Do enzymes bind their substrates in the ground state because of a physico-chemical requirement?

Transition state theory has provided no convincing explanation for the nearly universal observation of complexes of enzymes with substrates. Bimolecular catalytic reactions are assumed here to take place through reactive encounter complexes defined as the subset of reactant state species able to proceed directly to low lying energy levels at the transition state. By assessing the probability of these complexes from the maximum efficiency of intramolecular reactions, an upper limit for the rate constants promoted by hypothetical catalysts unable to bind substrates is deduced. This limit, which is below the ordinary range of bimolecular rate constants (k(cat)/K(M)) for enzyme reactions, results from a kinetic limitation in the formation of reactive encounter complexes. Exceeding this limit requires a stabilization of these complexes. Using the terminology of transition state theory, the need for enzymes to form complexes with substrates is then expressed as a necessity to restore Boltzmann distribution at the transition state.     

Mixed state on a sparsely encoded associative memory model

 We analyzed symmetric mixed states corresponding to the so-called concept formation on a sparsely encoded associative memory model with 0–1 neurons. Three types of mixed states – OR, AND, and a majority decision – are described as typical examples. Each element of the OR mixed state is composed of corresponding memory pattern elements by means of the OR operation. The other two types are similarly defined. By analyzing their equilibrium properties through self-consistent signal-to-noise analysis and computer simulation, we found that the storage capacity of the OR mixed state diverges in a sparse limit, but that the other states do not diverge. In addition, we found that the optimal threshold values, which maximize the storage capacity for the memory pattern and the OR mixed state, coincide with each other in the spare limit. We conclude that the OR mixed state is a reasonable representative of mixed state in the sparse limit. Received: 10 November 1999 / Accepted in revised form: 5 April 2001     

An olfactory recognition model based on spatio-temporal encoding of odor quality in the olfactory bulb

In order to study the problem how the olfactory neural system processes the odorant molecular information for constructing the olfactory image of each object, we present a dynamic model of the olfactory bulb constructed on the basis of well-established experimental and theoretical results. The information relevant to a single odor, i.e. its constituent odorant molecules and their mixing ratios, are encoded into a spatio-temporal pattern of neural activity in the olfactory bulb, where the activity pattern corresponds to a limit cycle attractor in the mitral cell network. The spatio-temporal pattern consists of a temporal sequence of spatial firing patterns: each constituent molecule is encoded into a single spatial pattern, and the order of magnitude of the mixing ratio is encoded into the temporal sequence. The formation of a limit cycle attractor under the application of a novel odor is carried out based on the intensity-to-time-delay encoding scheme. The dynamic state of the olfactory bulb, which has learned many odors, becomes a randomly itinerant state in which the current firing state of the bulb itinerates randomly among limit cycle attractors corresponding to the learned odors. The recognition of an odor is generated by the dynamic transition in the network from the randomly itinerant state to a limit cycle attractor state relevant to the odor, where the transition is induced by the short-term synaptic changes made according to the Hebbian rule under the application of the odor stimulus. Received: 28 July 1997 / Accepted in revised form: 6 May 1998     

Phase resetting and bifurcation in the ventricular myocardium.

With the dynamic differential equations of Beeler, G. W., and H. Reuter (1977, J. Physiol. [Lond.]. 268:177-210), we have studied the oscillatory behavior of the ventricular muscle fiber stimulated by a depolarizing applied current I app. The dynamic solutions of BR equations revealed that as I app increases, a periodic repetitive spiking mode appears above the subthreshold I app, which transforms to a periodic spiking-bursting mode of oscillations, and finally to chaos near the suprathreshold I app (i.e., near the termination of the periodic state). Phase resetting and annihilation of repetitive firing in the ventricular myocardium were demonstrated by a brief current pulse of the proper magnitude applied at the proper phase. These phenomena were further examined by a bifurcation analysis. A bifurcation diagram constructed as a function of I app revealed the existence of a stable periodic solution for a certain range of current values. Two Hopf bifurcation points exist in the solution, one just above the lower periodic limit point and the other substantially below the upper periodic limit point. Between each periodic limit point and the Hopf bifurcation, the cell exhibited the coexistence of two different stable modes of operation; the oscillatory repetitive firing state and the time-independent steady state. As in the Hodgkin-Huxley case, there was a low amplitude unstable periodic state, which separates the domain of the stable periodic state from the stable steady state. Thus, in support of the dynamic perturbation methods, the bifurcation diagram of the BR equation predicts the region where instantaneous perturbations, such as brief current pulses, can send the stable repetitive rhythmic state into the stable steady state.     

