. Here, a theoretical analysis of the control action of MLC-kinase (MLCK) and MLC-phosphatase (MLCP) in ▫$Ca^{2+}$▫ signalling is presented and related to the general control principles of these enzymes, which were previously studied by Reinhart Heinrich and his co-workers. The kinetic scheme of the mathematical model considers interactions among ▫$Ca^{2+}$▫, calmodulin (CaM) and MLCK and the well-known 4-state actomyosin latch bridge model, whereby a link between them is accomplished by the conservation relation of all species of MLCK. The mathematical model predicts the magnitude and velocity of isometric force in smooth muscles upon transient biphasic ▫$Ca^{2+}$▫ signal. The properties of signal transduction in the system such as the signalling time, signal duration and signal amplitude, which are reflected in the properties of force developed, are studied by the principles of the metabolic control theory. The analysis of our model predictions confirms as shown by Reinhart Heinrich and his co-workers that MLCK controls the amplitude of signal more than its duration, whereas MLCP controls both. Finally, the simulations of elevated total content of MLCK, a typical feature of bronchial muscles of asthmatic subjects and spontaneously hypertensive rats as well as potentiation of MLCP catalytic activity, are carried out and are discussed in view of an increase in the force magnitude. Ključne besede: cells, calcium, calcium oscillations, myosin light chains, enzyme activities, mathematical models Objavljeno: 07.06.2012; Ogledov: 1128; Prenosov: 9 Povezava na celotno besedilo |
5. Spatio-temporal modelling explains the effect of reduced plasma membrane Ca[sup]2+[/sup] efflux on intracellular Ca[sup]2+[/sup] oscillations in hepatocytesMarko Marhl, Marko Gosak, Matjaž Perc, C. Jane Dixon, Anne K. Green, 2008, izvirni znanstveni članek Opis: In many non-excitable eukaryotic cells, including hepatocytes, ▫$Ca^{2+}$▫ oscillations play a key role in intra- and intercellular signalling, thus regulating many cellular processes from fertilisation to death. Therefore, understanding the mechanisms underlying these oscillations, and consequently understanding how they may be regulated, is of great interest. In this paper, we study the influence of reduced ▫$Ca^{2+}$▫ plasma membrane efflux on ▫$Ca^{2+}$▫ oscillations in hepatocytes. Our previous experiments with carboxyeosin show that a reduced plasma membrane ▫$Ca^{2+}$▫ efflux increases the frequency of ▫$Ca^{2+}$▫ oscillations, but does not affect the duration of individual transients. This phenomenon can be best explained by taking into account not only the temporal,but also the spatial dynamics underlying the generation of ▫$Ca^{2+}$▫ oscillations in the cell. Here we divide the cell into a grid of elements and treat the ▫$Ca^{2+}$▫ dynamics as a spatio-temporal phenomenon. By converting an existing temporal model into a spatio-temporal one, we obtain theoretical predictions that are in much better agreement with the experimental observations. Ključne besede: cellular signalling, calcium oscillations, intracellular oscilations, spatio-temporal dynamics, hepatocytes, stochastic simulations Objavljeno: 07.06.2012; Ogledov: 822; Prenosov: 14 Povezava na celotno besedilo |
6. Role of cascades in converting oscillatory signals into stationary step-like responsesMarko Marhl, Vladimir Grubelnik, 2007, izvirni znanstveni članek Opis: 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. Ključne besede: physics, calcium oscillations, mathematical modelling, calcium, calcium oscillations, sygnalling cascade, protein kinase cascades, signal transduction, ultrasensitivity, biochemical switch, cellular dynamics Objavljeno: 07.06.2012; Ogledov: 1013; Prenosov: 29 Povezava na celotno besedilo |
7. Noise-induced spatial dynamics in the presence of memory lossMatjaž Perc, Marko Marhl, 2007, izvirni znanstveni članek Opis: We study the spatial dynamics of noise-induced waves in two-dimensional excitable media in dependence on the duration of the artificially imposed refractory time that is introduced to each constitutive system unit after an excitation. Due to the introduction of refractory times, a randomly induced spatial wave is temporarily unable to transmit information to the opposite site of its propagation direction. Thus, once the wave leaves the absorbing boundaries of the spatial grid the system has little or no recollection, depending on the duration of the refractory time, of its existence. We show that even in the presence of such memory loss, self-organization of excitatory events leads to noise-induced spatial periodicity in the media. We present a simple analytical treatment of a two-unit system to capture and explain the essence of the observed phenomenon. Since refractory times are widespread in biological systems, our results provide interesting insights into functioning of real-life organisms at the cellular as well as tissue level. Ključne besede: noise, spatiotemporal noise, intensity, pattern formation, refractory time, calcium oscillations Objavljeno: 07.06.2012; Ogledov: 1044; Prenosov: 57 Povezava na celotno besedilo |
