Steady-state and limit cycle activity of mass of neurons forming simple feedback loops (II): Distributed parameter model

It is shown that there exist spatial distributions of nonzero steady state mean pulse rates of the periglomerular and mitraltufted neuron populations and of nonzero EEG in the mammalian olfactory bulb. Such distributions are stable, i.e., if there are small perturbations, the population state variables return to the equilibrium states. It is predicted that the sensory and centrifugal inputs to the neuron populations in the bulb determine existence of such active states.This research was supported by a grant from the National Institute of Mental Health, MH 06686 and by a Fellowship from the National Institute of Neurological Diseases and Strokes, 5F 102 NS 544 56-02.     

Steady-state properties of a model ternary substrate cycle: theoretical predictions.

Numerous ternary substrate cycles are metabolically operative in vivo. The relative concentrations of the interconverted substrates are generally correlated with different physiological states. These cycles often include reversible and/or substrate-inhibited enzymic steps. The switch between one steady state (metabolic state) and another may be the consequence of either the effect of an exogeneous metabolite or signal, or the alteration of a cycle internal parameter. The interpretation of results obtained with currently designed experiments on substrate cycles seldom take into account the very dynamic and regulatory properties inherent in the cyclic and often autocatalytic nature of the pathway. In the present report, the various dynamic properties of a model ternary substrate cycle, bounded by moiety conservation, are investigated. Three situations with increasing complexity are considered: (i) the three enzymes are michaelian and catalyse irreversible steps; (ii) one of the enzymic steps is reversible; and (iii) one step is subjected to a destabilizing factor, i.e. inhibition by excess of substrate. The behavior(s) of the whole cycle is mainly controlled by four parameters, that is, ST, the total concentration of the substrate pool, and the three enzyme maximal velocities, VMi (i = 1,2,3). As ST (= S1 + S2 + S3) is constant, the Si steady-state concentrations (stable or not) can be represented in barycentric coordinates in a triangle (simplex). This convenient representation allows us to predict the different states of the system when one enzyme maximal activity is varied. The steady-state concentration dependencies as a function of one or several parameters may be either monostable (possibility of zero-order ultrasensitivity) or bistable (with or without reversible transitions). The physiological and experimental relevances of these observations are emphasized.     

Robust and sensitive control of a quorum‐sensing circuit by two interlocked feedback loops

The quorum‐sensing (QS) response of Vibrio fischeri involves a rapid switch between low and high induction states of the lux operon over a narrow concentration range of the autoinducer (AI) 3‐oxo‐hexanoyl‐L ‐homoserine lactone. In this system, LuxR is an AI‐dependent positive regulator of the lux operon, which encodes the AI synthase. This creates a positive feedback loop common in many bacterial species that exhibit QS‐controlled gene expression. Applying a combination of modeling and experimental analyses, we provide evidence for a LuxR autoregulatory feedback loop that allows LuxR to increase its concentration in the cell during the switch to full lux activation. Using synthetic lux gene fragments, with or without the AI synthase gene, we show that the buildup of LuxR provides more sensitivity to increasing AI, and promotes the induction process. Elevated LuxR levels buffer against spurious variations in AI levels ensuring a robust response that endows the system with enhanced hysteresis. LuxR autoregulation also allows for two distinct responses within the same cell population.     

Adrenergic neurons and short proprioceptive feedback loops involved in the integration of cardiac function in the rat

Summary Serial cryostat and paraffin-embedded sections through the atrioventricular junction of the rat heart were studied at the light-microscopic level after indirect immunohistochemical staining (tyrosine hydroxylase, neuropeptide Y, C-terminal flanking peptide of neuropeptide Y immunoreactivities) or silver impregnation. The distribution of these immunoreactivities in the Hissian ganglion (Moravec and Moravec 1984) as well as the relationships of the Hissian ganglion cells with the surrounding structures have been studied to assess its function. The results suggest that the Hissian ganglion is composed of large multipolar neurons displaying both tyrosine hydroxylase (TH) and related peptide (neuropeptide Y, C-terminal flanking peptide of neuropeptide Y) immunoreactivities. The dendritic projections of these adrenergic cells penetrate the reticular portion of the atrioventricular node and the upper segments of the interventricular septum where they constitute sensory-like corpuscles. The hypothesis that the adrenergic neurons of the atrioventricular junction are involved in short proprioceptive feedback loops necessary for beat-to-beat modulation of cardiac excitability and intracardiac conduction can thus be suggested.     

