Sergey M. Bezrukov
Surprising features of particle dynamics in channel-facilitated transport

We analyze the consequences of interactions between the pore and the translocating molecule within the framework of a continuous diffusion model using the Smoluchowski equation with the radiation boundary conditions. Several of our analytical findings are quite counter-intuitive (e.g., Biophysical Journal, 2005, 88:L17-L19 and Physical Review Letters, 2006, 97:020601). Three of the examples to be discussed in the talk are:
(i) "Sticking" to the channel slows down translocation (a particie spends more time in the channel) but increases the flux;
(ii) "Up-hill" and "downhill" particle translocation times (and their distributions) are identical;
(iii) An optimal channel should exhibit the most pronounced binding on the side that is opposite to the side of the oncoming particles.

Jerzy Łuczka
Biological and molecular motors

Biological motors like kinesin and dynein move on wighways called microtubules, which are located in living cells. They are responsible for intracellular transport of various substances and materials. The biological motors consume energy from ATP hydrolysis converting it into mechanical movement. Attempts to describe and understand mechanisms of their movement have inspired physicists to model a more general class of molecular motors, i.e. small objects that move on spatially periodic structures in dissipative environment. Generic properties of transport of classical and quntum Brownian motors are presented.

I.D. Kosinska, I. Goychuk, M. Kostur, G. Schmid, and P. Hänggi
Transport in nanopores.

Ion transport in biological and synthetic nanochannels is characterized by such phenomena as ion current fluctuations, and rectification. Recently, it has been shown that the nanofabricated synthetic pores can mimic some transport properties of biological ion channels [P. Yu. Apel et al., Nucl. Instrum. Methods Phys. Res. B 184, 337 2001; Z. Siwy et al., Europhys. Lett. 60, 349 2002]. The ion current rectification is studied within a reduced 1D PNP model for synthetic pores. A conical channel of nm to a few hundred of nm in diameter, and of µm long is considered in the limit where the channel length exceed much the Debye screening length. The channel wall is assumed to be weakly charged. Ion transport is described by the nonequillibrium steady-state solution of the Poisson-Nernst-Planck system within a singular perturbation treatment. The role of boundary conditions is discussed. A comparison between the numerical and the result of the singular perturbation theory is presented.

Andrzej Fuliński and I. D. Kosińska
Modelling ionic transport through nanochannels

Transport of ions through nanochannels exhibits several untypical modes of behaviour of the diffusional and conduction currents, absent in the normal (electro-)diffusion. Biological and synthetic nanochannels exhibit two essential biophysical properties: selective ion conduction and the ability to gate open in response to appropriate stimulus. The asymmetric channels rectify the electric currents: the relation I vs. U is asymmetric, moreover, for U=0 the magnitude of purely diffusional currents depends on the direction of the concentration gradient. Synthetic nanochannels under oscillating electric fields are able to pump ions against concentration gradients. All these phenomena can be described by a model based on the continuous description starting from the Smoluchowski equation, and are caused by asymmetries of the channel's geometry and of its internal electric fields.
Gating results, among others, in the appearance of the flicker noise in the power spectra of ionic currents measured both in very narrow biological and (some) synthetic channels. The results of Brownian Dynamics simulations are presented of the motion of K+ ions of the single-file type through a model channel with the gate which opens and closes under influence of both random noise (Wiener process), and interactions with ions present inside the channel. We found that there is a range of the parameters, in which the power spectrum has the characteristics of the flicker noise. Essential for the appearance of the flicker noise is the condition of single-file motion of ions through the channel (the single-file motion is also the condition for the appearance of subdiffusion). 1/f noise is accompanied by the long-tail distributions of the dwell times in open and closed states. Moreover, in the long runs, the K+ currents are self-similar, and the open-channel currents scale over the range of of Δt's as Io = Io,0 (Δt/Δ0 t)β with β=1 ±0.07.

A. F., I. D. K., and Z. Siwy, Europhys. Lett. 67, 683 (2004)
Z. Siwy, I. D. K., A. F., and C. R. Martin), Phys. Rev. Lett. 94, 048102 (2005)
A. F., I. D. K, and Z. Siwy, New J. Phys. 7, 132 (2005)
I. D. K, and A. F., Phys. Rev. E 72, 011201 (2005)
I. D. K., and A. F., Background processes and the generation of the flicker noise in nanochannel transport, in Unsolved Problems of Noise and Fluctuations: UPoN 2005, (ed. by L. Reggiani, C. Pennetta, V. Akimov, and M. Rosini), AIP CP800 (2005), pp. 287-292.
I. D. K., and A. F., Acta Phys. Polon. B 37, 1745 (2006); ArXiv physics/0603238
I. D. K., J. Chem. Phys. 124, 244707 (2006)

