Biomedical subjects

Marko Marhl

Publications and source records attributed to Marko Marhl.

17 recordsLinked to original sources

PubMed2006

Minimal model for spatial coherence resonance.

We show that a planar medium, locally modeled by a simple one-dimensional excitable system with a piece-wise linear potential, can serve as a minimal model for spatial coherence resonance. Via an analytical treatment of the spatially extended system, we derive the dependence of the resonant wave number on several crucial system parameters, ranging from the diffusion coefficient to the local excursion time of constitutive excitable units. Thus, we provide vital insights into mechanisms that enable the emergence of exclusively noise-induced spatial periodicity in excitable media.

Journal Article↗

PubMed2006

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.

Calcium Signaling↗

PubMed2005

A minimal model for decoding of time-limited Ca2+ oscillations.

Calcium oscillations regulate several cellular processes by activating particular proteins. Most theoretical studies focused on the idealized situation of infinitely long oscillations. Here we analyze information transfer by time-limited calcium spike trains. We show that proteins can be selectively activated in a resonance-like manner by time-limited spike trains of different frequencies, while infinitely long oscillations do not show this resonance phenomenon. We found that proteins are activated more specifically by shorter oscillatory signals with narrower spikes.

Biological Clocks↗

PubMed2005

Selective regulation of cellular processes via protein cascades acting as band-pass filters for time-limited oscillations.

We show by mathematical modelling that a two-level protein cascade can act as a band-pass filter for time-limited oscillations. The band-pass filters are then combined into a network of three-level signalling cascades that by filtering the frequency of time-limited oscillations selectively switches cellular processes on and off. The physiological relevance for the selective regulation of cellular processes is demonstrated for the case of regulation by time-limited calcium oscillations.

Calcium Signaling↗

PubMed2005

Transition from stochastic to deterministic behavior in calcium oscillations.

Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations on discrete particle basis are more accurate. Unfortunately, there are no general rules for determining which method should be employed for exactly which problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system, namely the signal transduction via calcium, especially calcium oscillations. We observe that the transition occurs within a range of particle numbers, which roughly corresponds to the number of receptors and channels in the cell, and depends heavily on the attractive properties of the phase space of the respective systems dynamics. We conclude that the attractive properties of a system, expressed, e.g., by the divergence of the system, are a good measure for determining which simulation algorithm is appropriate in terms of speed and realism.

Adenosine Triphosphate↗

PubMed2005

Modelling of calcium handling in airway myocytes.

Airway myocytes are the primary effectors of airway reactivity which modulates airway resistance and hence ventilation. Stimulation of airway myocytes results in an increase in the cytosolic Ca(2+) concentration ([Ca(2+)](i)) and the subsequent activation of the contractile apparatus. Many contractile agonists, including acetylcholine, induce [Ca(2+)](i) increase via Ca(2+) release from the sarcoplasmic reticulum through InsP(3) receptors. Several models have been developed to explain the characteristics of InsP(3)-induced [Ca(2+)](i) responses, in particular Ca(2+) oscillations. The article reviews the modelling of the major structures implicated in intracellular Ca(2+) handling, i.e., InsP(3) receptors, SERCAs, mitochondria and Ca(2+)-binding cytosolic proteins. We developed theoretical models specifically dedicated to the airway myocyte which include the major mechanisms responsible for intracellular Ca(2+) handling identified in these cells. These biocomputations pointed out the importance of the relative proportion of InsP(3) receptor isoforms and the respective role of the different mechanisms responsible for cytosolic Ca(2+) clearance in the pattern of [Ca(2+)](i) variations. We have developed a theoretical model of membrane conductances that predicts the variations in membrane potential and extracellular Ca(2+) influx. Stimulation of this model by simulated increase in [Ca(2+)](i) predicts membrane depolarisation, but not great enough to trigger a significant opening of voltage-dependant Ca(2+) channels. This may explain why airway contraction induced by cholinergic stimulation does not greatly depend on extracellular calcium. The development of such models of airway myocytes is important for the understanding of the cellular mechanisms of airway reactivity and their possible modulation by pharmacological agents.