A theory of steady-state activity in nerve-fiber networks II: The simple circuit

It is found that for a simple circuit of neurons, if this contains an odd number of inhibitory fibers, or none at all, or if the product of the activity parameters is less than unity, then the stimulus pattern always determines uniquely the steady-state activity. For circuits not of one of these types, it is possible to classify exclusively and exhaustively all possible activity patterns into three types, here called “odd”, “even”, and “mixed”. For any pattern of odd type and any pattern of even type there always exists a stimulus pattern consistent with both, but in no other way can such an association of activity patterns be made.     

A theory of steady-state activity in nerve-fiber networks III: The simple circuit in complete activity

Continuing the investigation previously introduced, it is shown here that when the product of the activity parameters of the circuit is not exceeded by unity (algebraically) a steady state is not possible in which all fibers of the circuit are active, whereas when this product is exceeded by unity, any stimulus pattern which is consistent with such a state of complete activity is inconsistent with any state of partial activity of the circuit.     

Negative feedback loops: nutrient starvation employs a new tr(IKK) to inhibit PI3K

The PI3K pathway promotes insulin signaling to regulate metabolism and survival and is subject to multiple inhibitory feedback loops. In this issue of Molecular Cell,Comb et al. (2012) provide evidence indicating that the PI3K pathway is negatively regulated in a new way: by NFkB signaling during nutrient starvation.     

Secondary ion mass spectrometry of nonvolatile isocyanide complexes of silver(I) and copper(I)

A series of silver and copper coordination complexes has been studied using secondary ion mass spectrometry (SIMS). Results are presented for the monomeric silver(I) complexes [Ag(CNR)₄]X, where R = cyclohexyl for X  ClO₄⁻, and R = methyl or t-butyl for X  PF₆⁻. Likewise, Cu(I) complexes [Cu(CNR)₄]PF₆, where R =methyl, t-butyl, or cyclohexyl, were examined. The presence of AgL₂⁺ (L represents the intact RNC ligand) and the absence of AgL₃⁺ and AgL₄⁺ species attests to the gas phase stability of two-coordinate silver(I). Similar results to these were obtained for the Cu(I) complexes, with the exception of [Cu(CNCH₃)₄]PF₆ whose spectrum contains CuL₄⁺, CuL₃⁺, CuL₂⁺, CuL⁺, and Cu⁺ ions. The latter result reflects the enhanced stability of the tetrahedral Cu(I) geometry compared to Ag(I) in the gas phase. Cross labeling experiments and isotopic labeling studies have provided insights into fragmentation mechanisms. Ligand exchange occurs when mixtures are examined. These exchange reactions provide evidence for extensive molecular mixing which can accompany SIMS even under low primary ion dose conditions. Cluster ion formation as well as the observation of α-cleavage of the NC bonds of RNC ligands have been observed and these results are discussed. Granulated graphite and ammonium chloride were employed to study matrix effects. Granulated graphite enhanced NC cleavage for the silver complexes but had little effect on the relative abundance of silver cluster ions. On the other hand, copper cluster ions were more sensitive to matrix effects.     

Solid-gas carbonylation of aryloxide rhodium(I) complexes: stepwise reaction forming Vaska-type complexes

Aryloxide rhodium(I) complexes Rh(OAr)(PPh₃)₃ (1a: Ar=C₆Cl₅, 1b: Ar=C₆F₅, 1c: Ar=C₆H₄-NO₂-4) react with CO in toluene solutions to produce Vaska-type complexes trans-Rh(OAr)(CO)(PPh₃)₂ (2a: Ar=C₆Cl₅, 2b: Ar=C₆F₅, 2c: Ar=C₆H₄-NO₂-4). Carbonylation of a similar complex with PMe₃ ligands, Rh(OC₆H₄-NO₂-4)(PMe₃)₃ (3c), also forms trans-Rh(OC₆H₄-NO₂-4)(CO)(PMe₃)₂ (4c). Molecular structures of the complexes are determined by X-ray crystallography and NMR spectroscopy. Complex 1a reacts with CO in the absence of solvent to produce a mixture of 2a and complex A, the latter of which shows the IR and ¹³C{¹H} signals due to the carbonyl ligand at different positions from those of 2a. Addition of Et₂O to the above mixture turns it into analytically pure 2a. Carbonylation of 1b and 1c under the solvent-free conditions produces complexes B and C as the respective products of the solid-gas reaction. Recrystallization of B and C turns them into 2b and 2c, respectively. Complex 3c also reacts with CO in the solid state to form a mixture of 4c and complex D, although the latter complex is converted slowly into 4c even in the solid state.     