Jerzy W. Mozrzymas
Kinetics and modulation of synaptic receptors: how it looks like in the time scale of synaptic transmission ?
The time course of excitatory and inhibitory synaptic currents plays a key role in determining the integration of synaptic signals in neurons. The kinetic shape of these currents depends on the amount and time course of neurotransmitter released from the nerve terminal and the kinetics of the postsynaptic receptors. In the central nervous system synaptic agonist (e.g. GABA and glutamate) is known to reach millimolar concentrations and is cleared out from the synaptic cleft within hundreds of microseconds. Notably, the synaptic currents usually outlast by far the time duration of agonist transient implying that intrinsic kinetic properties of receptors play a major role in determining the time course of synaptic currents. Moreover, extremely brief presence of agonist within synaptic cleft indicates that the postsynaptic receptors are activated in conditions of extreme non-equilibrium. In this presentation I shall concentrate our attention on the inhibitory synaptic transmission for which GABA is the major neurotransmitter in the adult brain. Synaptic currents can be routinely measured in the whole-cell mode of the patch-clamp technique. However, the analysis of the IPSCs is insufficient to characterize the kinetics of postsynaptic receptors. The description of kinetic properties of ligand-gated channels requires construction of dose-response relationships for current responses elicited by exogenous agonist applications. However, the perfusion of agonist should be sufficiently fast to mimic the synaptic transient of the neurotransmitter. Using the ultrafast, piezoelectric driven perfusion system a complete exchange of agonist can be achieved within 100 μs largely fulfilling thus this requirement. The analysis of current responses to ultrafast GABA applications allowed characterizing the kinetics of these receptors with time resolution adequate to the synaptic events. The application of this technique made it possible also to describe the mechanism of pharmacological modulation of GABAA receptors by several clinically relevant compounds such as benzodiazepines, phenothiazines, barbiturates as well as by other modulators such as e.g. pH, Zn ions. The native GABAA receptors are known to be extremely heterogeneous. GABAA receptors composed of different subunits show different kinetic and pharmacological properties. For this reason, the expression of recombinant receptors with a strictly defined subunit composition in cell lines provided the means to further characterize the kinetics and pharmacology of the GABAA receptors in strict relation to its tetriary structure.

Ian Mellor
Single-channel studies of voltage-gated sodium channels and their interaction with pyrethroid insecticides

Pyrethroids are synthetic analogues of natural insecticides known as pyrethrins that are found in some species of chrysanthemum plant. Pyrethrins and pyrethroids target voltage-gated sodium channels causing a slowing of their inactivation and deactivation processes and are selective for insect over mammalian channels. We have studied the effects of the pyrethroid deltamethrin on the single channel parameters of wild-type and I874M mutant rat NaV1.2 sodium channels expressed in Xenopus oocytes using patch-clamping. The I874M mutant is more susceptible to pyrethroids as it simulates an insect sodium channel at this position. The conductances of wild-type and mutant channels were 19.8pS and 19.6pS, respectively, and were unaffected by deltamethrin. However, the reversal potentials for both channels were increased by the pyrethroid. Histograms of open times were best-fit by single exponentials. The open time constants of wild-type and mutant channels were similarly voltage-dependent (0.01ms mV-1). For openings at -40mV, the mean open time constant of the wild-type channel was significantly shorter (0.48 ± 0.05ms) than that of the mutant channel (0.65 ± 0.08 ms). Deltamethrin (≥ 0.1μM wild-type; ≥ 1nM mutant) induced a second population of openings that were prolonged in duration. This population, and its open time constant, was increased when the concentration of deltamethrin was raised. When the proportion of prolonged channel openings was used as a measure of the potency of deltamethrin, the pyrethroid was found to be ~100 times more potent on the mutant than on the wild-type channel. Low concentrations of deltamethrin increased the frequency of opening (fo) of wild-type and mutant channels during a depolarisation, but fo was reduced by 1 μM (wild-type) and 0.01μM (mutant) deltamethrin. Following application of deltamethrin, both wild-type and mutant channels often remained open following membrane repolarisation to -100mV, with fo being dependent on the deltamethrin concentration.

Eli Zlotkin
Scorpion Neuropeptides Affecting the Insect Voltage Gated Sodium Channels - Diversity and Cooperativity

