Feedbacks, nonlinearities and nonequilibria: A thermodynamic perspective.

The feedback circuit approach to nonlinear dynamical systems pioneered by Thomas and coworkers is revisited in a thermodynamical perspective. The role of nonequilibrium conditions and of other types of constraints such as mass action kinetics or microscopic reversibility around thermodynamic equilibrium in the way positive feedback circuits are operating is analyzed. It is shown that the appearance of non-trivial steady-state and time-dependent behaviors necessitates that the strengths of the feedback loops present exceed some well-defined critical values. Illustrations are provided on prototypical systems giving rise to multiple steady states.

Modeling the early stages of self-assembly in nanophase materials. II. Role of symmetry and dimensionality.

We study the early stages of self-assembly of elementary building blocks of nanophase materials, considering explicitly their structure and the symmetry and the dimensionality of the reaction space. Previous work [Kozak et al., J. Chem. Phys. 134, 154701 (2007)] focused on characterizing self-assembly on small square-planar templates. Here we consider larger lattices of square-planar symmetry having N = 255 sites, and both hexagonal and triangular lattices of N = 256 sites. Furthermore, to assess the consequences of a depletion zone above a basal layer (λ = 1), we study self-assembly on an augmented diffusion space defined by λ = 2 and λ = 5 stacked layers having the same characteristics as the basal plane. The effective decrease in the efficiency of self-assembly of individual nanophase units when the diffusion space is expanded, by increasing the template size and/or by enlarging the depletion zone, is then quantified. The results obtained reinforce our earlier conclusion that the most significant factor influencing the kinetics of formation of a final self-assembled unit is the number of reaction pathways from one or more precursor states. We draw attention to the relevance of these results to zeolite synthesis and reactions within pillared clays.

Equality governing nonequilibrium fluctuations and its information theory and thermodynamic interpretations.

The master equation is cast in the form of an equality involving the variation, in the course of a transformation, of a quantity playing the role of a generalized potential, weighted with the probability of allowable transformations emanating from different initial states. In the most general case this equality cannot be formulated entirely in terms of thermodynamic variables and state functions. Some conditions under which such a reduction becomes possible are identified and a comparison with fluctuation and work type relationships previously reported in the literature is carried out.

Irreversible thermodynamics of multistep transitions.

Conditions under which the evolution equations of a multivariate system can be cast in a variational form are identified. A kinetic potential generating both the deterministic part of the evolution and the probabilistic properties in a suitably defined set of variables is derived and compared to the thermodynamic potentials. The results are illustrated on the kinetics of phase transitions involving intermediate metastable phases and chemical reactions giving rise to two or more intermediate species.

Stochastic resonance across bifurcation cascades.

The classical setting of stochastic resonance is extended to account for parameter variations leading to transitions between a unique stable state, bistability, and multistability regimes, across singularities of various kinds. Analytic expressions for the amplitude and the phase of the response in terms of key parameters are obtained. The conditions for optimal responses are derived in terms of the bifurcation parameter, the driving frequency, and the noise strength.

Coupling-enhanced stochastic resonance.

Stochastic resonance is analyzed in an array of nonlinear spatially coupled subsystems. Analytic expressions for the different steady-state solutions, for the rates of transitions between them in the presence of noise, and for the response to a weak external periodic forcing are derived. It is shown that the presence of spatial degrees of freedom modifies considerably the mechanisms of transitions between states and is responsible for a marked sensitivity of the response on the coupling constant and on the system size.

Detailed balance, nonequilibrium states, and dissipation in symbolic sequences.

Symbolic sequences arising from the coarse graining of deterministic dynamical systems continuous in phase space are considered. The extent to which signatures of the time irreversibility and of the nonequilibrium constraints at the level of the original system, such as fluxes or dissipation, can be identified at the coarse-grained level is analyzed. The roles of the partition, of the time window, and of time averaging in distinguishing in a clear-cut way the equilibrium versus nonequilibrium character of the sequence are brought out.

Glucose-induced hyperkalemia in diabetic subjects.

