Metrics from nonlinear dynamics adapted for characterizing the behavior of nonequilibrium enzymatic rate functions

Several metrics from nonlinear dynamics and statistical mechanics have been characterized on computer-generated number series with various signal-to-noise ratios, demonstrating their individual reliability as a function of sample size and their relationships to each other. The root mean square (RMS) evaluates amplitude, and the power spectral density (PSD) provides a visual display of the frequency spectrum; both measures have very high reliability even for an N as low as 50. The Fractal Dimension (D) is shown to converge rapidly and also to be reliable when N is as low as 50. These three measures (RMS, PSD, and D) have been applied to the complex kinetics of tyrosine hydroxylase time courses (50-point curves) at various BH4 concentrations (near physiological, but far from equilibrium levels). Recently developed measures of spectral entropy and the Liapunov Exponent, -lambda are also characterized.     

On measurements of the higher harmonics of transmembrane current

The higher harmonics of the current caused by an alternating voltage applied to bilayer lipid membranes made of diphytanoyl phosphatidylcholine (DPhPC) in decane and tetradecane were measured. A universal relation between the amplitudes of harmonics was proposed and experimentally verified. This allowed the coefficients of expansion of the capacitance in even powers of voltage to be calculated for the DPhPC membrane in tetradecane; it also permitted comparison of the inhomogeneity in the thickness of the DPhPC membranes in decane and tetradecane.     

Removing Cancer when it is Correlated with other Causes of Death

This paper presents an identifiability theorem in the theory of dependent competing risks and it applies the result by examining the effect of removing cancer from the United States population when cancer is correlated with the other causes of death. The paper shows how dependence can be modeled with copula functions and it shows that calculating the survival probabilities after cancer is removed is equivalent to solving a system of nonlinear differential equations.     

Prediction of nonlinear elastic behaviour of vaginal tissue: experimental results and model formulation

The mechanical properties of the vaginal tissue need to be characterised to perform accurate simulations of prolapse and other pelvic disorders that commonly affect women. This is also a fundamental step towards the improvement of therapeutic techniques such as surgery. Issues like the efficiency of using autologous tissue in pelvic reconstruction may be addressed. The goal of this study was to characterise the elastic behaviour of vaginal tissue. For this purpose, prolapsed vaginal tissue from eight different post-menopausal patients, excised during prolapse corrective surgery, was mechanically tested. The mechanical testing of vaginal tissue, consisting of uniaxial tension tests performed along the longitudinal axis of the vagina, revealed the nonlinear mechanical behaviour of the tissue. The material model parameters were fit to the experimental data using the Levenberg–Marquardt optimisation algorithm. All the curve fittings showed a good agreement between experimental and theoretical results, evidenced by R ² values close to 1 and by very low ? values.     

Second-harmonic generation from organic molecules incorporated in sol-gel matrices

Orientation of optically nonlinear organic molecules inside sol-gel matrices upon application of an external D.C. electrical field is demonstrated for the first time. The quadratic nonlinear response of silicon oxide or transition metal oxide based gels containing organic molecules has been determined from Electric Field Induced Second Harmonic (EFISH) measurements. Large concentrations of Optically Nonlinear Organic Molecules (ONOM) have been either incorporated inside the macromolecular network or chemically bonded to the oxide backbone of the gels. These results demonstrate the feasibility of permanently poled doped sol-gel matrices. Moreover, EFISH measurements performed on organic molecules appear to be a useful tool for monitoring the changes occurring during sol-gel transformations.     

Influence of feeding schedules on the chronobiology of renin activity,urinary electrolytes and blood pressure in dogs

