Parabolic bursting revisited

 Many excitable membrane systems display bursting oscillations, in which the membrane potential switches periodically between an active phase of rapid spiking and a silent phase of slow, quasi steady-state behavior. A burster is called parabolic when the spike frequency is lower both at the beginning and end of the active phase. We show that classes of voltage-gated conductance equations can be reduced to the mathematical mechanism previously analyzed by Ermentrout and Kopell in [7]. The reduction uses a series of coordinate changes and shows that the mechanism in [7] applies more generally than previously believed. The key hypothesis for the more general theory is that a certain slow periodic orbit must stay close to a curve of degenerate homoclinic points for the fast system, at least during the active phase. We do not require that the slow system have a periodic orbit when the voltage is held constant. Received 28 March 1995; received in revised form 20 October 1995     

Transport effects on surface–volume biological reactions

Many cellular reactions involve a reactant in solution binding to or dissociating from a reactant confined to a surface. This is true as well for a BIAcore, an optical biosensor that is widely used to study the interaction of biomolecules. In the flow cell of this instrument, one of the reactants is immobilized on a flat sensor surface while the other reactant flows past the surface. Both diffusion and convection play important roles in bringing the reactants into contact. Usually BIAcore binding data are analyzed using well known expressions that are valid only in the reaction-limited case when the Damk?hler number Da is small. Asymptotic and singular perturbation techniques are used to analyze dissociation of the bound state when Da is small and O(1). Linear and nonlinear integral equations result from the analysis; explicit and asymptotic solutions are constructed for physically realizable cases. In addition, effective rate constants are derived that illustrate the effects of transport on the measured rate constants. All these expressions provide a direct way to estimate the rate constants from BIAcore binding data.     

A GX2GX3G motif facilitates acyl chain sequestration by Saccharomyces cerevisiae acyl carrier protein

Saccharomyces cerevisiae acyl carrier protein (ScACP) is a component of the large fungal fatty acid synthase I (FAS I) complex. ScACP comprises two subdomains: a conserved ACP domain that shares extensive structural homology with other ACPs and a unique structural domain. Unlike the metazoan type I ACP that does not sequester the acyl chain, ScACP can partially sequester the growing acyl chain within its hydrophobic core by a mechanism that remains elusive. Our studies on the acyl-ScACP intermediates disclose a unique ¹⁸⁸GX₂GX₃G¹⁹⁵ sequence in helix II important for ACP function. Complete loss of sequestration was observed upon mutation of the three glycines in this sequence to valine (G188V/G191V/G195V), while G191V and G188V/G191V double mutants displayed a faster rate of acyl chain hydrolysis. Likewise, mutation of Thr216 to Ala altered the size of the hydrophobic cavity, resulting in loss of C₁₂- chain sequestration. Combining NMR studies with insights from the crystal structure, we show that three glycines in helix II and a threonine in helix IV favor conformational change, which in turn generate space for acyl chain sequestration. Furthermore, we identified the primary hydrophobic cavity of ScACP, present between the carboxyl end of helix II and IV. The opening of the cavity lies between the second and third turns of helix II and loop II. Overall, the study highlights a novel role of the GX₂GX₃G motif in regulating acyl chain sequestration, vital for ScACP function.     

Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios

We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration is not necessarily small. Simple analytical solutions are obtained when the reaction rates and the initial substrate concentration satisfy a certain condition. These analytical solutions compare favourably with numerical solutions of the full system of differential equations describing the reaction. Experimental methods are suggested which might permit the application of the quasi-steady state assumption to reactions where it may not have been obviously applicable before.     

A UV resonance Raman investigation of poly(rI): Evidence for cation-dependent structural perturbations