Acetylcholine↗

PubMed2005

Differential regulation of proteins by bursting calcium oscillations--a theoretical study.

Calcium in ionic form is a second messenger connecting several input signals to several target processes in the cell. The question arises how one second messenger can transmit more than one signal simultaneously (bow-tie structure of signalling). Experimental data on calcium dynamics often show patterns of successive low-peak and high-peak oscillatory phases, known as bursting. Here, we propose that bursting calcium oscillations can perform the function of simultaneous transmission of two signals at physiological calcium concentrations, for example, by selective activation of two calcium-binding proteins. This differential regulation by periodic bursting is investigated in a theoretical model. The two proteins are assumed to be activated by calcium, and one of them is assumed to be subject to biphasic regulation due to additional inhibitory binding sites. To explore which characteristics of the complex signal could be responsible for independent regulation of low-peak activated and spike activated targets, different bursting patterns of simplified square pulses are applied. Depending on the change in the bursting pattern, one protein can be gradually activated at a constant level of the other protein's activity, or the two proteins can be activated simultaneously, or one protein can be activated while the other one is deactivated simultaneously. Thus, the two proteins can be regulated virtually independently.

Animals↗

PubMed2005

Amplification of information transfer in excitable systems that reside in a steady state near a bifurcation point to complex oscillatory behavior.

We study the amplification of information transfer in excitable systems. We show that excitable systems residing in a steady state near a bifurcation point to complex oscillatory behavior incorporate several frequencies that can be exploited for a resonant amplification of information transfer. In particular, for excitable neurons that reside in a steady state near a bifurcation point to elliptic bursting oscillations, we show that in addition to the resonant frequency of damped oscillations around the stable focus, another frequency exists that resonantly enhances large amplitude bursts and thus amplifies the information transfer in the system. This additional frequency cannot be found by the local stability analysis and has never been used for amplifying the information transfer in a system. The results obtained for elliptic bursting oscillations can be generalized also to other complex oscillators, such as parabolic or square-wave bursters. Additionally, the biological importance of presented results in the field of neuroscience is outlined.

Adaptation, Physiological↗

PubMed2004

Detecting and controlling unstable periodic orbits that are not part of a chaotic attractor.

A method for controlling unstable periodic orbits (UPOs) that have not been controllable before is presented. The method is based on detecting UPOs that are situated outside the skeleton of a chaotic attractor. The main idea is to exploit flexible parts of the attractor, which under weak external perturbations allow variable excursions of the trajectory away from its originally determined path. After the perturbation, the trajectory of the autonomous system seeks its path back to the chaotic attractor and reveals additional UPOs that are otherwise not used by the system. It is shown that these UPOs can be controlled as easily as the UPOs that form the basic chaotic attractor. The effectiveness of the proposed method is demonstrated on two different chaotic systems with very distinct response abilities to external perturbations. Additionally, some applications of the method in the fields of laser technology, information encoding, and biomedical engineering are discussed.

Journal Article↗

PubMed2004

Local dissipation and coupling properties of cellular oscillators: a case study on calcium oscillations.

Synchronised signal transduction between cells is crucial, since it assures fast and immutable information processing, which is vital for flawless functioning of living organisms. The question arises how to recognise the ability of a cell to be easily coupled with other cells. In the present paper, we investigate the system properties that determine best coupling abilities and assure the most efficient signal transduction between cells. A case study is done for intercellular calcium oscillations. For a particular diffusion-like coupled system of cellular oscillators, we determined the minimal gap-junctional permeability that is necessary for synchronisation of initially asynchronous oscillators. Our results show that dissipation is a crucial system property that determines the coupling ability of cellular oscillators. We found that low dissipation assures synchronisation of coupled cells already at very low gap-junctional permeability, whereas highly dissipative oscillators require much higher gap-junctional permeability in order to synchronise. The results are discussed in the sense of their biological importance for systems where the synchronous responses of cells were recognised to be indispensable for appropriate physiological functioning of the tissue.