Sustainability without coexistence state in Durrett–Levin hawk–dove model

Models that explain the sustainability of an exploiter–victim ecosystem admit, generally, a coexistence state of both species in the well-mixed limit. Even if this state is unstable, the extinction-prone system may acquire stability on spatial domains where different patches oscillate incoherently around the coexistence state. New experiments, however, suggest that a spatially segregated system may be stable even in the absence of such a coexistence state. Here we revisit the hawk–dove (case 3) model of Durrett and Levin, which has been shown to support persistent population for system of interacting particles. It turns out that this model does not admit a (stable or unstable) coexistence state on a single habitat. We analyze the peculiar mechanism that leads to persistence in this case and the role of demographic stochasticity with and without self-interaction, using numerical simulations and exact solutions in the infinite diffusion limit.     

Creeping jurisdiction beyond 200 miles in the light of the 1982 law of the sea convention and state practice

Abstract

This article attempts a complex examination of problems pertaining to actual and potential extensions of coastal state rights and jurisdiction beyond the limit of 200 miles in the light of 1982 Law of the Sea Convention and state practice. Extension of the continental shelf regime, in the context of its outer limit beyond 200 miles, the entitlement of rocks to this limit, and the scope of coastal state rights and duties, is analyzed first. It is followed by discussion of the extension of the exclusive economic zone (EEZ) or fishery zone regime, which involves extension of certain coastal state fishery rights on the one hand, and the right of intervention in cases of maritime casualties and the liability regime for oil pollution damage on the other hand. Attention is also paid to presently speculative extensions of both regimes as a consequence of sea level rise. The author concludes that, if a continuing nontreaty situation deprives recourse to compulsory dispute settlement, the worst‐case scenario of spatial extension of the entire EEZ regime to the outer edge of the continental margin could not with certainty be excluded.     

Modeling experimental time series with ordinary differential equations

Recently some methods have been presented to extract ordinary differential equations (ODE) directly from an experimental time series. Here, we introduce a new method to find an ODE which models both the short time and the long time dynamics. The experimental data are represented in a state space and the corresponding flow vectors are approximated by polynomials of the state vector components. We apply these methods both to simulated data and experimental data from human limb movements, which like many other biological systems can exhibit limit cycle dynamics. In systems with only one oscillator there is excellent agreement between the limit cycling displayed by the experimental system and the reconstructed model, even if the data are very noisy. Furthermore, we study systems of two coupled limit cycle oscillators. There, a reconstruction was only successful for data with a sufficiently long transient trajectory and relatively low noise level.     

Control of oxidative phosphorylation by the extramitochondrial ATP/ADP ratio

The control of mitochondrial ATP synthesis by the extramitochondrial adenine nucleotide pattern was investigated with rat liver mitochondria. It is demonstrated that any stationary state between the two limit states of maximum activity (state 3) and of resting activity (state 4) can be obtained by a hexokinase-glucose trap as an ADP-regenerating system. These intermediate states are characterized by stationary respiratory rates, stationary redox levels of the cytochromes b and c and stationary levels of extramitochondrial ATP and ADP between the rates and levels of the limit states. At a constant concentration of inorganic phosphate the activity of mitochondria between the limit states is controlled by the extramitochondrial ATP/ADP ratio independent of the total concentration of adenine nucleotides present. The control range was found to be between ratios of about 5 and 100 at 10 mM phosphate. At lower ratios the mitochondria are in their maximum phosphorylating state. With succinate + rotenone and glutamate + malate the same control range was observed, indicating that it is independent of the nature of substrate oxidized.The results suggest that in the control range the mitochondrial activity is limited by the competition of ADP and ATP for the adenine nucleotide translocator.     

Possible functional roles of phase resetting during walking

The walking rhythm is known to show phase shift or "reset" in response to external impulsive perturbations. We tried to elucidate functional roles of the phase reset possibly used for the neural control of locomotion. To this end, a system with a double pendulum as a simplified model of the locomotor control and a model of bipedal locomotion were employed and analyzed in detail. In these models, a movement corresponding to the normal steady-state walking was realized as a stable limit cycle solution of the system. Unexpected external perturbations applied to the system can push the state point of the system away from its limit cycle, either outside or inside the basin of attraction of the limit cycle. Our mathematical analyses of the models suggested functional roles of the phase reset during walking as follows. Function 1: an appropriate amount of the phase reset for a given perturbation can contribute to relocating the system's state point outside the basin of attraction of the limit cycle back to the inside. Function 2: it can also be useful to reduce the convergence time (the time necessary for the state point to return to the limit cycle). In experimental studies during walking of animals and humans, the reset of walking rhythm induced by perturbations was investigated using the phase transition curve (PTC) or the phase resetting curve (PRC) representing phase-dependent responses of the walking. We showed, for the simple double-pendulum model, the existence of the optimal phase control and the corresponding PTC that could optimally realize the aforementioned functions in response to impulsive force perturbations. Moreover, possible forms of PRC that can avoid falling against the force perturbations were predicted by the biped model, and they were compared with the experimentally observed PRC during human walking. Finally, physiological implications of the results were discussed.     

