Nonlinear indicial response of complex nonstationary oscillations as pulmonary hypertension responding to step hypoxia

This paper is devoted to the quantization of the degree of nonlinearity of the relationship between two biological variables when one of the variables is a complex nonstationary oscillatory signal. An example of the situation is the indicial responses of pulmonary blood pressure (P) to step changes of oxygen tension (ΔpO2) in the breathing gas. For a step change of ΔpO2 beginning at time t1, the pulmonary blood pressure is a nonlinear function of time and ΔpO2, which can be written as P(t-t1 | ΔpO2). An effective method does not exist to examine the nonlinear function P(t-t1 | ΔpO2). A systematic approach is proposed here. The definitions of mean trends and oscillations about the means are the keys. With these keys a practical method of calculation is devised. We fit the mean trends of blood pressure with analytic functions of time, whose nonlinearity with respect to the oxygen level is clarified here. The associated oscillations about the mean can be transformed into Hilbert spectrum. An integration of the square of the Hilbert spectrum over frequency yields a measure of oscillatory energy, which is also a function of time, whose mean trends can be expressed by analytic functions. The degree of nonlinearity of the oscillatory energy with respect to the oxygen level also is clarified here. Theoretical extension of the experimental nonlinear indicial functions to arbitrary history of hypoxia is proposed. Application of the results to tissue remodeling and tissue engineering of blood vessels is discussed.

Structure and function in rhodopsin: Kinetic studies of retinal binding to purified opsin mutants in defined phospholipid–detergent mixtures serve as probes of the retinal binding pocket

In the current standard procedure for preparation of mammalian rhodopsin mutants, transfected COS-1 cells expressing the mutant opsin genes are treated with 5 μM 11-cis-retinal before detergent solubilization for purification. We found that binding of 11-cis-retinal to opsin mutants with single amino acid changes at Trp-265 (W265F,Y,A) and a retinitis pigmentosa mutant (A164V) was far from complete and required much higher concentrations of 11-cis-retinal. By isolation of the expressed opsins in a stable form, kinetic studies of retinal binding to the opsins in vitro have been carried out by using defined phospholipid–detergent mixtures. The results show wide variation in the rates of 11-cis-retinal binding. Thus, the in vitro reconstitution procedure serves as a probe of the retinal-binding pocket in the opsins. Further, a method is described for purification and characterization of the rhodopsin mutants after retinal binding to the opsins in vitro.

Kinetic stability as a mechanism for protease longevity

The folding of the extracellular serine protease, α-lytic protease (αLP; EC 3.4.21.12) reveals a novel mechanism for stability that appears to lead to a longer functional lifetime for the protease. For αLP, stability is based not on thermodynamics, but on kinetics. Whereas this has required the coevolution of a pro region to facilitate folding, the result has been the optimization of native-state properties independent of their consequences on thermodynamic stability. Structural and mutational data lead to a model for catalysis of folding in which the pro region binds to a conserved β-hairpin in the αLP C-terminal domain, stabilizing the folding transition state and the native state. The pro region is then proteolytically degraded, leaving the active αLP trapped in a metastable conformation. This metastability appears to be a consequence of pressure to evolve properties of the native state, including a large, highly cooperative barrier to unfolding, and extreme rigidity, that reduce susceptibility to proteolytic degradation. In a test of survival under highly proteolytic conditions, homologous mammalian proteases that have not evolved kinetic stability are much more rapidly degraded than αLP. Kinetic stability as a means to longevity is likely to be a mechanism conserved among the majority of extracellular bacterial pro-proteases and may emerge as a general strategy for intracellular eukaryotic proteases subject to harsh conditions as well.