Animals↗

PubMed2004

Role of sarcoplasmic reticulum and mitochondria in Ca2+ removal in airway myocytes.

The aim of this study was to use both a theoretical and experimental approach to determine the influence of the sarco-endoplasmic Ca2+-ATPase (SERCA) activity and mitochondria Ca2+ uptake on Ca2+ homeostasis in airway myocytes. Experimental studies were performed on myocytes freshly isolated from rat trachea. [Ca2+]i was measured by microspectrofluorimetry using indo-1. Stimulation by caffeine for 30 s induced a concentration-graded response characterized by a transient peak followed by a progressive decay to a plateau phase. The decay phase was accelerated for 1-s stimulation, indicating ryanodine receptor closure. In Na2+-Ca2+-free medium containing 0.5 mM La3+, the [Ca2+]i response pattern was not modified, indicating no involvement of transplasmalemmal Ca2+ fluxes. The mathematical model describing the mechanism of Ca2+ handling upon RyR stimulation predicts that after Ca2+ release from the sarcoplasmic reticulum, the Ca2+ is first sequestrated by cytosolic proteins and mitochondria, and pumped back into the sarcoplasmic reticulum after a time delay. Experimentally, we showed that the [Ca2+]i decay after Ca2+ increase was not altered by the SERCA inhibitor cyclopiazonic acid, but was slightly but significantly modified by the mitochondria uncoupler carbonyl cyanide 4-(trifluoromethoxy)phenylhydrazone. The experimental and theoretical results indicate that, although Ca2+ pumping back by SERCA is active, it is not primarily involved in [Ca2+]i decrease that is due, in part, to mitochondrial Ca2+ uptake.

Animals↗

PubMed2003

Under what conditions signal transduction pathways are highly flexible in response to external forcing? A case study on calcium oscillations.

Sensitivity and flexibility are typical properties of biological systems. These properties are here investigated in a model for simple and complex intracellular calcium oscillations. In particular, the influence of external periodic forcing is studied. The main point of the study is to compare responses of the system in a chaotic regime with those obtained in a regular periodic regime. We show that the response to external signals in terms of the range of synchronization is not significantly different in regular and chaotic Ca2+ oscillations. However, both types of oscillation are highly flexible in regimes with weak dissipation. Therefore, we conclude that dissipation of free energy is a suitable index characterizing flexibility. For biological systems this appears to be of special importance since for thermodynamic reasons, notably in view of low free energy consumption, dissipation should be minimized.

Animals↗

PubMed2003

Sensitivity and flexibility of regular and chaotic calcium oscillations.

Sensitivity and flexibility are important properties of biological systems. These properties are here investigated for intracellular calcium oscillations. For a particular model, we comparatively investigate sensitivity and flexibility of regular and chaotic Ca(2+) oscillations. For this model, we obtain two main results. First, sensitivity of the model system to parameter shifting does not depend on the complexity of Ca(2+) oscillations. We observe, however, that both regular and chaotic Ca(2+) oscillations are highly sensitive in regions close to bifurcation points. Second, also flexibility of Ca(2+) oscillations does not significantly depend on the type of Ca(2+) oscillations. Our results show that regular as well as chaotic Ca(2+) oscillations in the studied model are highly flexible in regimes with weak dissipation. Both results are discussed in the sense of possible biological importance.

Calcium↗

PubMed2002

The influence of different InsP(3) receptor isoforms on Ca(2+) signaling in tracheal smooth muscle cells.

