The kinetics of Ca-Na exchange in excitable tissue

A model is proposed to describe the Na-Ca exchange in excitable tissues. The present scheme requires a carrier mechanism that exchanges 3Na for 1Ca across the membrane under the electrochemical gradient of Na. The carriers, assumed to be trivalent anions, have monovalent and divalent sites; Ca and Na can compete only at the second site. The partially and fully loaded carrier-ion complexes are mobile and diffusible across the membrane. Subsequently, analytical expressions for Na and Ca unidirectional flux at steady state are derived in terms of intracellular concentration (Na(i) and Ca(i)) and extracellular concentration (Na(o) and Ca(o)) as well as membrane potential, E(M). Published experimental flux data on cardiac muscle, squid axon, and rat synaptosomes can be satisfactorily fitted with the flux equation simply by adjusting the numerical constants.     

Possible origin of action potential and birefringence change in nerve axon

In this theory, we propose that the action potential and the birefringence change in nerve axon are both originated from dipole reorientation at the membrane surface under stimulation. The calculation is based upon a dipole distribution in two energy bands with a population ratior. Coincidence of the action potential with the birefringence change is predicted to occur whenr is in the order of 0.1 which corresponds to severalkT for the energy separation between the two bands. Furthermore, at any value ofr, there is always a small delay of the birefringence change behind the action potential. The theory not only is in good agreement with the recent optical observations in nerve but also indicates a possible physical origin of action potential, a long unresolved problem in neurophysiology.     

A bumetanide-sensitive, potassium carrier-mediated transport system in excitable tissues

The binding of [3H]-bumetanide to rat brain synaptosomes revealed the existence of two binding sites. The high affinity site (R1 = 46.6 fmoles/mg protein) binds bumetanide and furosemide with Kd1 of 13 nM and 1.5 microM respectively, while the low affinity site (R2 = 1.37 nmoles/mg protein) is characterized by Kd2 of 200 microM and 680 microM for bumetanide and furosemide, respectively. Bumetanide sensitive 86Rb uptake was 34 +/- 14.5, 38.3 +/- 1.4, 18.6 +/- 1.3 and 29.0 +/- 6.1% of total 86Rb uptake in synaptic plasma membrane vesicles, rat brain synaptosomes, Neuroblastoma N1E115 cell line and chick chest muscle cells, respectively. Furosemide and bumetanide inhibited 86Rb uptake to rat brain SPM- vesicles in a dose dependent fashion. Half maximal inhibition (IC50) was observed at 20 nM and 4 microM for bumetanide and furosemide, respectively. Bumetanide-sensitive transport was dependent on extravesicular sodium and chloride concentrations with a Km of 21 and 25 mM for the two ions, respectively. These results demonstrate the existence of a "loop diuretic" sensitive carrier-mediated K+ transport system in brain and other excitable cells.     

A transition state theory approach to the kinetics of conductance changes in excitable membranes

Summary The kinetics of ionic current mechanisms in excitable membranes are analyzed. It is assumed that there are voltage-dependent reactions occurring in the membrane which are independent of the flow of ionic current. The experimental evidence for this assumption is reviewed in the light of more recent results on the kinetics of conductance changes in cardiac membranes. Rate equations are then obtained using transition state theory and assuming that each reaction is rate limited by only one energy barrier. These equations give simple exponential functions for the voltage dependence of the rates. More complex functions may be obtained by assuming that more than one energy barrier is rate limiting. The single-barrier equations are used to estimate the energies of formation of the transition state. In most cases, the entropy of formation is positive but there is no systematic order in the estimated enthalpies. These results are contrasted with those for the ion permeation process itself which normally has a negative entropy of activation. This contrast reinforces the assumption that the reactions controlling membrane permeability are distinct from the ion permeation process itself. The significance of the positive entropy of formation of the transition state in the permeability reactions is discussed, and it is suggested that the membrane structures underlying these reactions may change their degree of hydration during the formation of the transition state.     

A Tris-induced change in the midpoint potential of Z,the donor to photosystem II,as determined by the kinetics of the back reaction

A new method of measuring the rate of the back reaction from the state Z⁺ P680 Q_A^? in Tris-washed chloroplasts is described. By using ratios of back reaction rates we demonstrate a Tris-induced change in the equilibrium between Z and P680 and attribute this change to an alteration of the midpoint potential of Z by Tris treatment. We also demonstrate that the previously observed inhibition of the back reaction by ADRY reagents can be localized at Z and understood in terms of electron donation to Z⁺ by ADRY reagents.     

Switches, excitable responses and oscillations in the Ring1B/Bmi1 ubiquitination system

In an active, self-ubiquitinated state, the Ring1B ligase monoubiquitinates histone H2A playing a critical role in Polycomb-mediated gene silencing. Following ubiquitination by external ligases, Ring1B is targeted for proteosomal degradation. Using biochemical data and computational modeling, we show that the Ring1B ligase can exhibit abrupt switches, overshoot transitions and self-perpetuating oscillations between its distinct ubiquitination and activity states. These different Ring1B states display canonical or multiply branched, atypical polyubiquitin chains and involve association with the Polycomb-group protein Bmi1. Bistable switches and oscillations may lead to all-or-none histone H2A monoubiquitination rates and result in discrete periods of gene (in)activity. Switches, overshoots and oscillations in Ring1B catalytic activity and proteosomal degradation are controlled by the abundances of Bmi1 and Ring1B, and the activities and abundances of external ligases and deubiquitinases, such as E6-AP and USP7.     