Long-chain neurotoxins derived from the venom of the Buthidae scorpions, which affect voltage-gated sodium channels (VGSCs) are divided to the α category (which affects sodium inactivation) and ß category (affecting the sodium activation stage). The excitatory and depressant insect-selective toxins from scorpion venom belong to the ß category. We provide here two pieces of information concerning the chemistry and agrotechnical significance of the insect-selective toxins. The efficacy of the recombinant baculovirus (expressing an anti-insect toxin) is attributed mainly to its ability (a) to continuously provide and translocate the gene of the expressed toxin to the insect central nervous system; (b) to provide a mechanism for insecticide resistance management. The latter is based on the pharmacological flexibility of the voltage-gated sodium channel. Thus, channel mutations conferring resistance to a given class of insecticidal agents (such as the KDR phenomenon) may greatly increase susceptibility to the toxin-expressing baculoviral bioinsecticides. The study reveals an insect-selective toxin derived from the α category of scorpion neuropeptides. By the aid of reverse-phase HPLC column chromatography, RT-PCR, cloning and various toxicity assays, a new insect selective toxin designated as BjαIT was isolated from the venom of the Judean Black Scorpion (Buthotus judaicus), and its full primary sequence was determined: MNYLVVICFALLLMTVVESGRDAYIADNLNCAY-TCGSNSYCNTEWCTKNGAVSGYCQWLGKYGNACWCINLPDKVPIRIPGACR (leader sequence is underlined). Despite its lack of toxicity to mammals and potent toxicity to insects, BjαIT reveals an amino acid sequence and an inferred spatial arrangement that is characteristic of the well-known scorpion α-toxins highly toxic to mammals. BjαITs sharp distinction between insects and mammals was also revealed by its effect on sodium conductance of two cloned neuronal VGSCs heterologously expressed in Xenopus laevis oocytes and assayed with the two-electrode voltage-clamp technique. BjαIT completely inhibits the inactivation process of the insect para/tipE VGSC at a concentration of 100 nM, in contrast to the rat brain Nav1.2/ß1 which is resistant to the toxin.

Krzysztof Dołowy
Is the sodium micro-channel responsible for axon properties? Hodgkin and Huxley - from empirical equations to physical modeling.

Hodgkin and Huxley solved the problem of formation and propagation of action potential in nerve axon half a century ago. They founded out that the sodium conductance increases to a maximum value within 1ms and than is inhibited within next 1ms. The sodium conductance is a very complex function of both membrane potential and time. Hodgkin and Huxley described sodium conductance by an empirical function which requires 6 functions and 20 adjustable parameters. Almost 30 years ago Sigworth and Neher showed that it is opening probability of sodium channel which is the function of time, and its amplitude is 2.5pA. Since then problem of kinetics of sodium channel seemed to be almost solved. Unfortunately, this is not the case. To explain axon properties by the 2.5pA channel found by Sigworth and Neher it’s density at axon membrane should be 1-2 per µm2 and local electric behavior of axon membrane should be erratic. Such behavior have never been shown experimentally. Moreover there are 30 to 500 fold more sodium channels in the axon membrane than measured by Sigworth and Neher.
Due to electric noise it is not possible to measure fast ion channels of amplitude lower than 0.5pA directly by the patch clamp method. Such channels do exist. It is possible to built a model low amplitude voltage gated sodium channel in which amplitude is a function of both time and potential. Such model channel stores up to a dozen of ions like in magazine of automatic rifle. When open the model channel conducts in a short time only limited number of ions in series. Its current amplitude is in order of 1fA and conductance less than 0.1pS. The Hodgkin and Huxley empirical equation can be described by a model channel in which there are only 8 constants of clear physical meaning.

Adam Gadomski Z. Pawlak, I. Santamaria-Holek
"On a formation of ion channels in internal- and external- friction driven systems"

Ion channels occur not only in cellular environments, in which certain ions are transported across the biomembranes between intra- and extracellular phase. The may also appear in some related problems such as:
(i) formation of soft (protein/colloid) crystals and aggregates controlled by their (electric) double-layer featured depletion zones (A. Gadomski, Physica A374, 43 (2007), with an isotropic but non-constant friction, C Malaga et al., Physica A369, 291 (2006);
(ii) by-water-pressurisation enhanced biolubrication, characteristic of time-dependent coupling of tribopolimerization fields, leading to a departure from acid base-equilibrium, Z. Pawlak et al., J. Mater. Process. Technol. (2007), accepted, by means of a tribomicellization kernel, leading, in some model articular cartilages, to adequate description of the energy dissipation during (external) friction under a certain heavy normal/lateral load, A. Gadomski, J. Math. Chem. 22, 167 (1997)

Piotr Garbaczewski
Thermodynamics of diffusion processes

We discuss the role of various information theory functionals in the thermodynamical description of diffusion-type processes. The inherent uncertainty (indeterminacy) measures are established.

Przemysław Borys
On the recovery from inactivation in ball and chain model

The ball and chain is a widely known model of ion channel inactivation. Much less attention is put to the recovery from inactivation. A possible physical mechanism of inactivation based on the ball-chain interactions is shown and analysed.

Michał Kurzyński
Statistical properties of dichotomous noise generated in biomolecular processes

Dichotomous signals detected with the help of patch-clamp technique or single-molecule fluorescence spectroscopy are the most convincing manifestation of the actual occurrence of a stochastic transition dynamics between multitude conformational substates in native proteins. The nature of this dynamics is determined by particular stochastic properties if the dichotomous noise observed. These involve non-exponential and possibly oscillatory time decay of the second order autocorrelation function, its relation to the third order autocorrelation function as well as a relation to waiting time distribution densities and their correlations. Besides a general introduction to the problem, the simple model of biological processes gated by specific conformational substates is considered in detail. The study throws light on an intriguing matter of a multiple stepping possibility of the myosin motor along the actin filament per one ATP molecule hydrolysed.

