Inversion of Markov processes to determine rate constants from single-channel data

The determination of rate constants from single-channel data can be very difficult, in part because the single-channel lifetime distributions commonly analyzed by experimenters often have a complicated mathematical relation to the channel gating mechanism. The standard treatment of channel gating as a Markov process leads to the prediction that lifetime distributions are exponential functions. As the number of states of a channel gating scheme increases, the number of exponential terms in the lifetime distribution increases, and the weights and decay constants of the lifetime distributions become progressively more complicated functions of the underlying rate constants. In the present study a mathematical strategy for inverting these functions is introduced in order to determine rate constants from single-channel lifetime distributions. This inversion is easy for channel gating schemes with two or fewer states of a given conductance, so the present study focuses on schemes with more states. The procedure is to derive explicit equations relating the parameters of the lifetime distribution to the rate constants of the scheme. Such equations can be derived using the equality between symmetric functions of eigenvalues of a matrix and sums over principle minors, as well as expressions for the moments, derivatives, and weights of a lifetime distribution. The rate constants are then obtained as roots to this system of equations. For a gating scheme with three sequential closed states and a single gateway state, exact analytical expressions were found for each rate constant in terms of the parameters of the three-exponential closed-time distribution. For several other gating schemes, systems of equations were found that could be solved numerically to obtain the rate constants. Lifetime distributions were shown to specify a unique set of real rate constants in sequential gating schemes with up to five closed or five open states. For kinetic schemes with multiple gating pathways, the analysis of simulated data revealed multiple solutions. These multiple solutions could be distinguished by examining two-dimensional probability density functions. The utility of the methods introduced here are demonstrated by analyzing published data on nicotinic acetylcholine receptors, GABA(A) receptors, and NMDA receptors

Curare binding and the curare-induced subconductance state of the acetylcholine receptor channel

The curare-induced subconductance state of the nicotinic acetylcholine receptor (AChR) of mouse skeletal muscle was examined using the patch-clamp technique. Two mechanisms for the generation of subconductance states were considered. One of these mechanisms entails allosteric induction of a distinct channel conformation through the binding of curare to the agonist binding site. The other mechanism entails the binding of curare to a different site on the protein. Occupation of this site would then limit the flow of ions through the channel. The voltage dependence and concentration dependence of subconductance state kinetics are consistent with curare binding to a site within the channel. The first order rate constant for binding is 1.2 X 10(6) M-1s-1 at 0 mV, and increases e-fold per 118 mV of membrane hyperpolarization. The rate of curare dissociation from this site is 1.9 X 10(2)s-1 at 0 mV, and decreases e-fold per 95 mV hyperpolarization. The equilibrium constant is 1.4 X 10(-4) M at 0 mV, and decreases e-fold per 55 mV hyperpolarization. This voltage dependence suggests that the fraction of the transmembrane potential traversed by curare in binding to this site is 0.46 or 0.23, depending on whether one assumes that one or both charges of curare sense the electric field. Successive reduction and alkylation of the AChR agonist binding sites with dithiothreitol (DTT) and N-ethyl maleimide (NEM), a treatment which results in the loss of responsiveness of the AChR to agonists, produced no change in curare-induced subconductance events, despite the fact that after this treatment most of the channel openings occurred spontaneously. Mixtures of high concentrations of carbamylcholine (CCh) with a low concentration of curare, which produce channel openings gated predominantly by CCH, resulted in subconductance state kinetics similar to those seen in curare alone at the same concentration. Thus displacement by CCh of curare from the agonist binding sites does not prevent curare from inducing subconductances. The results presented here support the hypothesis that curare induces subconductance states by binding to a site on the receptor other than the agonist binding sites, possibly within the channel pore. It is the occupation of this site by curare that limits the flow of ions through an otherwise fully opened channel

Use of cumulative mortality data in patients with acute myocardial infarction for early detection of variation in clinical practice: observational study

OBJECTIVES: Use of cumulative mortality adjusted for case mix in patients with acute myocardial infarction for early detection of variation in clinical practice. DESIGN: Observational study. SETTING: 20 hospitals across the former Yorkshire region. PARTICIPANTS: All 2153 consecutive patients with confirmed acute myocardial infarction identified during three months. MAIN OUTCOME MEASURES: Variable life­adjusted displays showing cumulative differences between observed and expected mortality of patients; expected mortality calculated from risk model based on admission characteristics of age, heart rate, and systolic blood pressure. RESULTS: The performance of two individual hospitals over three months was examined as an example. One, the smallest district hospital in the region, had a series of 30 consecutive patients but had five more deaths than predicted. The variable life­adjusted display showed minimal variation from that predicted for the first 15 patients followed by a run of unexpectedly high mortality. The second example was the main tertiary referral centre for the region, which admitted 188 consecutive patients. The display showed a period of apparently poor performance followed by substantial improvement, where the plot rose steadily from a cumulative net lives saved of - 4 to 7. These variations in patient outcome are unlikely to have been revealed during conventional audit practice. CONCLUSIONS: Variable life­adjusted display has been integrated into surgical care as a graphical display of risk­adjusted survival for individual surgeons or centres. In combination with a simple risk model, it may have a role in monitoring performance and outcome in patients with acute myocardial infarction

Nanoindentation modeling of a nanodot-patterned surface on a deformable substrate