Four insulin-deprived patients with diabetes mellitus and normal baseline potassium and aldosterone levels became hyperkalemic when given 100 g of glucose orally. The increases in plasma potassium concentrations averaged 1.3 mEq/L (range, 0.7 to 1.8 mEq/L) and were accompanied by increases in plasma aldosterone level. Four other insulin-deprived diabetics had normal plasma potassium and aldosterone responses when given 50 mEq of potassium chloride orally. These findings suggest that glucose-induced hyperkalemia is not infrequent in diabetics and that it is not usually associated with hypoaldosteronism. The acute suppression of aldosterone biosynthesis with aminoglutethimide did not lead to increased plasma potassium levels following oral potassium loads. This suggests that the acute responses of aldosterone to potassium loads may not be important in preventing postprandial hyperkalemia.

Gonadotropin-producing pituitary adenoma in a man with long-standing primary hypogonadism.

Pituitary adenomas that secrete gonadotropins are generally believed to arise spontaneously rather than as a response to chronic primary gonadal failure. However, two women who were found to have gonadotroph adenomas several years after ovarian ablation have been reported. We describe a middle-aged man who developed bitemporal hemianopia and was found to have a large pituitary tumor 35 yr after castration. He had never received any replacement therapy. The tumor was considered to be a primary gonadotroph adenoma, rather than secondary gonadotroph hyperplasia, on the basis of its secretory capabilities, its reticulin patterns, and its specific immunostaining for human FSH beta, human LH beta, and alpha-subunit. Furthermore, the tumor did not decrease appreciably in size after 12 months of testosterone treatment, although plasma gonadotropin levels decreased. Unless the association of primary gonadal failure with a gonadotroph adenoma was coincidental, it suggests that some human gonadotroph adenomas may be secondary to failure of the gonads.

Pathogenesis of hypertension in Cushing's syndrome.

Steroid production, plasma renin activity (PRA) and plasma renin substrate (PRS) were measured in eight patients with hypertension due to Cushing's syndrome of benign origin. Despite elevation of cortisol secretion in all patients, hypokalemia and suppressed PRA was noted in the one subject with a functioning adrenal adenoma. PRA was normal in six patients on an unrestricted sodium intake but was markedly increased in the two patients on low salt diets. PRS was significantly increased during active disease, but decreased substantially with treatment. The absence of uniform hypokalemia and of suppression of renin indicates that mineralocorticoid production could not account for the increase in arterial pressure. It is suggested that glucocorticoid-induced hypertension may be initiated by alterations in vascular responsiveness to pressor agents and that elevated PRS levels may contribute to increase angiotensin formation.

Thermostating by deterministic scattering: construction of nonequilibrium steady states

We present a novel approach for constructing nonequilibrium steady states. It is based on a deterministic and time-reversible mechanism for dissipating energy from a subsystem into a thermal reservoir. The key idea is to thermalize a moving particle by appropriately modeling its microscopic collision rules with a boundary mimicking a thermal reservoir with arbitrarily many degrees of freedom. We demonstrate our method for the periodic Lorentz gas with an external electric field. By applying our thermostat we do not find an ergodic breakdown with increasing field strength.

Peripheral blood steroid levels in Cushing syndrome due to adrenocortical carcinoma or adenoma.

Measurement of the peripheral vein levels of the steroids in the adrenal biosynthetic pathway affords a further possible definitive method of differentiating adrenocortical carcinoma from adrenal adenoma in the presence of Cushing syndrome. In patients with adrenal carcinoma the blood levels of 17-hydroxyprogesterone, testosterone, androstenedione, and dehydroepiandrosterone are far higher than those seen in association with adenoma. In addition, the adrenal cortical carcinoma appears to have a higher ratio of precursors to product in the early part of the biosynthetic path and a lower one in the distal portion than adrenal adenomas. In Cushing syndrome due to adrenal tumor the measurement of serum cortisol is preferably made after chromatographic separation from 11-deoxycortisol in view of the marked cross reactivity in the protein binding procedure.

Sustained oscillations and threshold phenomena in an operon control circuit.

A genetic regulatory model involving a positive feedback (via induction) and a negative feedback (via catabolite repression) is analyzed and applied to the problem of the lac operon regulation in E. coli. Damped and sustained oscillations of the limit cycle type are found along with threshold phenomena corresponding to multiple limit cycles or to multiple steady states, for values of the parameters compatible with experimental data. A comparison with the observations of Knorre and Goodwin is outlined.

Geometrical effects in protein nucleation.