Mustafa B.A. Djamgoz
Voltage-gated Na+ channel hyperactivity and control of metastatic cell behaviours in breast and prostate cancer

In an electro-physiological approach to understanding the pathophysiology of metastatic disease, we have found that strongly metastatic cells express voltage-gated Na+ channels (VGSCs) in neonatal splice forms. Most work has been done on breast cancer (BCa) and prostate cancer (PCa) where VGSC activity potentiates a range of metastatic cell behaviours, including "motility" (Fraser et al.,2003, 2005; Brackenbury et al.,2007). This presentation will highlight a number of aspects of cancer cell motility in relation to VGSC control, as follows:
1.Types of motility. Cellular motility has been measured and quantified in a number of ways: a) 'wound-heal' assays [cf. early, lateral local motile activity]; (b) 'transverse migration' [cf. intra/extravasation]; and (c) 'galvanotaxis' [cf. (b) taking into account also local field or trans-cellular voltage gradients]. All three types of cellular motility were suppressed significantly by suppressing VGSC activity using the highly specific blocker, tetrodotoxin (TTX). In the case of MDA-MB-231 BCa cells, even ~30% reduction in VGSC (neonatal Nav1.5) activity by siRNA completely removed the VGSC-dependent enhancement of motility.
2.Mechanisms upstream of VGSC expression. Our data are consistent with VGSC upregulation occurring when BCa and PCa becomes hormone-independent and switches to dependence on growth factors. Two major growth factors were found to be involved in PCa: Nerve growth factor and epidermal growth factor (EGF). Although both potentiated motile activity, it was only EGF that signalled through VGSCs. Interestingly, in media containing a high level of insulin, VGSC activity suppressed motility, raising the possibility of cellular motility being under servo-like control.
3.Mechanisms downstream of functional VGSC expression / activity. We know much less about these. On the whole, there are two sets of possibilities: a) protein-protein interactions and (b) enzyme activity stimulated by VGSC-mediated Na+ influx and/or subsequent changes in intracellular Ca2+ or pH. As an example of the latter, evidence will be presented for VGSC/Na+-dependent PKA activity.

Brackenbury WJ et al. (2007). The neonatal splice variant of Nav1.5 potentiates in vitro invasive behaviour of MDA-MB-231 human breast cancer cells. Breast Cancer Res Treat. 101 : 149-160.
Fraser SP et al. (2005). Voltage-gated sodium channel expression and potentiation of human breast cancer metastasis. Clin Cancer Res. 11 : 5381-5389.
Fraser SP et al. (2003). Contribution of functional voltage-gated Na+ channel expression to cell behaviours involved in the metastatic cascade in rat prostate cancer. I Lateral motility. J Cell Physiol 195: 479-487.

Ralf Metzler
Anomalous stochastic processes and biological relevance
Many processes in Nature deviate from the standard laws of Brownian motion or exponential relaxation. I will introduce the continuous time random walk and the related fractional Fokker-Planck equation as general tools to model such dynamic anomalies. Four examples from cellular biology are introduced:
(1) Due to the superdense environment of a variety of biomacromolecules (molecular crowding), it has been claimed from experiments and simulations that the diffusion of proteins and polynucleotides in the cell is subdiffusive. I will show that, e.g. for transcription factors, this will give rise to a weak ergodicity breaking, whose potentially beneficial effects to the stability and efficiency of gene regulation are discussed. Similar effects would be expected for larger molecules that intermittently bind to the cell membrane or pass through membrane channels
(2) The passage of longer biomolecules through membrance pores as such is also reported to be subdiffusive. Some recent models will be introduced.
(3) The opening time of certain ion channels was reported to follow logarithmic oscillations around a general power-law trend. A model taking these oscillations into account by a scaling of characteristic times and amplitudes of single exponential contributions is presented.
(4) Finally, the rebinding dynamics of ligands to proteins such as myoglobin are discussed.

Monika Krasowska, M.B.A. Djamgoz, I. Ozerlat, M. Mycielska, Z.J. Grzywna
A mathematical description of wound healing assay

Cell migration is a complex phenomenon that requires the coordination of numerous cellular processes. Investigation of cell migration is of common as well as for clinicians. The wound healing assay is simple, inexpensive, and one of the earliest developer methods to study directional cell migration in vitro. The basic steps involve creating a "wound" in a cell monolayer, capturing the images at the beginning and at regular intervals during cell migration to close the wound. The above process is modeled in this work by symmetric sorption and described by the hyperbolic diffusion equation (correlated random walk process). We have compared this model with experimental data showing quite a good agreement.

