Universal approach for local higher-order wavefront tracing equations for complex optical systems.

Analytical wave tracing, including higher-order aberrations, is the state of the art, but at present it is only provided for single propagation or refraction. A complex optical system being a sequence of many refractive surfaces and gaps in between can only be treated by successive application of elementary wave-tracing steps, which is time-consuming for a large number of surfaces or even impossible if a system specification by surfaces is not available. Provided the ray transfer properties of a system are summarized as a nonlinear function f whose Jacobian is the ABCD matrix of the system, by multiple derivative we obtain wave-tracing equations for the wavefront's local derivatives of any desired order. The outgoing wavefront derivative of any order can be written as a sum of multinomials of derivatives of the incoming wavefront, weighted by system-dependent coefficients and by powers of the factor ß=(A-BE2)-1, where E2 is the second-order aberration of the incoming wavefront. Compared to stepwise wave tracing, this approach is extremely efficient when tracing many different wavefronts through one fixed optical system.

Derivation of the refraction equations for higher-order aberrations of local wavefronts at oblique incidence.

From the literature the calculation of power and astigmatism of a local wavefront after refraction at a given surface is known from the vergence and Coddington equations. For higher-order aberrations (HOAs) equivalent analytical equations do not exist. Since HOAs play an increasingly important role in many fields of optics, e.g., ophthalmic optics, it is the purpose of this study to extend the "generalized Coddington equation" to the case of HOA (e.g., coma and spherical aberration). This is done by local power series expansions. In summary, with the results presented here, it is now possible to calculate analytically the local HOA of an outgoing wavefront directly from the aberrations of the incoming wavefront and the refractive surface.

[High resolution fluorescence microscopy in combination with mathematical modelling. First evidence of sub-cellular anesthetic effects on Ca2+ sparks in situ]. / Hoch auflösende Fluoreszenzmikroskopie in Kombination mit mathematischer Modellierung. Erstmaliger Nachweis von subzellulären Anästhetikawirkungen auf Ca2+-Sparks in situ.

Volatile anesthetics used in daily clinical routine, are associated with a rare but life-threatening disease, malignant hyperthermia. To date it is well known that, with the exception of xenon and nitrous oxide, all volatile anesthetics have the potential to trigger calcium (Ca(2+)) release from the sarcoplasmic reticulum, thereby influencing the Ca(2+) homeostasis in muscle fibers. The effects of volatile anesthetics have been previously studied by recording Ca(2+)-activated force transients in muscle fibers and by quantifying the effects on isolated intracellular Ca(2+)-release channels (ryanodin receptors). The use of high resolution fluorescence microscopy methods in combination with spatio-temporal mathematical models allows the effects of volatile anesthetics on functional clusters of ryanodin receptors in mammalian skeletal muscle fibers to be studied in situ for the first time.Thus, the analysis of cellular Ca(2+)-activated force production and single channel properties in conjunction with mathematical models allows the quantification of the effects of volatile anesthetics on Ca(2+)-release in the natural physiological environment on the basis of the underlying molecular architecture. In addition to the basic understanding of alterations in the Ca(2+) homeostasis induced by volatile anesthetics in muscle and nerve cells, the results are also of direct clinical importance for the understanding of the pathogenesis of malignant hyperthermia,where ryanodin receptor mutations are currently thought to result in an increased Ca(2+) release under the influence of volatile anesthetics.

Spark- and ember-like elementary Ca2+ release events in skinned fibres of adult mammalian skeletal muscle.

1. Using laser scanning confocal microscopy, we show for the first time elementary Ca2+ release events (ECRE) from the sarcoplasmic reticulum in chemically and mechanically skinned fibres from adult mammalian muscle and compare them with ECRE from amphibian skinned fibres. 2. Hundreds of spontaneously occurring events could be measured from individual single skinned mammalian fibres. In addition to spark-like events, we found ember-like events, i.e. long-lasting events of steady amplitude. These two different fundamental release types in mammalian muscle could occur in combination at the same location. 3. The two peaks of the frequency of occurrence for ECRE of mammalian skeletal muscle coincided with the expected locations of the transverse tubular system within the sarcomere, suggesting that ECRE mainly originate at triadic junctions. 4. ECRE in adult mammalian muscle could also be identified at the onset of the global Ca2+ release evoked by membrane depolarisation in mechanically skinned fibres. In addition, the frequency of ECRE was significantly increased by application of 0.5 mM caffeine and reduced by application of 2 mM tetracaine. 5. We conclude that the excitation-contraction coupling process in adult mammalian muscle involves the activation of both spark- and ember-like elementary Ca2+ release events.

Numerical analysis of Ca2+ depletion in the transverse tubular system of mammalian muscle.