Unexpected signals in a system subject to kinetic proofreading

When multivalent ligands attach to IgEs bound to the receptors with high affinity for IgE on mast cells, the receptors aggregate, tyrosines on the receptors become phosphorylated, and a variety of cellular responses are stimulated. Prior studies, confirmed here, demonstrated that the efficiency with which later events are generated from earlier ones is inversely related to the dissociation rate of the aggregating ligand. This finding suggests that the cellular responses are constrained by a “kinetic proofreading” regimen. We have now observed an apparent exception to this rule. Doses of the rapidly or slowly dissociating ligands that generated equivalent levels of tyrosine-phosphorylated receptors comparably stimulated a putatively distal event: transcription of the gene for monocyte chemoattractant protein 1. Possible explanations of this apparent anomaly were explored.

Kinetic proofreading models for cell signaling predict ways to escape kinetic proofreading

In the context of cell signaling, kinetic proofreading was introduced to explain how cells can discriminate among ligands based on a kinetic parameter, the ligand-receptor dissociation rate constant. In the kinetic proofreading model of cell signaling, responses occur only when a bound receptor undergoes a complete series of modifications. If the ligand dissociates prematurely, the receptor returns to its basal state and signaling is frustrated. We extend the model to deal with systems where aggregation of receptors is essential to signal transduction, and present a version of the model for systems where signaling depends on an extrinsic kinase. We also investigate the kinetics of signaling molecules, “messengers,” that are generated by aggregated receptors but do not remain associated with the receptor complex. We show that the extended model predicts modes of signaling that exhibit kinetic discrimination for some range of parameters but for other parameter values show little or no discrimination and thus escape kinetic proofreading. We compare model predictions with experimental data.

The generation of oscillations in networks of electrically coupled cells

In several biological systems, the electrical coupling of nonoscillating cells generates synchronized membrane potential oscillations. Because the isolated cell is nonoscillating and electrical coupling tends to equalize the membrane potentials of the coupled cells, the mechanism underlying these oscillations is unclear. Here we present a dynamic mechanism by which the electrical coupling of identical nonoscillating cells can generate synchronous membrane potential oscillations. We demonstrate this mechanism by constructing a biologically feasible model of electrically coupled cells, characterized by an excitable membrane and calcium dynamics. We show that strong electrical coupling in this network generates multiple oscillatory states with different spatio-temporal patterns and discuss their possible role in the cooperative computations performed by the system.

Force and kinetic barriers to unzipping of the DNA double helix

A theory of the unzipping of double-stranded DNA is presented and is compared to recent micromanipulation experiments. It is shown that the interactions that stabilize the double helix and the elastic rigidity of single strands simply determine the sequence-dependent ≈12-pN force threshold for DNA strand separation. Using a semimicroscopic model of the binding between nucleotide strands, we show that the greater rigidity of the strands when formed into double-stranded DNA, relative to that of isolated strands, gives rise to a potential barrier to unzipping. The effects of this barrier are derived analytically. The force to keep the extremities of the molecule at a fixed distance, the kinetic rates for strand unpairing at fixed applied force, and the rupture force as a function of loading rate are calculated. The dependence of the kinetics and of the rupture force on molecule length is also analyzed.

Kinetic coupling between electron and proton transfer in cytochrome c oxidase: simultaneous measurements of conductance and absorbance changes.

Bovine heart cytochrome c oxidase is an electron-current driven proton pump. To investigate the mechanism by which this pump operates it is important to study individual electron- and proton-transfer reactions in the enzyme, and key reactions in which they are kinetically and thermodynamically coupled. In this work, we have simultaneously measured absorbance changes associated with electron-transfer reactions and conductance changes associated with protonation reactions following pulsed illumination of the photolabile complex of partly reduced bovine cytochrome c oxidase and carbon monoxide. Following CO dissociation, several kinetic phases in the absorbance changes were observed with time constants ranging from approximately 3 microseconds to several milliseconds, reflecting internal electron-transfer reactions within the enzyme. The data show that the rate of one of these electron-transfer reactions, from cytochrome a3 to a on a millisecond time scale, is controlled by a proton-transfer reaction. These results are discussed in terms of a model in which cytochrome a3 interacts electrostatically with a protonatable group, L, in the vicinity of the binuclear center, in equilibrium with the bulk through a proton-conducting pathway, which determines the rate of proton transfer (and indirectly also of electron transfer). The interaction energy of cytochrome a3 with L was determined independently from the pH dependence of the extent of the millisecond-electron transfer and the number of protons released, as determined from the conductance measurements. The magnitude of the interaction energy, 70 meV (1 eV = 1.602 x 10(-19) J), is consistent with a distance of 5-10 A between cytochrome a3 and L. Based on the recently determined high-resolution x-ray structures of bovine and a bacterial cytochrome c oxidase, possible candidates for L and a physiological role for L are discussed.