Features of the chemical models of a nonideal atomic plasma at high temperatures

The equation of state for a hydrogen plasma at high temperatures is considered in a physical and a chemical model. A simple expression is obtained that relates the pressure correction in chemical models to the high-temperature limit of the atom partition function. This expression ensures a correct asymptotic behavior of the equation of state in the high-temperature limit. It is explained why the familiar astrophysical model of Hummer, Mihalas, and Däppen, as applied to helioseismology, yields worse results than a physical model. A modification of the astrophysical model is proposed that makes it possible to use the nearest neighbor approximation to calculate the atom partition function in chemical models in solving astrophysical problems and problems concerning low-temperature plasmas.     

Some conditions for sustained oscillations in chain processes with feedback inhibition and saturable removal

A biochemical chain with feedback inhibition, enzymatic removal and catalyzed input is considered. Some conditions on the parameters are given for which the result is a simple limit cycle behavior or a limit cycle surrounding an unstable limit cycle and a stable point. In the latter case, the system in the steady state can either be at rest or oscillate around the point at rest, depending on the initial conditions. Presented at the May 23–24, 1975 meeting of the Society for Mathematical Biology, Bowling Green State University, Bowling Green, Ohio.     

固态发酵的参数周期变化及对微生物发酵的影响

研究了压力脉动固态发酵反应器内环境参数的周期性变化以及这些周期性的环境刺激对于固态培养的斜卧青霉发酵的影响。研究结果显示:在这种反应器中,在空气压力脉动的带动下,反应器内的温度和空气湿度也会发生较大幅度的周期性变化,变化的周期和空气压力脉动的周期相同,变化的幅度随着压力脉动的幅度增大而增加;在外界周期刺激的条件下,较未加外界周期刺激斜卧青霉的生物量增加了104% ,二氧化碳的产生总量增加了229%和纤维素酶的产量增加了320 % ,数据显示外界周期刺激不仅增加了菌体的生物量同时增加了其代谢活性。     

Cellular senescence in cancer and aging

Cellular senescence, a state of irreversible growth arrest, can be triggered by multiple mechanisms including telomere shortening, the epigenetic derepression of the INK4a/ARF locus, and DNA damage. Together these mechanisms limit excessive or aberrant cellular proliferation, and so the state of senescence protects against the development of cancer. Recent evidence suggests that cellular senescence also may be involved in aging.     

Beyond the EX1 limit: probing the structure of high-energy states in protein unfolding

Hydrogen exchange kinetics in native solvent conditions have been used to explore the conformational fluctuations of an immunoglobulin domain (CD2.domain1). The global folding/unfolding kinetics of the protein are unaltered between pH 4.5 and pH 9.5, allowing us to use the pH-dependence of amide hydrogen/deuterium exchange to characterise conformational states with energies up to 7.2kcal/mol higher than the folded ground state. The study was intended to search for discreet unfolding intermediates in this region of the energy spectrum, their presence being revealed by the concerted exchange behaviour of subsets of amide groups that become accessible at a given free energy, i.e. the spectrum would contain discreet groupings. Protection factors for 58 amide groups were measured across the pH range and the hydrogen-exchange energy profile is described.More interestingly, exchange behaviour could be grouped into three categories; the first two unremarkable, the third unexpected. (1) In 33 cases, amide exchange was dominated by rapid fluctuation, i.e. the free energy difference between the ground state and the rapidly accessed open state is sufficiently low that the contribution from crossing the unfolding barrier is negligible. (2) In 18 cases exchange is dominated by the global folding transition barrier across the whole pH range measured. The relationship between hydroxyl ion concentration and observed exchange rate is hyperbolic, with the limiting rate being that for global unfolding; the so-called EX1 limit. For these, the free energy difference between the folded ground state and any rapidly-accessed open state is too great for the proton to be exchanged through such fluctuations, even at the highest pH employed in this study. (3) For the third group, comprising five cases, we observe a behaviour that has not been described. In this group, as in category 2, the rate of exchange reaches a plateau; the EX1 limit. However, as the intrinsic exchange rate (k(int)) is increased, this limit is breached and the rate begins to rise again. This unintuitive behaviour does not result from pH instability, rather it is a consequence of amide groups experiencing two processes; rapid fluctuation of structure and crossing the global barrier for unfolding. The boundary at which the EX1 limit is overcome is determined by the equilibrium distribution of the fluctuating open and closed states (K(O/C)) and the rate constant for unfolding (k(u)). This critical boundary is reached when k(int)K(O/C)=k(u). Given that, in a simple transition state formalism: k(u)=K(#)k' (where K(#) describes the equilibrium distribution between the transition and ground state and k' describes the rate of a barrierless rearrangement), it follows that if the pH is raised to a level where k(int)=k', then the entire free energy spectrum from ground state to transition state could be sampled.     