Hopf bifurcation and bursting synchronization in an excitable systems with chemical delayed coupling

In this paper we consider the Hopf bifurcation and synchronization in the two coupled Hindmarsh–Rose excitable systems with chemical coupling and time-delay. We surveyed the conditions for Hopf bifurcations by means of dynamical bifurcation analysis and numerical simulation. The results show that the coupled excitable systems with no delay have supercritical Hopf bifurcation, while the delayed system undergoes Hopf bifurcations at critical time delays when coupling strength lies in a particular region. We also investigated the effect of the delay on the transition of bursting synchronization in the coupled system. The results are helpful for us to better understand the dynamical properties of excitable systems and the biological mechanism of information encoding and cognitive activity.     

On the potential for evolutionary change in meristematic cell lineages through intraorganismal selection

In the absence of sexual recombination somatic mutations represent the only source of genetic variation in clonally propagating plants. We analyse the probability of such somatic mutations in the shoot apical meristem being fixed in descendant generations of meristems. A model of meristem cell dynamics is presented for the unstratified shoot apical meristem. The fate of one mutant initial is studied for a two- and three-celled shoot apical meristem. The main parameters of the model are the number of apical initials, the time between selection cycles, number of selection cycles and cell viability of the mutant genotype. As the number of mitotic divisions per selection cycle and number of selection cycles increases the chimeric state dissipates and the probability of mutation fixation approaches an asymptote. The value of this fixation asymptote depends primarily on cell viability, while the time to reach it is mainly influenced by the total number of mitotic divisions as well as the number of initials. In contrast to the presumed operation of Muller’s Ratchet in plants the chimeric state may represent an opportunity for deleterious mutations to be eliminated through intraorganismal selection or random drift. We conclude that intraorganismal selection not only can be a substantial force for the elimination of deleterious mutations, but also can have the potential to confer an evolutionary change through a meristematic cell lineage alone.     

Continuation and bifurcation analysis of a periodically forced excitable system

The response of an excitable cell to periodic electrical stimulation is modeled using the FitzHugh-Nagumo (FHN) system submitted to a gaussian-shaped pacing, the width of which is small compared with the action potential duration. The influence of the amplitude and the period of the stimulation is studied using numerical continuation and bifurcation techniques (AUTO97 software). Results are discussed in the light of prior experimental and theoretical findings. In particular, agreement with the documented behavior of periodically stimulated cardiac cells and squid axons is discussed. As previously reported, we find many different "M:N" periodic solutions, period-doubling sequences leading to seemingly chaotic regimes, and bistability phenomena. In addition, the use of continuation techniques has allowed us to track unstable solutions of the system and thus to determine how the different stable rhythms are connected with each other in a bifurcation diagram. Depending on the stimulus amplitude, the aspect of the bifurcation diagram with the stimulus period as main varying parameter can vary from very simple to very complex. In its most developed structure, this bifurcation diagram consists of a main "tree" of period-2(P) branches, where the 1:1, 1:0, 2:2, 2:1,... rhythms are located, and of several closed loops made up of period-{N x 2(P)} branches (N>2), isolated from each other and from the main tree. It is mainly on such loops that N:1 rhythms (N>2) on one hand, and N:N-1 or Wenckebach rhythms (N>2) on the other hand, are located. Stable M:N and M:N-1 rhythms (M>or=N) can be found on the same branch of solutions. They are separated by a region of unstable solutions at small stimulus amplitudes, but this region shrinks gradually as the stimulus amplitude is raised, until it finally disappears. We believe that this property is related to the excitability characteristics of the FHN system. It would be interesting to know if it has any correspondence in the behavior of real excitable cells.     

On the formation of circulating patterns of excitation in anisotropic excitable media

We present a model of excitable media with the feature that it has a vulnerable phase during which a premature current stimulus will result in the formation of a reentrant selfsustained wave of excitation. The model exploits anisotropic coupling of identical cells, and is therefore useful as a model for the myocardium. We give rigorous verification that there is a vulnerable phase, and demonstrate numerically that permanently rotating waves are formed. Finally, it is shown that the direction of fastest propagation in myocardium is not necessarily the direction of highest safety factor, contrary to commonly accepted opinion.     

Metabolic dependence of cooling-induced action potential generation in excitable cells of pumpkin stem

The presence of strongly pronounced metabolic dependence of cooling-induced action potentials (APs) in excitable cells of pumpkin stem was shown using NaN3, DCCD, and IAA. This dependence might be connected with participation of the plasma-membrane ATP-dependent pump in the excitation process. The decrease of extracellular Ca2+ concentration had as strong depressive effect on the AP as that of the inhibition of metabolism. It has been supposed that the calcium signal is important coupling factor between the AP generation and the metabolism of excitable cells.     

