A new double-chamber model of ion channels. Beyond the Hodgkin and Huxley model

This paper proposes a new double-chamber model (DCM) of ion channels. The model ion channel consists of a series of three pores alternating with two chambers. The chambers are net negatively charged. The chamber's electric charge originates from dissociated amino acid side chains and is pH dependent. The chamber's net negative charge is compensated by cations present inside the chamber and in a diffuse electric layer outside the chamber. The pore's permeability is constant independent of time. One pore of the sodium channel and one of the potassium channel is a voltage-sensing pore. Due to the channel's structure, ions flow through the pores and chambers in a time-dependent manner. The model reproduces experimental voltage clamp and action potential data. The current flowing through a single sodium channel is less then one femtoampere. The DCM is considerably simpler then the Hodgkin and Huxley model (HHM) used to describe the electrophysiological properties of an axon. Unlike the HHM, the DCM can explain refractoriness, anode break excitation, accommodation and the effect of pH and temperature on the channels without additional parameters. In the DCM, the axon membrane shows repetitive activity depending on the channel density, sodium to potassium channel ratio and external potassium concentration. In the DCM, the action potential starts from 'hot spot areas' of higher channel densities and a higher sodium to potassium channel ratio, and then propagates through the whole axon.     

On numerical integration of the Hodgkin and Huxley equations for a membrane action potential

Several methods of numerical integration of the Hodgkin and Huxley equations (6·3°C) for a membrane action potential have been compared for speed and accuracy of computations. Conversational languages make it possible to write compact programs for these equations which will run on minicomputers with only 4000 words of core memory.The shape of the computed action potential was found to be rather method-invariant but the latency (for a given stimulus) was found to depend on the method of integration and the size of the time increment. For stimuli near threshold, the computed response was found to be especially sensitive to these two variables. A new threshold value independent of integration method, has been determined to be ? 6·50790 mV by linear extrapolations of threshold-time step relations to a zero step size.The simple Euler method was found to be fast but gave large latency errors compared to the true solution. The Runge-Kutta (RK) method (in the sequential mode, defined in the section on numerical integration methods) was slower but gave smaller latency errors. The Adams corrector-predictor method was still slower, gave less stable solutions, and had large latency errors. A hybrid program which combined a RK numerical integration for the membrane potential with analytic expressions for the variables m, n, and h gave errors indistinguishable from the RK method, but ran much faster. Modified Euler methods run in the parallel mode gave very accurate solutions with moderate computation times. Solutions run with the RK method in the parallel mode took about twice as long but gave no appreciable improvement in accuracy.We were able to develop a simple method for correcting the Euler integration, resulting in quite accurate solutions which were essentially independent of step size and stimuli. Because this method is not only accurate but also runs about as fast as the simple Euler, it appears to be the method of choice for most purposes.     

Hodgkin–Huxley type modelling and parameter estimation of GnRH neurons

In this paper a simple one compartment Hodgkin–Huxley type electrophysiological model of GnRH neurons is presented, that is able to reasonably reproduce the most important qualitative features of the firing pattern, such as baseline potential, depolarization amplitudes, sub-baseline hyperpolarization phenomenon and average firing frequency in response to excitatory current. In addition, the same model provides an acceptable numerical fit of voltage clamp (VC) measurement results. The parameters of the model have been estimated using averaged VC traces, and characteristic values of measured current clamp traces originating from GnRH neurons in hypothalamic slices. The resulting parameter values show a good agreement with literature data in most of the cases. Applying parametric changes, which lead to the increase of baseline potential and enhance cell excitability, the model becomes capable of bursting. The effects of various parameters to burst length have been analyzed by simulation.     

A new twist for DNA

A computer-aided design strategy allows scientists to 'staple' DNA molecules into a wide variety of two-dimensional shapes, generating precisely arranged scaffolds that could serve as promising platforms for nanoscale research applications.     

A new twist to coiled coil

Spectrin repeats have been largely considered as passive linkers or spacers with little functional role other than to convey flexibility to a protein. Whilst this is undoubtedly part of their function, it is by no means all. Whilst the overt structure of all spectrin repeats is a simple triple-helical coiled coil, the linkages between repeats and the surface properties of repeats vary widely. Spectrin repeats in different proteins can act as dimerisation interfaces, platforms for the recruitment of signalling molecules, and as a site for the interaction with cytoskeletal elements and even direct association with membrane lipids. In the case of dystrophin several of these functions overlap in the space of a few repeats.     

A new twist in the transmembrane signaling tool-kit

In this issue, Schlessinger and his colleagues (Yuzawa et al., 2007) describe crystal structures of the complete extracellular region of the Kit receptor tyrosine kinase, both alone and in complex with its activating ligand, stem cell factor (SCF). The structures explain how SCF drives dimerization of the receptor. They also reveal important receptor-receptor contacts that may explain how several Kit mutations lead to cancer.     

A new twist in the hijacking of the actin-nucleating machinery

Many microbial pathogens have evolved specific adaptations to harness the host cell actin cytoskeleton. The understanding of these mechanisms reveals a striking level of complexity and diversity in the strategies utilized by different pathogens to module actin dynamics.     

A new twist in trypanosome RNA metabolism: cis-splicing of pre-mRNA

It has been known for almost a decade and a half that in trypanosomes all mRNAs are trans-spliced by addition to the 5' end of the spliced leader (SL) sequence. During the same time period the conviction developed that classical cis-splicing introns are not present in the trypanosome genome and that the trypanosome gene arrangement is highly compact with small intergenic regions separating one gene from the next. We have now discovered that these tenets are no longer true. Poly(A) polymerase (PAP) genes in Trypanosoma brucei and Trypanosoma cruzi are split by intervening sequences of 653 and 302 nt, respectively. The intervening sequences occur at identical positions in both organisms and obey the GT/AG rule of cis-splicing introns. PAP mRNAs are trans-spliced at the very 5' end as well as internally at the 3' splice site of the intervening sequence. Interestingly, 11 nucleotide positions past the actual 5' splice site are conserved between the T. bruceiand T. cruzi introns. Point mutations in these conserved positions, as well as in the AG dinucleotide of the 3' splice site, abolish intron removal in vivo. Our results, together with the recent discovery of cis-splicing introns in Euglena gracilis, suggest that both trans- and cis-splicing are ancient acquisitions of the eukaryotic cell.     

Microtubule cytoskeleton: a new twist at the end

A diverse group of proteins known as +TIPs specifically recognize the growing plus ends of microtubules in cells. Two recent papers on one such protein, CLIP-170, provide new insights into the cellular functions of +TIPs as well as the mechanism by which they track microtubule ends.     

Bifurcation phenomena appearing in the Lotka-Volterra competition equations: a numerical study

Bifurcation phenomena appearing in the Lotka-Volterra competition equations with periodically varying coefficients are studied numerically. We assume sinusoidal oscillations of the coefficients and use phase differences between them as free parameters. We are mainly concerned with the case where a pair of stable and unstable positive periodic solutions exists, although one of the trivial periodic solutions is stable and the other is unstable. We obtain a very curious bifurcation diagram in which two branches of stable and unstable positive periodic solutions are connected at both ends, but are connected with no other branches. We show how this unusual diagram can be viewed as a cross-section of a multidimensional bifurcation diagram. The region in a 3-dimensional parameter space where a pair of stable and unstable positive periodic solutions exists is shown in an example, and the ecological meaning of the phase differences necessary for stable coexistence of two species is considered. Finally, a bifurcation problem with the average intrinsic growth rate as a parameter is also dealt with numerically, in relation with Cushing's result.