Kinetic analysis of peptide loading onto HLA-DR molecules mediated by HLA-DM.

The nonclassical major histocompatibility complex class II molecule HLA-DM (DM) has recently been shown to play a central role in the class II-associated antigen presentation pathway: DM releases invariant chain-derived CLIP peptides (class II-associated invariant chain protein peptide) from HLA-DR (DR) molecules and thereby facilitates loading with antigenic peptides. Some observations have led to the suggestion that DM acts in a catalytic manner, but so far direct proof is missing. Here, we investigated in vitro the kinetics of exchange of endogenously bound CLIP for various peptides on DR1 and DR2a molecules: we found that in the presence of DM the peptide loading process follows Michaelis-Menten kinetics with turnover numbers of 3-12 DR molecules per minute per DM molecule, and with KM values of 500-1000 nM. In addition, surface plasmon resonance measurements showed that DM interacts efficiently with DR-CLIP complexes but only weakly with DR-peptide complexes isolated from DM-positive cells. Taken together, our data provide evidence that DM functions as an enzyme-like catalyst of peptide exchange and favors the generation of long-lived DR-peptide complexes that are no longer substrates for DM.

Inhibition of sustained gamma oscillations (35-80 Hz) by fast transient responses in cat visual cortex.

Interactions between stimulus-induced oscillations (35-80 Hz) and stimulus-locked nonoscillatory responses were investigated in the visual cortex areas 17 and 18 of anaesthetized cats. A single square-wave luminance grating was used as a visual stimulus during simultaneous recordings from up to seven electrodes. The stimulus movement consisted of a superposition of a smooth movement with a sequence of dynamically changing accelerations. Responses of local groups of neurons at each electrode were studied on the basis of multiple unit activity and local slow field potentials (13-120 Hz). Oscillatory and stimulus-locked components were extracted from multiple unit activity and local slow field potentials and quantified by a combination of temporal and spectral correlation methods. We found fast stimulus-locked components primarily evoked by sudden stimulus accelerations, whereas oscillatory components (35-80 Hz) were induced during slow smooth movements. Oscillations were gradually reduced in amplitude and finally fully suppressed with increasing amplitudes of fast stimulus-locked components. It is argued that suppression of oscillations is necessary to prevent confusion during sequential processing of stationary and fast changing retinal images.

Oscillations in KATP channel activity promote oscillations in cytoplasmic free Ca2+ concentration in the pancreatic beta cell.

Pancreatic beta cells exhibit oscillations in electrical activity, cytoplasmic free Ca2+ concentration ([Ca2+](i)), and insulin release upon glucose stimulation. The mechanism by which these oscillations are generated is not known. Here we demonstrate fluctuations in the activity of the ATP-dependent K+ channels (K(ATP) channels) in single beta cells subject to glucose stimulation or to stimulation with low concentrations of tolbutamide. During stimulation with glucose or low concentrations of tolbutamide, K(ATP) channel activity decreased and action potentials ensued. After 2-3 min, despite continuous stimulation, action potentials subsided and openings of K(ATP) channels could again be observed. Transient suppression of metabolism by azide in glucose-stimulated beta cells caused reversible termination of electrical activity, mimicking the spontaneous changes observed with continuous glucose stimulation. Thus, oscillations in K(ATP) channel activity during continuous glucose stimulation result in oscillations in electrical activity and [Ca2+](i).