Gerhard Schmid, Igor Goychuk and Peter Hänggi
Channel noise in excitable membranes

Single-channel recordings demonstrate that the switching of ion channels between open and closed configurations is a stochastic process. Moreover, the random switching of voltage-gated channels is connected with movement of charge within the cell membrane. These properties of channel gating affect the excitability of cell membrane patches. We investigate the influence of gating charge effects on the channel noise-induced spontaneous spiking activity of excitable membrane patches within a stochastic Hodgkin-Huxley modeling. Our study revealed that while the deterministic modeling with gating charge effects does not differ dramatically from the original Hodgkin-Huxley model for the standard set of parameters, the corresponding stochastic model which takes into account the channel noise -- i.e. the fluctuations of the number of open ion channels -- does behave very differently for intermediate-to-large membrane patch sizes. A main finding is that spontaneous spiking activity becomes drastically reduced.

Stanisław Przestalski, Jerzy Hładyszowski
Forces acted in living cells


Mieczysław Torchała and Michał Kurzyński
Numerical study of vibrational nonequilibrium in early stages of photosynthesis

Ultrafast laser spectroscopy studies show clearly that the primary electron transfer in photosynthesis last no longer than few picoseconds. Of a similar rate are processes of vibrational relaxation which, consequently, have to be taken into account in the correct description of the phenomenon. A simple theory is proposed combining transition processes with diffusion in an energy space. Analytical formulae for effective transition rate constants are derived and a transient kinetics is considered. Quality of analytical approximations is verified by numerical simulations for various physical conditions. Possibility of efficient parallel computations is also shown. The model explains a peculiar temperature and wavelength dependence of pomp-probe spectra observed.

Katarzyna Choma, Piotr Bednarczyk, Adam Szewczyk, Krzysztof Dołowy
Single channel measurements of ATP regulated potassium channel from rat brain mitochondria

Various types of ion channels are present in mitochondria membrane. During last ten years they have become object of many studies. It was proved that mitochondrial ATP-regulated potassium channel (mitoKATP) and mitochondrial Ca-activated large conductance potassium channel (mitoBKCa) are involved in cytoprotection but the mechanism of this event is still unclear. In our study, single channel activity was measured after reconstitution of inner mitochondrial membrane from rat brain into a planar lipid bilayer. The potassium channel with a mean conductance of 219 ± 15 pS in symmetrical 450/450 mM KCl (cis/trans) solution was recorded. The effect of different channel modulators on single channel activity was examined. The channel activity was inhibited by complex ATP/Mg2+ and the effect was reversed by BMS 191095and the channel activity was reduced. The reason of that amplitude decrease is the presence of magnesium ions. Magnesium ions change channel activity only after addition to the trans compartment in our experimental conditions. Apart from, inhibitor of mitoBKCa channel - iberiotoxin IbTx and inhibitor of mitochondrial voltage gated potassium channel (mitoKv1.3) - margatoxin MrTx have no effect on channel activity. Additionally, inhibitor of mitoKATP channels - 5-hydroxydecanoid acid (5-HD) does not change channel activity. Thus, we conclude that the mitoKATP is present in rat brain mitochondria but in opposite to mitoKATP from other tissues it is insensitive to 5-HD.

Koszela-Piotrowska I., Bednarczyk P., Dołowy K., Skalska J., Głab M., Wieczorek R., Szewczyk A.
Ion channels from rat skeletal muscle mitochondria

Chloride and potassium selective ion channels are present in inner mitochondrial membrane. Potassium uptake upon mitochondrial energization may partly compensate the electric charge transfer produced by proton pumping and thus enable the formation of a pH gradient along with transmembrane electric potential. Chloride channels may be involved in several crucial processes such as regulation of mitochondrial volume or membrane potential. Single channel activity was measured after reconstitution of the inner mitochondrial membranes from rat skeletal muscle into a planar lipid bilayer. Two potassium channels types and one chloride channel were observed. After incorporation, in gradient 50/450 and 50/150 mM KCl (cis/trans) the potassium channels were recorded with a mean conductance of ~ 300 pS (mito BKCa) and 91 ± 10 pS, respectively. Chloride channel conductance was 56 ± 4 pS under gradient 50/450 mM KCl (cis/trans) conditions. In gradient 50/450 mM KCl we observed increase propability of the big potassium channel opening in the presence of Ca2+ (cis/trans) (n = 6) and inhibition by iberiotoxin (IbTx) (cis/trans) (n = 2). The presence of mito BKCa channel in skeletal muscle mitochondria was further confirmed with the use of isolated skeletal muscle mitochondria. Furthermore, it was shown that chloride channels are inhibited by 4,4'-diisothiocyanostilbene-2,2'-disulfonic acid (DIDS) and 4-acetamido-4'-isothiocyanostilbene-2,2'-disulfonic acid (SITS) but only from trans side. Our results suggest that there are potassium and chloride selective ion channels in inner mitochondrial membrane from rat skeletal muscle. This study was supported by the Ministry of Science and Information Society Technologies grant No PBZ-MIN-001/P05/11.