To understand the importance of protein anisotropy and the influence of translational and rotational degrees of freedom on the nucleation event, we calculate numerically-exact values for the mean encounter time for two non-spherically symmetric molecules to form a cluster, regarded here as a precursor to nucleation. A lattice model is formulated in which the asymmetry of the molecules is accounted for by representing each as a 'dimer' in the sense that each molecule is specified to occupy two lattice sites. The two dimers undergo simultaneously translation and/or rotation, and the mean times for their encounter are determined. Exact numerical results are obtained for small lattices via application of the theory of finite Markov processes, and the results corroborated and extended to large lattices by performing Monte Carlo simulations. These calculations allow one to understand in a detailed way the interplay among geometrical anisotropy, translational and internal (rotational) degrees of freedom and system size in influencing the seminal nucleation event.

Immunological study of keratoacanthomas.

Twelve patients with keratoacanthoma were studied to assess the role and importance of immunological factors in tumor regression. Direct immunofluorescence was determined with immunoglobulins, complement (C3), and fibrin to estimate the deposition of these factors in the lesion area. Indirect immunofluorescence was also undertaken using pemphigus and bullous pemphigoid sera against the keratoacanthoma lesion to study the presence or absence of tissue-specific antigens (T.S.A.) in intercellular substance and basement membrane. Finally, the cell-mediated immunity was studied using two in vitro parameters: (a) The estimation of T-lymphocytes through the formation of E-rosettes and (b) the estimation of the leukocyte migration inhibition factor (LIF). Our findings show that specific humoral immune mechanisms are apparently not involved in the spontaneous regression of keratoacanthoma. Cell-mediated immune mechanisms are evidently not responsible for the resolution of the tumor.

Transitions across a barrier induced by deterministic forcings.

The response of a bistable dynamical system to a deterministic forcing is studied with emphasis on the kinetics of the passage across the barrier separating the two states, and compared to classical Kramers' theory describing the response to a Gaussian white noise forcing. The existence of nontrivial thresholds for the occurrence of transitions is established. Analytic results complemented by numerical simulations are derived for the characteristics of these transitions for periodic and chaotic forcings. The probabilistic properties of the response are finally addressed and some connections are established with the universal stable distributions of probability theory.

Three-state model for cooperative desorption on a one-dimensional lattice.

We develop a master equation approach to the dynamics of immobile reactants on a one-dimensional lattice, in the presence of two different species undergoing cooperative desorption. A common feature of all the schemes studied is the strong dependence of the final coverage on the initial conditions, associated with the lack of ergodicity of the invariant state. Our approach leads to full agreement with Monte Carlo simulations, both asymptotically and transiently.

Nonlinear reactive systems on a lattice viewed as Boolean dynamical systems.

We present a stochastic, time-discrete Boolean model that mimics the mesoscopic dynamics of the desorption reactions A+A-->A+S and A+A-->S+S in a one-dimensional lattice. In the continuous-time limit, we derive a hierarchy of dynamical equations for the subset of moments involving contiguous lattice sites. The solution of the hierarchy allows to compute the exact dynamics of the mean coverage for both microscopic and coarse-grained initial conditions, which turn out to be different from the mean field predictions. The evolution equations for the mean coverage and the second-order moments are shown to be equivalent to those provided by a time-continuous master equation. The important role of higher-order fluctuations is brought out by the failure of a truncation scheme retaining only two-particle fluctuation correlations.

Moment evolution and level-crossing statistics in dichotomous and multilevel flows with time-dependent control parameters.

We study the dynamics of the first two moments and of threshold crossings by the stochastic trajectory in dichotomous diffusion x=xi(t), where xi(t) is a dichotomous Markov process. The transition rate of the latter is regarded as a control parameter and allowed to have specified time variations. The stabilizing or destabilizing effect of this variation is demonstrated, and qualitative changes in the statistical properties of the system are shown to occur. The analysis is then extended to linear dichotomous flow, and to a generalization of dichotomous diffusion in which x is driven by a multilevel Markov noise.

Lattice model of the early stages of the electrification of a cloud.

The early stages of the microphysics of the electrification process within a cloud are considered using a two-dimensional lattice model. Using insights generated from Monte Carlo simulations and the theory of finite Markov processes, the mean walk length statistics of the particles, the instantaneous electric potential and electric field profiles, the time evolution of electrostatic energy and their dependence on system size are studied. Some unexpected features of the kinetics of electrification and of the statistics of crossings of the threshold for an electric discharge to occur are brought out.