The "battle of the sexes": a genetic model with limit cycle behavior

A two-locus genetic model, based on Dawkins "sex war" game, with the fitness of the genotypes at each locus depending on the gene frequencies at the other, is shown to give rise to a stable limit cycle. The mathematical analysis involves averaging techniques and elliptic integrals.     

Gold(I) and silver(I) complexes of 2,3-bis(diphenylphosphino)maleic acid: Structural studies and antitumour activity

The 2:1 and 1:2 adducts of Au(I) and 1:2 adducts of Ag(I) with the diphosphine 2,3-bis(diphenylphosphino)maleic acid (dpmaa) have been prepared in high yields. Crystal structures have been determined for the neutral digold complex (AuCl)₂(dpmaa) · 2thf (1) and the bis-chelated complex [Au(dpmaa)₂]Cl · H₂O · CH₃OH (2). For 1, conformational rigidity imposed by the ethylenic bridge facilitates the formation of short intramolecular Au-Au contacts with no evidence of similar intermolecular contacts. Complex 2 crystallizes with [Au(dpmaa)₂]⁺ cations hydrogen bonded through the carboxyl groups to a water molecule and chloride anion to form a H-bonded chain along the a axis. ³¹P NMR titration of 1 with dpmaa in acetone shows conversion to 2 at Au:P-P ratios less than 1:1 indicating similar high thermodynamic and kinetic stabilities to other bis-chelated [Au(P-P)₂]⁺ complexes containing 5- or 6-membered chelate rings. The ionic Au(I) complex 2 and the analogous Ag(I) complex [Ag(dpmma)₂]NO₃ (3) are highly water soluble. The in vitro cytotoxic activity of 2 was assessed against eight different cell lines and no significant activity was found. The solubility properties and solution behaviour of the complexes are compared to the analogous 1,2-bis(diphenylphosphino)ethane (dppe) complexes and the potential significance of these results to the antitumour properties of chelated 1:2 Au(I)diphosphine complexes are discussed.     

A simple mathematical model of the bovine estrous cycle: follicle development and endocrine interactions

Bovine fertility is the subject of extensive research in animal sciences, especially because fertility of dairy cows has declined during the last decades. The regulation of estrus is controlled by the complex interplay of various organs and hormones. Mathematical modeling of the bovine estrous cycle could help in understanding the dynamics of this complex biological system. In this paper we present a mechanistic mathematical model of the bovine estrous cycle that includes the processes of follicle and corpus luteum development and the key hormones that interact to control these processes. The model generates successive estrous cycles of 21 days, with three waves of follicle growth per cycle. The model contains 12 differential equations and 54 parameters. Focus in this paper is on development of the model, but also some simulation results are presented, showing that a set of equations and parameters is obtained that describes the system consistent with empirical knowledge. Even though the majority of the mechanisms that are included in the model are based on relations that in the literature have only been described qualitatively (i.e. stimulation and inhibition), the output of the model is surprisingly well in line with empirical data. This model of the bovine estrous cycle could be used as a basis for more elaborate models with the ability to study effects of external manipulations and genetic differences.     

Modulation of Na,K-ATPase and Na-ATPase activity by phospholipids and cholesterol. I. Steady-state kinetics

The effects of phospholipid acyl chain length (n(c)), degree of acyl chain saturation, and cholesterol on Na,K-ATPase reconstituted into liposomes of defined lipid composition are described. The optimal acyl chain length of monounsaturated phosphatidylcholine in the absence of cholesterol was found to be 22 but decreased to 18 in the presence of 40 mol % cholesterol. This indicates that the hydrophobic matching of the lipid bilayer and the transmembrane hydrophobic core of the membrane protein is a crucial parameter in supporting optimal Na,K-ATPase activity. In addition, the increased bilayer order induced by both cholesterol and saturated phospholipids could be important for the conformational mobility of the Na,K-ATPase changing the distribution of conformations. Lipid fluidity was important for several parameters of reconstitution, e.g., the amount of protein inserted and the orientation in the liposomes. The temperature dependence of the Na,K-ATPase as well of the Na-ATPase reactions depends both on phospholipid acyl chain length and on cholesterol. Cholesterol increased significantly both the enthalpy of activation and entropy of activation for Na,K-ATPase activity and Na-ATPase activity of Na,K-ATPase reconstituted with monounsaturated phospholipids. In the presence of cholesterol the free energy of activation was minimum at a lipid acyl chain length of 18, the same that supported maximum turnover. In the case of ATPase reconstituted without cholesterol, the minimum free energy of activation and the maximum turnover both shifted to longer acyl chain lengths of about 22.     