Irreversible transitions in the 6-phosphofructokinase/fructose 1,6-bisphosphatase cycle.

The dynamics of the fructose 6-phosphate fructose-1,6-bisphosphate cycle operating in an open and homogeneous system reconstituted from purified enzymes was extensively studied. In addition to 6-phosphofructokinase and fructose-1,6-bisphosphatase, pyruvate kinase, adenylate kinae and glucose-6-phosphate isomerase were involved. In that multi-enzyme system, the main source of non-linearity is the reciprocal effect of AMP on the activities of 6-phosphofructokinase and fructose-1,6-bisphosphatase. Depending upon the experimental parameter values, stable attractors, various types of multiple states and sustained oscillations were shown to occur. In the present report we show that irreversible transitions are also likely to occur for realistic operating conditions. Two parameters of the system, that is the adenylate energy charge of the influx and the fructose-1,6-bisphosphatase maximal activity, are potential candidates to provoke such irreversible transitions from one steady state to the other: (a) when varying the maximal activity of fructose-1,6-bisphosphatase, the system can jump irreversibly from a low to a high stable steady state, and (b) when the adenylate energy charge of the influx is the changing parameter, irreversible transitions occur from a high stable steady state to a stable oscillatory state (limit cycle motion). This behavior can be predicted by constructing the loci of limit points and Hopf bifurcation points.     

The study of photo-induced rhodopsin aggregation in the photoreceptor membrane by electron paramagnetic resonance

The ESR measuring of UV-induced free radicals concentration limit has been used for studying rhodopsin aggregate state in the photoreceptor membrane.     

Limit cycle model for brain waves

The extraordinary high sensitivity of certain biological systems to weak electromagnetic signals motivated Fröhlich to establish his brain wave model. Although the basic assumptions of such a model are still highly speculative, it seems worth while to investigate the quantitative dynamics of it. In this model coherent excitations in the 10¹¹ Hz region in combination with a collective enzyme-substrate reaction create and stabilize a limit cycle oscillation. In the present paper the existence of the limit cycle and its collapse due to external stimulation is studied. The bifurcation of this periodically oscillating resting state is analysed and the stability of additional steady states is proven. Approximations are discussed and a correspondence between the limit cycle model and nerve impulse generating models is established.     

Simple chemical reaction systems with limit cycle behaviour

It is shown that for exhibiting limit cycle behaviour a two-component chemical reaction system has to involve at least three reactions among which one must be autocatalytic of the type 2X + … ? 3X + … Under this condition, possible candidates for chemical limit cycle systems are selected by postulating their steady state to be an instable focus. This procedure can be reduced to the selection of appropriate stoichiometric coefficients and is readily performed by a medium size computer. The result is quite a lot of limit cycle systems which are altogether simpler than, for example, the “Brusselator” with its number of four reactions. One of the results is briefly discussed.     

The Onset and Extinction of Neural Spiking: A Numerical Bifurcation Approach

We study the onset of neural spiking when the equilibrium rest state loses stability by the change of a critical parameter, the applied current. In the case of the well-known Morris-Lecar model, we start from a complete numerical study of the bifurcation diagram in the most relevant two-parameter range. This diagram includes all equilibrium and limit cycle bifurcations, thus correcting and completing earlier studies.We discuss and classify the behavior of the spiking orbits, when increasing or decreasing the applied current. A complete classification can be extracted from the complete bifurcation diagram. It is based on three components: bifurcation type of the equilibrium at the loss of stability, subcritical behavior in the limit of decreasing the applied current and supercritical behavior in the limit of increasing the applied current.     

Understanding bursting oscillations as periodic slow passages through bifurcation and limit points

We consider a biochemical system consisting of two allosteric enzyme reactions coupled in series. The system has been modeled by Decroly and Goldbeter (J. Theor. Biol. 124, 219 (1987)) and is described by three coupled, first-order, nonlinear, differential equations. Bursting oscillations correspond to a succession of alternating active and silent phases. The active phase is characterized by rapid oscillations while the silent phase is a period of quiescence. We propose an asymptotic analysis of the differential equations which is based on the limit of large allosteric constants. This analysis allows us to construct a time-periodic bursting solution. This solution is jumping periodically between a slowly varying steady state and a slowly varying oscillatory state. Each jump follows a slow passage through a bifurcation or limit point which we analyze in detail. Of particular interest is the slow passage through a supercritical Hopf bifurcation. The transition is from an oscillatory solution to a steady state solution. We show that the transition is delayed considerably and characterize this delay by estimating the amplitude of the oscillations at the Hopf bifurcation point.