The contribution of the renin–angiotensin–aldosterone system (RAAS) to the development of congestive heart failure (CHF) and hypertension (HT) has long been recognized. Medications that are commonly used in the course of CHF and HT are most often given with morning food for the sake of convenience and therapeutic compliance. However, biological rhythms and their responsiveness to environmental clues such as food intake may noticeably impact the effectiveness of drugs used in the management of cardiovascular disorders. Only sparse information about the effect of feeding schedules on the biology of the RAAS and blood pressure (BP) is presently available. Two studies were designed to explore the chronobiology of renin activity (RA), BP, renal sodium (U_Na,fe) and potassium (U_K,fe) handling in relation to meal timing in dogs. In a first experiment (Study a), blood and urinary samples for measurement of RA, U_Na,fe and U_K,fe were drawn from 18 healthy beagle dogs fed a normal-sodium diet at either 07:00, 13:00 or 19:00?h. In a second experiment (Study b), BP was recorded continuously from six healthy, telemetered beagle dogs fed a similar diet at 07:00, or 19:00?h. Data were collected throughout 24-h time periods, and analyzed by means of nonlinear mixed-effects models. Differences between the geometric means of early versus late time after feeding observations were further compared using parametric statistics. In agreement with our previous investigations, the results indicate that RA, U_Na,fe, U_K,fe, systolic, and diastolic BP oscillate with a circadian periodicity in dogs fed a regular diet at 07:00?h. A cosine model with a fixed 24-h period was found to fit the variations of RA, U_K,fe and BP well, whereas cyclic changes in U_Na,fe were best characterized by means of a combined cosine and surge model, reflecting a postprandial sodium excretion followed by a monotonous decay. Our data show that feeding time has a marked influence on the chronobiology of the renin cascade, urinary electrolytes, and BP. Introducing a 6- or 12-h delay in the dogs’ feeding schedule caused a shift of similar magnitude (05:06 and 12:32?h for Studies a and b, respectively) in the rhythm of these biomarkers. In all study groups, RA and BP exhibited a marked fall just after food intake. The drop in RA is consistent with sodium and water-induced body fluid expansion, while the reduction of BP could be related to the decreased activity of renin and the secretion of vasodilatory gut peptides. An approximately 1.5-fold (1.2–1.6-fold) change between the average early and late time after feeding observations was found for RA (p?<?0.0001), U_Na,fe (p?<?0.01) and U_K,fe (p?<?0.05). Postprandial variations in BP, albeit small (ca. 10?mmHg), were statistically significant (p?<?0.01) and supported by the model-based analysis.

In conclusion, the timing of food intake appears to be pivotal to the circadian organization of the renin cascade and BP. This synchronizing effect could be mediated by feeding-related signals, such as dietary sodium, capable of entraining circadian oscillators downstream of the master, light–dark-adjusted pacemaker in the suprachiasmatic nucleus.     

A Nonadiabatic Theory for Ultrafast Catalytic Electron Transfer: A Model for the Photosynthetic Reaction Center

A non-adiabatic theory of Electron Transfer (ET), which improves the standard theory near the inversion point and becomes equivalent to it far from the inversion point, is presented. The complex amplitudes of the electronic wavefunctions at different sites are used as Kramers variables for describing the quantum tunneling of the electron in the deformable potential generated by its environment (nonadiabaticity) which is modeled as a harmonic classical thermal bath. After exact elimination of the bath, the effective electron dynamics is described by a discrete nonlinear Schrödinger equation with norm preserving dissipative terms and a Langevin random force, with a frequency cut-off, due to the thermalized phonons. This theory reveals the existence of a specially interesting marginal case when the linear and nonlinear coefficients of a two electronic states system are appropriately tuned for forming a Coherent Electron-Phonon Oscillator (CEPO). An electron injected on one of the electronic states of a CEPO generates large amplitude charge oscillations (even at zero temperature) associated with coherent phonon oscillations and electronic level oscillations. This fluctuating electronic level may resonate with a third site which captures the electron so that Ultrafast Electron Transfer (UFET) becomes possible. Numerical results are shown where two weakly interacting sites, a donor and a catalyst, form a CEPO that triggers an UFET to an acceptor. Without a catalytic site, a very large energy barrier prevents any direct ET. This UFET is shown to have many qualitative features similar to those observed in the primary charge separation in photosynthetic reaction centers. We suggest that more generally, CEPO could be a paradigm for understanding many selective chemical reactions involving electron transfer in biosystems.     

Finite Element Analysis of Tibial Implants — Effect of Fixation Design and Friction Model

Abstract

A three dimensional nonlinear finite element model was developed to investigate tibial fixation designs and friction models (Coulomb's vs nonlinear) in total knee arthroplasty in the immediate postoperative period with no biological attachment. Bi-directional measurement-based nonlinear friction constitutive equations were used for the bone-porous coated implant interface. Friction properties between the polyethylene and femoral components were measured for this study. Linear elastic isotropic but heterogeneous mechanical properties taken from literature were considered for the bone. The Tensile behaviour of polyethylene was measured and subsequently modeled by an elasto-plastic model. Based on the earlier finite element and experimental pull-out studies, pegs and screws were also realistically modeled. The geometry of every component was obtained through measurement. The PCA tibial baseplate with three different configurations was considered; one with three screws, one with one screw and two short inclined porous-coated pegs, and a third one with no fixation for the sake of comparison. The axial load of 2000N was applied through the femoral component on the medial plateau of articular insert. It was found that Coulomb's friction significantly underestimates the relative micromotion at the bone-implant interface. The lowest micromotion and lift-off were found for the design with screws. Relative micromotion and stress transfer at the bone-implant interface depended significantly on the friction model and on the baseplate anchorage configuration. Cortical and cancellous bones carried, respectively, 10–13% and 65–86% of the axial load depending on the fixation configuration used. The remaining portion was transmitted as shear force by screws and pegs. Normal and Mises stresses as well as contact area in the polyethylene insert were nearly independent of the baseplate fixation design. The Maximum Mises stress in the polyethylene exceeded yield and was found 1–2 mm below the contact surface for all designs.