Gudaniec A.,Kruszewska N.,Gadomski A., Pawlak Z.
Transport of water and charge carriers through biopolymer micelles-containing interspaces.
A nonequilibrium-thermodynamics model of friction-lubrication in an articular cartilege (ac) will be presented. A microscopic mechanism of friction facilitated by pressurisation of water will be drawn. A physicochemical situation, pointing to a departure from acid- base equilibria in the ac will be sketched, and compared with experiments. A transport of ions in terms of the random walk theory will be considered, and an anomalous chemical reaction, due to a confinement and external load, will thoroughly be characterized. The paper is based on: Z. Pawlak et al. J. Mater. Proc. Techn. (in press) and A. Gadomski, J. Mathem. Chemistry 22, 161 (1997).

Siódmiak J., Gadomski A., Uher J.J.
Diffusion of lysozyme macroions along the crystal surface and its influence on the crystal growth

A superdiffusive random walk in the depletion zone around a growing protein/colloid crystal is considered. It stands for a dynamic boundary condition of the growing process, and competes with a static, curvuture-involving boundary condition, while eventually constituting the overall diffusion function of the process. This function, in turn, indicates whether the new phase grows as an orderly phase, or a converse scenario appears. This situation can be treated both numerically (J. Siodmiak et al., Int. J. Modern Phys. C 17/9 1359-1366 (2006)) and/or analytically, within a generalized Smoluchowski framework (A. Gadomski, Physica A, 373 43-57 (2007)).

Adamkiewicz B., Grajpel B., Katkowska M.J., Tęgowska E., Stankiewicz M.
Modulating effect of synthetic proctolin on spontaneous bioelectrical activity of DUM neurons in American cockroach, Periplaneta americana L.

A large number of neuropeptides modulating synaptic strength and cellular excitability has been identified in nervous system of insects. The first insect neuropeptide to be purified was proctolin - it was isolated from the hindgut of the American cockroach (Periplaneta americana). It is commonly known, that proctolin stimulates the contraction of visceral and skeletal muscles and these properties allow to classify proctolin as a neurotransmitter. Moreover, to investigate the activity of proctolin, many different biological tests have been set up using foregut, heart, oviductus or else jumping leg. The immunohistochemistry tests performed on the dorsal surface of the third thoracic ganglion identified the proctolin-immunoreactive neuron. This neuron is known as the slow coxal depresor motoneuron. At the same time it was found that the somata of dorsal unpaired median neurons (DUM) were proctolin-nonimmunoreactive [O'Shea & Bishop, 1982]. However, earlier studies suggested that the DUM cells were highly sensitive to applied proctolin (Walker et al., 1980). The octopaminergic dorsal unpaired median neurons are pacemaker–type neurons. Their soma is able to generate action potentials of an amplitude of 80-120 mV at resting potential ranging from -45 to -60 mV without any external stimuli. This endogenous activity results from the cooperation of several membrane ionic conductances: sodium, potassium, calcium and chloride (Grolleau & Lapied, 2000). Each modification of this activity may disturb the stability of cells and consequently modify nervous system functioning. DUM neurons are used as a good model for different pharmacological studies. The purpose of presented investigations was to establish the presence of proctolin receptors in DUM neurons. We expected that spontaneous regular beating discharges of these neurons can be modified by activation of proctolin receptors by synthetic proctolin. Experiments were performed using a conventional glass microelectrode technique. The spontaneous action potentials were recorded for ~10 min, then proctolin (synthetized at the Faculty of Chemistry, University of Wrocław) was applied in concentration 10-9, 10-11 and 10-12 mol/l by means of microinjection. Our experiments revealed that proctolin (10-9 mol/l) induced a modification of DUM neuron activity. Two modes of neuronal response to proctolin can distinguished: (1) it induced a small decrease of neuronal firing frequency from about 2,5 Hz to 2 Hz or (2) it caused an increase of spontaneous discharge at first, and then the decrease (the magnitude of this decrease was similar to that observed in the case of the first mode of the response). These two modes of cell responses were observed during first 0.2-0.5 min following proctolin application. A longer observation of the cells showed that in 60% of cells representing the first mode of the response and in 29% of cells responding according to the second mode, action potentials disappeared; simultaneously a few mV hyperpolarization was noticed. In the other DUM neurons, firing frequency returned to control values after 10-15 min. We have been found a relationship between the firing frequency and the type of the effect elicited by proctolin. When control spontaneous firing frequency was higher than 2 Hz, we observed proctolin-induced a decrease of the frequency. When spontaneous discharges frequency was lower than 2 Hz, we noticed an increase of firing frequency resulting from application of proctolin. The effect of lower proctolin concentrations (10-11 and 10-12 mol/l) was similar, however, first activity modification appeared several minutes later than it was in the case of higher concentration. Our results provide an evidence for the presence of proctolin receptors in DUM neurons and their participation in regulation of bioelectrical activity in these neurons.
Grolleau F., Lapied B., 2000, J. Exp. Biol., 203: 1633-1648,
O'Shea M., Bishop C. A.,1982, J. Neurosci., 2 (9): 1242-1251,
Walker R.J., James V.A., Roberts C.J., Kerkut G.A.,1980, Neurotransmitter receptors in invertebrates, [In] Receptors for Neurotransmitters, Hormones and Pheromones in Insects, eds. D.B. Sattelle, L.M. Hall, J.G. Hildebrand, 41-57, Elsevier/North-Holland Biomedical Press, Amsterdam & New York