8. Fluctuating excitability : a mechanism for self-sustained information flow in excitable arraysMatjaž Perc, 2007, izvirni znanstveni članek Opis: We show that the fluctuating excitability of FitzHugh-Nagumo neurons, constituting a diffusively coupled excitable array, can induce phase slips that lead to a symmetry break yielding a preferred spreading direction of excitatory events, thus enabling persistent self-sustained and self-organized information flow in a periodic array long after a localized stimulus perturbation has sized. Possible oscillation frequencies of the information-carrying signal are expressed analytically, and necessary conditions for the phenomenon are derived. Our results suggest that cellular diversity in neural tissue is crucial for maintaining self-sustained and organized activity in the brain even in the absence of immediate stimuli, thus facilitating continuous evolution of its mechanisms for information retrieval and storage. Ključne besede: physics, complex systems, dynamical systems, flexibility, chaos, chaotic systems, oscillations, perturbation Objavljeno: 07.06.2012; Ogledov: 1109; Prenosov: 55 Povezava na celotno besedilo |
9. Selective regulation of protein activity by complex Ca[sup]2+ oscillations : a theoretical studyBeate Knoke, Marko Marhl, Stefan Schuster, 2007, samostojni znanstveni sestavek ali poglavje v monografski publikaciji Opis: Calcium oscillations play an important role in intracellular signal transduction. As a second messenger, ▫$Ca^{2+}$▫ represents a link between several input signals and several target processes in the cell. Whereas the frequency of simple ▫$Ca^{2+}$▫ oscillations enables a selective activation of a specific protein and herewith a particular process, the question arises of how at the same time two or more classes of proteins can be specifically regulated. The question is general and concerns the problem of how one second messenger can transmit more than one signal simultaneously (bow-tie structure of signalling). To investigate whether a complex ▫$Ca^{2+}$▫ signal like bursting, a succession of low-peak and high-peak oscillatory phases, could selectively activate different proteins, several bursting patterns with simplified square pulses were applied in a theoretical model. The results indicate that bursting ▫$Ca^{2+}$▫ oscillations allow a differential regulation of two different calcium-binding proteins, and hence, perform the desired function. Ključne besede: biophysics, calcium oscillations, cellular dynamics, mathematical models, signalling, bow-tie structures, bursting, decoding Objavljeno: 07.06.2012; Ogledov: 1002; Prenosov: 9 Povezava na celotno besedilo |
10. Theoretical and experimental investigation of calcium-contraction coupling in airway smooth musclePrisca Mbikou, Aleš Fajmut, Milan Brumen, Etienne Roux, 2006, izvirni znanstveni članek Opis: We investigated theoretically and experimentally the ▫$Ca^{2+}$▫-contraction couplingin rat tracheal smooth muscle. ▫$[Ca^{2+}]_i$▫, isometric contraction and myosin light chain (MLC) phosphorylation were measured in response to 1 mM carbachol. Theoretical modeling consisted in coupling a model of ▫$Ca^{2+}-dependent$▫ MLC kinase (MLCK) activation with a four-state model of smooth muscle contractile apparatus. Stimulation resulted in a short-time contraction obtained within 1 min, followed by a long-time contraction up to the maximal force obtained in 30 min. ML-7 and Wortmannin (MLCK inhibitors) abolished the contraction. Chelerythrine (PKC inhibitor) did not change the short-time, but reduced the long-time contraction. ▫$[Ca^{2+}]_i$▫ responses of isolated myocytes recorded during the first 90 s consisted in a fast peak, followed by a plateau phase and, in 28 % of the cells, superimposed ▫$Ca^{2+}$▫ oscillations. MLC phosphorylation was maximal at 5 s and then decreased, whereas isometric contraction followed a Hill-shaped curve. The model properlypredicts the time course of MLC phosphorylation and force of the short-time response. With oscillating ▫$Ca^{2+}$▫ signal, the predicted force does not oscillate. According to the model, the amplitude of the plateau and the frequency of oscillations encode for the amplitude of force, whereas the peak encodes for force velocity. The long-time phase of the contraction, associated with a second increase in MLC phosphorylation, may be explained, at least partially, by MLC phosphatase (MLCP) inhibition, possibly via PKC inhibition. Ključne besede: biophysics, mathematical modelling, modelling, calcium oscillations, contractions, force development, muscle cells, smooth muscles, myosin kinase Objavljeno: 07.06.2012; Ogledov: 918; Prenosov: 48 Povezava na celotno besedilo |