Poly(rI) stabilized by either Na⁺ or K⁺ was investigated using uv resonance Raman (UVRR) spectroscopy. Raman excitation profiles of inosine 5′-monophosphate demonstrated the 250 nm excitation selectively enhances base stacking interactions, while ribose and carbonyl stretching vibrations are preferentially enhanced with 210 nm excitation. These wavelengths were used to examine the structure of poly(rI) in the presence of either K⁺ or Na⁺ as a function of temperature. UVRR studies revealed that the K⁺ stabilized form is more thermally stable, yielding a T_m of ∼ 47°C compared to a T_m of ∼ 30°C for the Na⁺ stabilized form. We observed that both the ribosyl conformation and the coordination of the carbonyl groups depend on the nature of the cation. The C₆O stretching frequency indicates that Na⁺ coordinates much more strongly to the carbonyl groups than K⁺ (1672 cm⁻¹ Na⁺ vs 1684 cm⁻¹ K⁺ at 4°C). Conformationally sensitive modes of the phosphate backbone and the ribosyl ring indicate that Na⁺ stabilized poly(rI) predominantly exists in a C_3′-endo ribose conformation, whereas K⁺ stabilized poly(rI) adopts a C_2′-endo conformation possibly as a consequence of the larger ionic radius of the K⁺ ion. © 1998 John Wiley & Sons, Inc. Biopoly 46: 475–487, 1998     

Anticipatory postural adjustments in children with hemiplegia and diplegia

Anticipatory postural adjustments (APAs) play an important role in the performance of many activities requiring the maintenance of standing posture. However, little is known about if and how children with cerebral palsy (CP) generate APAs. Two groups of children with CP (hemiplegia and diplegia) and a group of children with typical motor development performed arm flexion and extension movements while standing on a force platform. Electromyographic activity of six trunk and leg muscles and displacement of center of pressure (COP) were recorded. Children with CP were able to generate anticipatory postural adjustments and produce directionally specific APAs and COP displacements similar to those described in adults and typically developing children. However, children with diplegia were unable to generate APAs of the same magnitude as children with typical development and hemiplegia and had higher baseline muscle activity prior to movement. In children with diplegia, COP was posteriorly displaced and peak acceleration was smaller during bilateral extension compared to children with hemiplegia. The outcomes of the study highlight the role of APAs in the control of posture of children with CP and point out the similarities and differences in anticipatory control in children with diplegia and hemiplegia. These differences may foster ideas for treatment strategies to enhance APAs in children with CP.     

Structural resilience of the gut microbiota in adult mice under high-fat dietary perturbations

Disruption of the gut microbiota by high-fat diet (HFD) has been implicated in the development of obesity. It remains to be elucidated whether the HFD-induced shifts occur at the phylum level or whether they can be attributed to specific phylotypes; additionally, it is unclear to what extent the changes are reversible under normal chow (NC) feeding. One group (diet-induced obesity, DIO) of adult C57BL/6J mice was fed a HFD for 12 weeks until significant obesity and insulin resistance were observed, and then these mice were switched to NC feeding for 10 weeks. Upon switching to NC feeding, the metabolic deteriorations observed during HFD consumption were significantly alleviated. The second group (control, CHO) remained healthy under continuous NC feeding. UniFrac analysis of bar-coded pyrosequencing data showed continued structural segregation of DIO from CHO on HFD. At 4 weeks after switching back to NC, the gut microbiota in the DIO group had already moved back to the CHO space, and continued to progress along the same age trajectory and completely converged with CHO after 10 weeks. Redundancy analysis identified 77 key phylotypes responding to the dietary perturbations. HFD-induced shifts of these phylotypes all reverted to CHO levels over time. Some of these phylotypes exhibited robust age-related changes despite the dramatic abundance variations in response to dietary alternations. These findings suggest that HFD-induced structural changes of the gut microbiota can be attributed to reversible elevation or diminution of specific phylotypes, indicating the significant structural resilience of the gut microbiota of adult mice to dietary perturbations.     

N‐dimensional hypervolumes to study stability of complex ecosystems

Although our knowledge on the stabilising role of biodiversity and on how it is affected by perturbations has greatly improved, we still lack a comprehensive view on ecosystem stability that is transversal to different habitats and perturbations. Hence, we propose a framework that takes advantage of the multiplicity of components of an ecosystem and their contribution to stability. Ecosystem components can range from species or functional groups, to different functional traits, or even the cover of different habitats in a landscape mosaic. We make use of n‐dimensional hypervolumes to define ecosystem states and assess how much they shift after environmental changes have occurred. We demonstrate the value of this framework with a study case on the effects of environmental change on Alpine ecosystems. Our results highlight the importance of a multidimensional approach when studying ecosystem stability and show that our framework is flexible enough to be applied to different types of ecosystem components, which can have important implications for the study of ecosystem stability and transient dynamics.