Machura Ł., Rogoziński S., Łuczka J., Hanggi P.
Current fluctuations in inertia Brownian motors

The quantity of foremost interest in the context of transport in periodic systems like Brownian ratchets, is the mean velocity of the particle. However, there are several quantifiers that can be used in more detailed description of the transport phenomena. One can describe the quality of transport by mean of the effective diffusion or Peclet number. On the other hand, the energetic efficiency of a Brownian motor is also an important issue. We show that by inspecting the fluctuations, both in the velocity and the position space, the above questions can be answered. We use simulations to investigate the connection between the fluctuations and the system's modus operandi. The optimal vs common transport conditions are presented.

A. Wozinski, J. Iwaniszewski,
Kinetic model for stochastically modified ionic channel

Ionic channels form pores in the biomembranes which are huge macromolecular structures. Thus thermal fluctuations of an enormous number of degrees-of- freedom of the biomembrane material generate stochastic modifications of the form of pores. Here we present some results on the influence of the fluctuations of the internal pore structure on the channel conductivity. We consider some simple kinetic models for ion permeation through a membrane channel with conformational changes mimicked by means of Markovian dichotomic noises. Depending on the combination of channel and noises parameters a significant increase or decrease of ionic current is observed. The underlying biophysical mechanism of these features is discussed.

N. I. Ryabokon, Artur Cieslar-Pobuda, Bogusz Przybylski and J. Rzeszowska-Wolny
Ionizing radiation induced synthesis of poly (ADP-ribose) correlates with the amount of cellular DNA but the speed of synthesis and decomposition is not cell cycle dependent

Poly (ADP-ribose) (PAR) is a polymer synthesized in a cell nuclei from NAD+ by the polymerases PARP-1 and PARP-2 .Due to PARPs’ ability to recognise DNA strand breaks, poli ADP-rybose plays an important role in a repair of DNA. We induced the formation of poly(ADP-ribose) by irradiation of cultured Raji cells with 2 Gy of X-rays and compared the kinetics of its metabolism in cells differing with the DNA content. The level of poly (ADP-ribose) in cells was estimated by reaction with anti-PAR antibody and scoring the fluorescence intensity and the amount of DNA was assessed on the basis of fluorescent staining. The computer program automatically identifying the cells on microscopic pictures and calculating the fluorescence intensity for both types of stain was adapted for this work. PAR levels were significantly higher in cells with the higher amount of DNA however the PARP activity (calculated as PAR per DNA unit) and the kinetics of polymer change did not differ in G1, S or G2 phases. These studies have also shown that determination of cell cycle using flow cytometry can be sometimes replaced by cytoimmunochemistry techniques

Maria Jolanta Katkowska, Barbara Grajpel, Beata Adamkiewicz, Eugenia Tęgowska
Diversity of electrophysiological and thermoregulatory responses to insecticides in insects of markedly different haemolymph ionic content