The kinetics of chemotactic peptide-induced change in F-actin content, F-actin distribution, and the shape of neutrophils

Formyl-met-leu-phe (fMLP) induces actin assembly in neutrophils; the resultant increase in F-actin content correlates with an increase in the rate of cellular locomotion at fMLP concentrations less than or equal to 10(-8) M (Howard, T.H., and W.H. Meyer, 1984, J. Cell Biol., 98:1265-1271). We studied the time course of change in F-actin content, F-actin distribution, and cell shape after fMLP stimulation. F-actin content was quantified by fluorescence activated cell sorter analysis of nitrobenzoxadiazole-phallacidin-stained cells (Howard, T.H., 1982, J. Cell Biol., 95(2, Pt. 2:327a). F-actin distribution and cell shape were determined by analysis of fluorescence photomicrographs of nitrobenzoxadiazole-phallacidin-stained cells. After fMLP stimulation at 25 degrees C, there is a rapid actin polymerization that is maximal (up to 2.0 times the control level) at 45 s; subsequently, the F-actin depolymerizes to an intermediate F-actin content 5-10 min after stimulation. The depolymerization of F-actin reflects a true decrease in F-actin content since the quantity of probe extractable from cells also decreases between 45 s and 10 min. The rate of actin polymerization (3.8 +/- 0.3-4.4 +/- 0.6% increase in F-actin/s) is the same for 10(-10) - 10(-6) M fMLP and the polymerization is inhibited by cytochalasin D. The initial rate of F-actin depolymerization (6.0 +/- 1.0-30 +/- 5% decrease in F-actin/min) is inversely proportional to fMLP dose. The F-actin content of stimulated cells at 45 s and 10 min is greater than control levels and varies directly with fMLP dose. F-actin distribution and cell shape also vary as a function of time after stimulation. 45 s after stimulation the cells are rounded and F-actin is diffusely distributed; 10 min after stimulation the cell is polarized and F-actin is focally distributed. These results indicate that actin polymerization and depolymerization follow fMLP stimulation in sequence, the rate of depolymerization and the maximum and steady state F-actin content but not the rate of polymerization are fMLP dose dependent, and concurrent with F-actin depolymerization, F-actin is redistributed and the cell changes shape.     

Climatic change and fire potential in South-Central British Columbia, Canada

The incidence and severity of forest fires are linked to the interaction between climate, fuel and topography. Increased warming and drying in the future is expected to have a significant impact on the risk of forest fire occurrence. An increase in fire risk is linked to the synchronous relationship between climate and fuel moisture conditions. A warmer, drier climate will lead to drier forest fuels that will in turn increase the chance of successful fire ignition and propagation. This interaction will increase the severity of fire weather, which, in turn, will increase the risk of extreme fire behaviour. A warmer climate will also extend fire season length, which will increase the likelihood of fires occurring over a greater proportion of the year. In this study of the North Okanagan area of British Columbia, Canada, the impacts of climate change of fire potential were evaluated using the Canadian Forest Fire Danger Rating System and multiple climate scenario analysis. Utilizing this approach, a 30% increase in fire season length was modelled to occur by 2070. In addition, statistically significant increases in fire severity and fire behaviour were also modelled. Fire weather severity was predicted to increase by 95% during the summer months by 2070 while fire behaviour was predicted to shift from surface fire‐intermittent crown fire regimes to a predominantly intermittent‐full crown fire regime by 2070 onwards. An increase in fire season length, fire weather severity and fire behaviour will increase the costs of fire suppression and the risk of property and resource loss while limiting human‐use within vulnerable forest landscapes. An increase in fire weather severity and fire behaviour over a greater proportion of the season will increase the risks faced by ecosystems and biodiversity to climatic change and increase the costs and difficulty of achieving sustainable forest management.     

Calorific, chemical and physical values of potential duck foods

Calorific values of thirty-three species of aquatic invertebrates, representing various life stages, from small prairie wetlands are given. The values for twenty-seven species are new to the literature. Percentage crude protein for fifteen species and the amino acid composition for eleven taxa are presented. The majority of the species dealt with are eaten by waterfowl.     

Evaluations of reduction potential data in relation to coupling, kinetics and function

 This commentary addresses the effect and measurement of time-dependent contributions to reduction potentials. Reduction potentials form the basis for many quantitative or semi-quantitative judgements in biological redox chemistry. However, since data are obtained under an assumption of equilibrium being established, their relevance to biological functions requires consideration of the kinetics of the subprocesses that contribute to or influence the overall free energy change. Initial and final states effective in rapid and complex biological functions may differ considerably from those analysed after slow equilibration in a sample tube. A shortcoming of traditional potentiometric measurements is that the time domain is not probed. Voltammetry, a technique that has been much less widely applied in biological chemistry than in chemistry, examines redox transformations in both potential and time domains, and may enable a more realistic picture to be derived. Received, accepted: 26 November 1996