Intracortical and corticothalamic coherency of fast spontaneous oscillations.

We report that fast (mainly 30- to 40-Hz) coherent electric field oscillations appear spontaneously during brain activation, as expressed by electroencephalogram (EEG) rhythms, and they outlast the stimulation of mesopontine cholinergic nuclei in acutely prepared cats. The fast oscillations also appear during the sleep-like EEG patterns of ketamine/xylazine anesthesia, but they are selectively suppressed during the prolonged phase of the slow (<1-Hz) sleep oscillation that is associated with hyperpolarization of cortical neurons. The fast (30- to 40-Hz) rhythms are synchronized intracortically within vertical columns, among closely located cortical foci, and through reciprocal corticothalamic networks. The fast oscillations do not reverse throughout the depth of the cortex. This aspect stands in contrast with the conventional depth profile of evoked potentials and slow sleep oscillations that display opposite polarity at the surface and midlayers. Current-source-density analyses reveal that the fast oscillations are associated with alternating microsinks and microsources across the cortex, while the evoked potentials and the slow oscillation display a massive current sink in midlayers, confined by two sources in superficial and deep layers. The synchronization of fast rhythms and their high amplitudes indicate that the term "EEG desynchronization," used to designate brain-aroused states, is incorrect and should be replaced with the original term, "EEG activation" [Moruzzi, G. & Magoun, H.W. (1949) Electroencephalogr. Clin. Neurophysiol. 1, 455-473].

Kinetic discrimination in T-cell activation.

We propose a quantitative model for T-cell activation in which the rate of dissociation of ligand from T-cell receptors determines the agonist and antagonist properties of the ligand. The ligands are molecular complexes between antigenic peptides and proteins of the major histocompatibility complex on the surfaces of antigen-presenting cells. Binding of ligand to receptor triggers a series of biochemical reactions in the T cell. If the ligand dissociates after these reactions are complete, the T cell receives a positive activation signal. However, dissociation of ligand after completion of the first reaction but prior to generation of the final products results in partial T-cell activation, which acts to suppress a positive response. Such a negative signal is brought about by T-cell ligands containing the variants of antigenic peptides referred to as T-cell receptor antagonists. Results of recent experiments with altered peptide ligands compare favorably with T-cell responses predicted by this model.

A combined kinetic and modeling study of the catalytic center subsites of human angiogenin.

Kinetic analysis and molecular modeling have been used to map the ribonucleolytic center of angiogenin (Ang). Pyrimidine nucleotides were found to interact very weakly with Ang, consistent with the inaccessible B1 pyrimidine binding site revealed by x-ray crystallography. Ang also lacks an effective phosphate binding site on the 5' side of B1. Although the B2 site that preferentially binds purines on the 3' side of B1 is also weak, its associated phosphate subsites make substantial contributions: both 3',5'-ADP and 5'-ADP have Ki values 6-fold lower than for 5'-AMP, and adding a 3'-phosphate to the substrate CpA increases Kcat/Km by 9-fold. Thus Ang has a functional P2 site on the 3' side of B2 and a site for a second phosphate on the 5' side of B2. Modeling of an Ang-d(ApTpApA) complex suggested that Arg-5 forms part of the P2 site and that a 2'-phosphate might bind more tightly than a 3'-phosphate. Both predictions were confirmed kinetically. The subsite map obtained by this combined approach indicated that 5'-diphosphoadenosine 2'-phosphate might be a more potent inhibitor than any of the nucleotides tested thus far. Indeed, its Ki value of 150 microM is 50-fold lower than that for the best nucleotide previously reported and 400-fold lower than the Km for the best dinucleotide substrate. This compound may serve as a suitable starting point for the eventual design of tight-binding inhibitors of Ang as antiangiogenic agents for human therapy.