A variety of neuroreceptors and ion channels have been identified as major target sites of neurotoxic insecticides. Pyrethroids keep the sodium channel open for unusually long time causing a prolonged flow of sodium current while indoxacarb is a highly potent blocker of sodium channels. Pyrethroids toxicity exhibits a negative and indoxacarb - a positive temperature correlation. Insects chosen for this study differ markedly in their haemolymph ionic content (only 2 mmol/l of Na+ in the beetle while as much as 200 mmol/l in the cockroach). The present study was undertaken to investigate how topically applied ß-cyfluthrin (Bulldock 025 EC, Bayer AG, Germany) - 0.19 ml/l H2O and indoxacarb (Steward 30 WG, DuPont, France) - 170 mg/l H2O and 340 mg/l H2O affect thermoregulatory behaviour (automatically recorded in a horizontal thermal gradient system for at least two days) and muscle resting potential (RP) in adult Colorado potato beetles, Leptinotarsa decemlineata Say (both sexes) and Periplaneta americana L. (males only). Electrophysiological experiments were performed in situ on indirect flight muscles of the beetle and on dorsoventral muscles of the cockroach. The conventional microelectrode technique was used. The RP in Colorado beetle's muscles was -72.4±0.3 mV (±SEM) and in muscles of the cockroach -66.3±0.4 mV (±SEM) and it did not change much in time. The application of ß-cyfluthrin strongly affected muscle RP in cockroach giving rise to a fast significant depolarisation (by about 11 mV, P < 0.05), what is a typical reaction to pyrethroid intoxication. However, the muscles of Colorado beetle did not respond in this way to intoxication with this insecticide. Their muscle RP was only slightly affected by ß-cyfluthrin and a minor hyperpolarisation rather than depolarisation was observed. The effect of indoxacarb on cockroach muscles was opposite to that of pyrethroid insecticide. It hyperpolarised the muscle RP by up to 12 mV (P < 0.05). A previous study showed that the response of DUM neurons to indoxacarb is similar - a slight hyperpolarisation of neurons at the beginning of experiments increasing up to 11±6 mV after 60 min has been observed. The amplitude of spontaneous action potentials progressively decreased with time and after 60 min the potentials almost disappeared. Lapied et al. found that pure indoxacarb exerted a similar effect on cultured cockroach DUM neurons. They explained it as the result of an inhibitory effect of the insecticide on the neuronal sodium current. The effect of indoxacarb on Colorado beetle muscles was exactly opposite. Only its higher concentration affected the RP causing a slight gradual membrane depolarisation, up to 4 mV at most. Behavioural observations of thermal preferences in the studied insects showed that intoxicating them with any insecticide modifies their thermoregulatory behaviour. ß-cyfluthrin-treated Colorado beetles preferred at the beginning of experiments (up to 8 hours) a warmer environment (by about 5oC) than that selected by control insects, but later on they were gradually moving towards slightly lower temperatures than those in the controls. The cockroaches intoxicated with pyrethroid were selecting for at least 24 h much higher temperatures (by up to 7oC) than the control insects and indoxacarb-treated cockroaches preferred the temperatures slightly (by 5oC at most) lower than those selected by the insects in the control. Poisoning Colorado beetle with indoxacarb, on the contrary, caused selecting somewhat higher temperatures for at least the first two days as compared to those preferred by control insects. The mechanism of different thermal preferences of cockroaches depending on the insecticide applied can be explained in terms of insecticide-induced changes of sodium conductance in excitable cells, which is enhanced by pyrethroid and reduced by indoxacarb. In insects, like Colorado beetle, with unconventional ion levels in their haemolymph, at least the Na+ gradient may be in the reverse direction. A flow of Na+ could then travel in the reverse direction giving rise to opposite in comparison to the cockroach changes in the intraneuronal sodium concentration. This could account for the differences in Colorado beetle electrophysiological and behavioural reactions to insecticides applied, especially to indoxacarb, when compared to the cockroach. According to the body temperature set-point theory, based on balance between sodium and calcium ions concentration in the thermoregulatory centre, a decreased calcium or increased sodium concentration results in both increased heat production and raised body temperature, which can give rise to preferential seeking for lower ambient temperatures. It is known that at least some insects are endothermic and they can increase actively their body temperature (warm itself up) and then stabilize the internal temperature well above the ambient temperature level.

K. Jelonek, M. Pietrowska, P. Widłak , G. Dudek, Z. J. Grzywna
Polymorphisms and mutations of DNA repair genes as a risk factor for cancer development

This paper describes one of the methods to examine the risk factor for cancer development. To do it we use Single Nucleotide Polymorphism (SNP). SNPs examine in this work are mostly connected with genes participated in DNA repair pathways like: NBS1, APE1, XPD312, XPD751, XPA, XRCC1, hOGG1. Polymorphism determination of the individual gene is run using PCR-RFLP method. In the first step PCR method is used for the individual gene fragment amplification. Then these fragments are digested using appropriate restrictive enzymes and to visualize the results the agarose gel is used. The aim of this work is statistical analyses of genetic polymorphism in selected cancer-related genes in groups of head and neck cancer patients, colon cancer patients, healthy controls and comparison of the genotype frequency of selected genes between cancer patients and control patients groups. One of the methods used in these statistical analyses is fuzzy set theory.

K.Pawełek, R.Herok, Z.Grzywna J.Rzeszowska-Wolny
Analysis of changes in gene expression profiles induced by ionizing radiation in Me45 and K562 cells.
The levels of transcripts from all actually active genes (transcriptome, transcription profile) characterize the cell type and its physiological state. Microarray techniques allow determining transcription levels of thousands of genes in one experiment. In our studies change of transcriptome in cells exposed to ionizing radiation was followed by oligonucleotide Affymetrix microarray method. Transcription profiles in two human cancer cell lines – Me45 and K562 were determined in control cells and at 4 different time points (20 min, 12h, 24h, 36h) after irradiation with 4Gy. Affymetrix microarrays HU-133 allowed for assessment of the transcription levels of 22283 genes for each time point. New approach based on calculations of average speed of change of genes expression levels (Vex) was applied to the analysis and Vex distributions were approximated by normal distributions. We observed that in both cell lines the change of transcription level was the highest at first moments after irradiation (SD=225.43 for Me45 cell line and SD=281.9312 for K562 cell line for 20 min time point). In next time point (12 h) changes were much slower but they have a tendency to increase 24 and 36h later. The dynamics of changes was different in both cell lines. Analysis of processes that showed the highest change after irradiation showed that genes coding for proteins of proteasom, oxidative phosforylation and ribosome were characterized by the highest Vex. The expression levels of some genes belonging to these pathways were tested by the Q-RT PCR method.