Calcium currents were recorded in contracting and actively shortening mammalian muscle fibers. In order to characterize the influence of extracellular calcium concentration changes in the small unstirred lumina of the transverse tubular system (TTS) on the time course of the slow L-type calcium current (I(Ca)), we have combined experimental measurements of I(Ca) with quantitative numerical simulations of Ca2+ depletion. I(Ca) was recorded both in calcium-buffered and unbuffered external solutions using the two-microelectrode voltage clamp technique (2-MVC) on short murine toe muscle fibers. A simulation program based on a distributed TTS model was used to calculate the effect of ion depletion in the TTS. The experimental data obtained in a solution where ion depletion is suppressed by a high amount of a calcium buffering agent were used as input data for the simulation. The simulation output was then compared with experimental data from the same fiber obtained in unbuffered solution. Taking this approach, we could quantitatively show that the calculated Ca2+ depletion in the transverse tubular system of contracting mammalian muscle fibers significantly affects the time-dependent decline of Ca2+ currents. From our findings, we conclude that ion depletion in the tubular system may be one of the major effects for the I(Ca) decline measured in isotonic physiological solution under voltage clamp conditions.

Motion determination in actin filament fluorescence images with a spatio-temporal orientation analysis method.

We present a novel approach of automatically measuring motion in series of microscopic fluorescence images. As a differential method, the three-dimensional structure tensor technique is used to calculate the displacement vector field for every image of the sequence, from which the velocities are subsequently derived. We have used this method for the analysis of the movement of single actin filaments in the in vitro motility assay, where fluorescently labeled actin filaments move over a myosin decorated surface. With its fast implementation and subpixel accuracy, this approach is, in general, very valuable for analyzing dynamic processes by image sequence analysis.

Myosin binding protein C, a phosphorylation-dependent force regulator in muscle that controls the attachment of myosin heads by its interaction with myosin S2.

Myosin binding protein C (MyBP-C) is one of the major sarcomeric proteins involved in the pathophysiology of familial hypertrophic cardiomyopathy (FHC). The cardiac isoform is tris-phosphorylated by cAMP-dependent protein kinase (cAPK) on beta-adrenergic stimulation at a conserved N-terminal domain (MyBP-C motif), suggesting a role in regulating positive inotropy mediated by cAPK. Recent data show that the MyBP-C motif binds to a conserved segment of sarcomeric myosin S2 in a phosphorylation-regulated way. Given that most MyBP-C mutations that cause FHC are predicted to result in N-terminal fragments of the protein, we investigated the specific effects of the MyBP-C motif on contractility and its modulation by cAPK phosphorylation. The diffusion of proteins into skinned fibers allows the investigation of effects of defined molecular regions of MyBP-C, because the endogenous MyBP-C is associated with few myosin heads. Furthermore, the effect of phosphorylation of cardiac MyBP-C can be studied in a defined unphosphorylated background in skeletal muscle fibers only. Triton skinned fibers were tested for maximal isometric force, Ca(2+)/force relation, rigor force, and stiffness in the absence and presence of the recombinant cardiac MyBP-C motif. The presence of unphosphorylated MyBP-C motif resulted in a significant (1) depression of Ca(2+)-activated maximal force with no effect on dynamic stiffness, (2) increase of the Ca(2+) sensitivity of active force (leftward shift of the Ca(2+)/force relation), (3) increase of maximal rigor force, and (4) an acceleration of rigor force and rigor stiffness development. Tris-phosphorylation of the MyBP-C motif by cAPK abolished these effects. This is the first demonstration that the S2 binding domain of MyBP-C is a modulator of contractility. The anchorage of the MyBP-C motif to the myosin filament is not needed for the observed effects, arguing that the mechanism of MyBP-C regulation is at least partly independent of a "tether," in agreement with a modulation of the head-tail mobility. Soluble fragments occurring in FHC, lacking the spatial specificity, might therefore lead to altered contraction regulation without affecting sarcomere structure directly.

Mathematical modeling and fluorescence imaging to study the Ca2+ turnover in skinned muscle fibers.

A mathematical model was developed for the simulation of the spatial and temporal time course of Ca2+ ion movement in caffeine-induced calcium transients of chemically skinned muscle fiber preparations. Our model assumes cylindrical symmetry and quantifies the radial profile of Ca2+ ion concentration by solving the diffusion equations for Ca2+ ions and various mobile buffers, and the rate equations for Ca2+ buffering (mobile and immobile buffers) and for the release and reuptake of Ca2+ ions by the sarcoplasmic reticulum (SR), with a finite-difference algorithm. The results of the model are compared with caffeine-induced spatial Ca2+ transients obtained from saponin skinned murine fast-twitch fibers by fluorescence photometry and imaging measurements using the ratiometric dye Fura-2. The combination of mathematical modeling and digital image analysis provides a tool for the quantitative description of the total Ca2+ turnover and the different contributions of all interacting processes to the overall Ca2+ transient in skinned muscle fibers. It should thereby strongly improve the usage of skinned fibers as quantitative assay systems for many parameters of the SR and the contractile apparatus helping also to bridge the gap to the intact muscle fiber.