In airway myocytes, like in many cells, Ca(2+) signaling is controlled by inositol 1,4,5-trisphosphate (InsP(3)) via InsP(3) receptors (InsP(3)R) located in the sarco-endoplasmic reticulum. Three types of InsP(3)R exist, labeled Types 1, 2, and 3, which differ in their gating kinetics. We analyze a possible impact of the different gating kinetics of Type 1 and Type 3 InsP(3)R on the time course of cytosolic Ca(2+) concentration in tracheal smooth muscle cells upon agonist stimulation. Previous experimental data in rat tracheal myocytes showed that upon gradually increased stimulation with acetylcholine (ACh), a contractile agonist that acts via InsP(3) production, signal spikes, several spikes with declining maxima, and sustained oscillations appear. Our model reproduces the time courses of cytosolic Ca(2+) measured in tracheal myocytes. Moreover, by postulating slight variations in the model parameters which determine the total number of receptors expressed and the ratio between Type 1 and Type 3 InsP(3)R, it offers an explanation to the experimental observation of qualitatively different responses of cells within a presumably homogeneous tissue.

Calcium↗

PubMed2002

Modelling of simple and complex calcium oscillations. From single-cell responses to intercellular signalling.

This review provides a comparative overview of recent developments in the modelling of cellular calcium oscillations. A large variety of mathematical models have been developed for this wide-spread phenomenon in intra- and intercellular signalling. From these, a general model is extracted that involves six types of concentration variables: inositol 1,4,5-trisphosphate (IP3), cytoplasmic, endoplasmic reticulum and mitochondrial calcium, the occupied binding sites of calcium buffers, and the fraction of active IP3 receptor calcium release channels. Using this framework, the models of calcium oscillations can be classified into 'minimal' models containing two variables and 'extended' models of three and more variables. Three types of minimal models are identified that are all based on calcium-induced calcium release (CICR), but differ with respect to the mechanisms limiting CICR. Extended models include IP3--calcium cross-coupling, calcium sequestration by mitochondria, the detailed gating kinetics of the IP3 receptor, and the dynamics of G-protein activation. In addition to generating regular oscillations, such models can describe bursting and chaotic calcium dynamics. The earlier hypothesis that information in calcium oscillations is encoded mainly by their frequency is nowadays modified in that some effect is attributed to amplitude encoding or temporal encoding. This point is discussed with reference to the analysis of the local and global bifurcations by which calcium oscillations can arise. Moreover, the question of how calcium binding proteins can sense and transform oscillatory signals is addressed. Recently, potential mechanisms leading to the coordination of oscillations in coupled cells have been investigated by mathematical modelling. For this, the general modelling framework is extended to include cytoplasmic and gap-junctional diffusion of IP3 and calcium, and specific models are compared. Various suggestions concerning the physiological significance of oscillatory behaviour in intra- and intercellular signalling are discussed. The article is concluded with a discussion of obstacles and prospects.

Animals↗

PubMed2002

Frequency encoding of intracellular Ca2+ signals.

In a very recent theoretical study, we showed that simple mitochondrial kinetics, originally proposed by Marhl et al., could be easily used as a plug-in element in other models describing intracellular Ca2+ dynamics. We analysed several previously published models and showed that mitochondria could indeed maintain the constant amplitude of intracellular Ca2+ oscillations very effectively. We also pointed out the importance of amplitude regulation for the frequency encoding of intracellular Ca2+ signals. This paper focuses on giving a more exhaustive demonstration of this phenomenon of frequency encoding for the model of Dupont et al.

Calcium↗

PubMed2002

The small world in biophysical systems structural properties of glycolysis and the TCA cycle in Escherichia coli.

It has been shown that the central metabolic network of Escherichia coli is of the small-world type. In this paper, we present that the metabolic network of glycolysis and TCA cycle as a part of the E. coli metabolism is also a small-world network. We found that the hubs of the studied network are consistent with those found in the complete metabolic network. The evolutionary meaning of this finding is discussed.

Biological Evolution↗