AbstractA numerical model was developed to simulate the nanoindentation of a Ni nanodot-patterned surface (NDPS) on a deformable Si substrate. Each contacting nanodot on the Si substrate was treated individually in this model and the interaction among the nanodots was considered through the elastic deformation of the Si substrate. The load–deformation relationship for the single-asperity contact between the indenter tip and a nanodot was determined using finite element analysis. A nanoindentation experiment on a Ni NDPS was performed to test the developed model. The simulation and experimental results were found to be in good agreement. The experimentally verified model was used to explore the effects of substrate deformation and surface roughness caused by the Ni nanodots on the nanoindentation behavior. It was found that the effect of the substrate and the effect of roughness must be considered. A detailed study of the substrate deformation shows that the interaction among nanodots, through the substrate, can contribute a considerable portion of the total deformation under a nanodot. The yield strength of the nanodot was found to have a significant effect on the contact deformation, while the elastic modulus was found to have little effect

Long Lived Large Type II Strings: decay within compactification

Motivated also by recent revival of interest about metastable string states (as cosmic strings or in accelerator physics), we study the decay, in presence of dimensional compactification, of a particular superstring state, which was proven to be remarkably long-lived in the flat uncompactified scenario. We compute the decay rate by an exact numerical evaluation of the imaginary part of the one-loop propagator. For large radii of compactification, the result tends to the fully uncompactified one (lifetime T = const M^5/g^2), as expected, the string mainly decaying by massless radiation. For small radii, the features of the decay (emitted states, initial mass dependence,....) change, depending on how the string wraps on the compact dimensions.Comment: 32 pages, 24 text plus appendices, 4 figure

Extending the Ehresmann-Schein-Nambooripad Theorem

We extend the `join-premorphisms' part of the Ehresmann-Schein-Nambooripad Theorem to the case of two-sided restriction semigroups and inductive categories, following on from a result of Lawson (1991) for the `morphisms' part. However, it is so-called `meet-premorphisms' which have proved useful in recent years in the study of partial actions. We therefore obtain an Ehresmann-Schein-Nambooripad-type theorem for meet-premorphisms in the case of two-sided restriction semigroups and inductive categories. As a corollary, we obtain such a theorem in the inverse case.Comment: 23 pages; final section on Szendrei expansions removed; further reordering of materia

On the evolution of cosmic-superstring networks

We model the behaviour of a network of interacting (p,q) strings from IIB string theory by considering a field theory containing multiple species of string, allowing us to study the effect of non-intercommuting events due to two different species crossing each other. This then has the potential for a string dominated Universe with the network becoming so tangled that it freezes. We give numerical evidence, explained by a one-scale model, that such freezing does not take place, with the network reaching a scaling limit where its density relative to the background increases with N, the number of string types.Comment: Extra references added showing constraints on cosmic superstrings, 7 pages, 7 figure

Vortex Rings in two Component Bose-Einstein Condensates

We study the structure of the vortex core in two-component Bose-Einstein condensates. We demonstrate that the order parameter may not vanish and the symmetry may not be restored in the core of the vortex. In this case such vortices can form vortex rings known as vortons in particle physics literature. In contrast with well-studied superfluid $^4He$, where similar vortex rings can be stable due to Magnus force only if they move, the vortex rings in two-component BECs can be stable even if they are at rest. This beautiful effect was first discussed by Witten in the cosmic string context, where it was shown that the stabilization occurs due to condensation of the second component of the field in the vortex core. This second condensate trapped in the core may carry a current along the vortex ring counteracting the effect of string tension that causes the loop to shrink. We speculate that such vortons may have been already observed in the laboratory. We also speculate that the experimental study of topological structures in BECs can provide a unique opportunity to study cosmology and astrophysics by doing laboratory experiments.Comment: 21 pages, 2 figure

Searching for Signatures of Cosmic Superstrings in the CMB

Because cosmic superstrings generically form junctions and gauge theoretic strings typically do not, junctions may provide a signature to distinguish between cosmic superstrings and gauge theoretic cosmic strings. In cosmic microwave background anisotropy maps, cosmic strings lead to distinctive line discontinuities. String junctions lead to junctions in these line discontinuities. In turn, edge detection algorithms such as the Canny algorithm can be used to search for signatures of strings in anisotropy maps. We apply the Canny algorithm to simulated maps which contain the effects of cosmic strings with and without string junctions. The Canny algorithm produces edge maps. To distinguish between edge maps from string simulations with and without junctions, we examine the density distribution of edges and pixels crossed by edges. We find that in string simulations without Gaussian noise (such as produced by the dominant inflationary fluctuations) our analysis of the output data from the Canny algorithm can clearly distinguish between simulations with and without string junctions. In the presence of Gaussian noise at the level expected from the current bounds on the contribution of cosmic strings to the total power spectrum of density fluctuations, the distinction between models with and without junctions is more difficult. However, by carefully analyzing the data the models can still be differentiated.Comment: 15 page

The effect of extra dimensions on gravity wave bursts from cosmic string cusps

We explore the kinematical effect of having extra dimensions on the gravity wave emission from cosmic strings. Additional dimensions both round off cusps, and reduce the probability of their formation. We recompute the gravity wave burst, taking into account these two factors, and find a potentially significant damping on the gravity waves of the strings.Comment: 33 pages, 8 figures, published versio