Steady-state kinetic mechanism of the proline:ubiquinone oxidoreductase activity of proline utilization A (PutA) from Escherichia coli

The multifunctional proline utilization A (PutA) flavoenzyme from Escherichia coli performs the oxidation of proline to glutamate in two catalytic steps using separate proline dehydrogenase (PRODH) and Δ¹-pyrroline-5-carboxylate (P5C) dehydrogenase domains. In the first reaction, the oxidation of proline is coupled to the reduction of ubiquinone (CoQ) by the PRODH domain, which has a β₈α₈-barrel structure that is conserved in bacterial and eukaryotic PRODH enzymes. The structural requirements of the benzoquinone moiety were examined by steady-state kinetics using CoQ analogs. PutA displayed activity with all the analogs tested; the highest k_cat/K_m was obtained with CoQ₂. The kinetic mechanism of the PRODH reaction was investigated use a variety of steady-state approaches. Initial velocity patterns measured using proline and CoQ₁, combined with dead-end and product inhibition studies, suggested a two-site ping-pong mechanism for PutA. The kinetic parameters for PutA were not strongly influenced by solvent viscosity suggesting that diffusive steps do not significantly limit the overall reaction rate. In summary, the kinetic data reported here, along with analysis of the crystal structure data for the PRODH domain, suggest that the proline:ubiquinone oxidoreductase reaction of PutA occurs via a rapid equilibrium ping-pong mechanism with proline and ubiquinone binding at two distinct sites.     

Influence of inorganic pyrophosphate on the kinetics of muscle pyruvate kinase: a simple nonallosteric feedback model

Potassium pyrophosphate was used instead of ATP as a model ligand for magnesium cation for the study of effector influence on the kinetics of pyruvate kinase muscle isozyme M(1). The pyruvate kinase activation by low concentration of pyrophosphate and inhibition by high concentration of pyrophosphate was considered to be the result of reversible reactions of magnesium cation with pyrophosphate, ADP, ATP, and PEP. The apparent K(m) and V(m) or in some cases the pseudo-first order reaction rate constant (instead of K(m) and V(m)) of pyruvate kinase at any given pyrophosphate concentration were analysed as a function of concentration of free magnesium cation and its complexes with all ligands present in an assay mixture. The functions of reaction parameters with respect to concentration of magnesium complexes indicate the coexistence in the reaction mixture of simple and mixed complexes of magnesium cation with substrates, pyrophosphate, and an enzyme-substrate complex. The parameters of the simulated reaction for the proposed interactions fit the measured experimental data. A simple model with nonallosteric feedback has been proposed. According to this model, mutual and simultaneous interactions of reaction products with substrates and with an enzyme result in the coexistence of simple and mixed, labile and inert complexes.     

Spiny versus stubby: 3D reconstruction of human myenteric (type I) neurons

We have compared the three-dimensional (3D) morphology of stubby and spiny neurons derived from the human small intestine. After immunohistochemical triple staining for leu-enkephalin (ENK), vasoactive intestinal peptide (VIP) and neurofilament (NF), neurons were selected and scanned based on their immunoreactivity, whether ENK (stubby) or VIP (spiny). For the 3D reconstruction, we focused on confocal data pre-processing with intensity drop correction, non-blind deconvolution, an additional compression procedure in z-direction, and optimizing segmentation reliability. 3D Slicer software enabled a semi-automated segmentation based on an objective threshold (interrater and intrarater reliability, both 0.99). We found that most dendrites of stubby neurons emerged only from the somal circumference, whereas in spiny neurons, they also emerged from the luminal somal surface. In most neurons, the nucleus was positioned abluminally in its soma. The volumes of spiny neurons were significantly larger than those of stubby neurons (total mean of stubbies 806 ± 128 μm³, of spinies 2,316 ± 545 μm³), and spiny neurons had more dendrites (26.3 vs. 11.3). The ratios of somal versus dendritic volumes were 1:1.2 in spiny and 1:0.3 in stubby neurons. In conclusion, 3D reconstruction revealed new differences between stubby and spiny neurons and allowed estimations of volumetric data of these neuron populations.