Influence of the conservative force on transport coefficients in the DPD method

The transport coefficients of a dissipative particle dynamics system are investigated numerically taking into account the conservative force. The influence of the conservative force parameter on kinetic and dissipative viscosity is considered and compared with theoretical predictions. The analytical solution of the potential term that arises from the conservative force is generally very complicated; therefore, this term has been ignored in most previous work and deemed negligible. In the present work, an expression for the effect of the conservative force on potential viscosity is semi-empirically obtained revealing the dependence of the latter on various parameters such as conservative force strength, density number and temperature. This relation offers a proper approximation of conservative force impact on potential viscosity.     

Mechanics of the tapered interference fit in dental implants

In evaluation of the long-term success of a dental implant, the reliability and the stability of the implant-abutment interface plays a great role. Tapered interference fits provide a reliable connection method between the abutment and the implant. In this work, the mechanics of the tapered interference fits were analyzed using a closed-form formula and the finite element (FE) method. An analytical solution, which is used to predict the contact pressure in a straight interference, was modified to predict the contact pressure in the tapered implant-abutment interface. Elastic-plastic FE analysis was used to simulate the implant and abutment material behavior. The validity and the applicability of the analytical solution were investigated by comparisons with the FE model for a range of problem parameters. It was shown that the analytical solution could be used to determine the pull-out force and loosening-torque with 5-10% error. Detailed analysis of the stress distribution due to tapered interference fit, in a commercially available, abutment-implant system was carried out. This analysis shows that plastic deformation in the implant limits the increase in the pull-out force that would have been otherwise predicted by higher interference values.     

Uncovering the Fate of Critical Metals: Tracking Dissipative Losses along the Product Life Cycle

An increasing number of elements from the periodic table are being used in a growing number of products, enabling new material and product functionalities. Materials of high importance and high supply risks are usually referred to as critical materials. Many materials that are often considered critical are used in ways leading to their dissipative loss along the product life cycle. So far, the issue of material dissipation has been dealt with mainly on a rather aggregated level. Detailed knowledge on the occurrence and amount of dissipative losses in the life cycle of specific products is only scarcely available. Addressing this, a substance flow analysis of different critical metals along the life cycle of selected products is presented in this article. With regard to products used in Germany, the flows of indium and gallium used in copper‐indium‐gallium‐selenide (CIGS) photovoltaic cells, germanium used in polymerization catalysts, and yttrium used in thermal barrier coatings (TBCs) have been analyzed. The results comprise detailed knowledge about the life cycle stages in which dissipative losses occur and about the receiving media. In all case studies, a complete or almost complete dissipative loss can be observed, mainly to landfills and other material flows. In all case studies, material production can be identified as hotspots for dissipative losses. In two case studies fabrication and manufacturing (F&M for CIGS and TBCs) and in one case study end of life (polymerization catalysts) can be identified as further hotspots for dissipative losses. In addition, actions for reducing dissipation along the life cycle are discussed, targeting aspects such as the recovery of critical metals as by‐products, efficiency in F&M processes, and lack of recycling processes. Lack of economic incentives to apply more‐efficient technologies and processes already available is a key aspect in this regard.     

Motionless dissipative structures formed by soil bacteria

A model of the stationary distribution of bacteria in soil, formed upon filtration of soil solution was constructed. The region of parameter values was determined at which the distribution is dissipative and has the form of alternating strips. Regularities in the degeneration of the dissipative structure as the parameters approach the boundary of the region were discovered. The analysis was made using qualitative, analytical and quantitative investigation of differential equations of the transfer. Data on the growth, nourishment, and death of copiotrophic bacteria were used in the calculations.     

CORGEN: A FORTRAN-77 generator of standard and non-standard DNA helices from the sequence

An analytical procedure CORGEN generates a variety of DNA double-strandedstructures from user-supplied sequence using a nucleic aciddatabase incorporated into a standard FORTRAN-77 program. Alternatively,the cylindrical polar coordinates of DNA components may be suppliedfrom the external table. An algorithm that performs intercalationsites in DNA is described. This procedure can be used to generatecomplexes of antibiotics with DNA. Non-standard DNA structurescan be built by alternating the global helical twist and globalhelical rise in the regular DNA helix. The procedures describedcan be used for computer generation of a variety of non-standardDNA structures which can be subjected to molecular mechanicsand dynamics simulations. Received on February 20, 1989; accepted on June 27, 1989     

Spatio-temporal structure of migrating chemotactic band of Escherichia coli. I. Traveling band profile.

We developed a rapid-scanning, light-scattering densitometer by which extensive measurements of band migration speeds and band profiles of chemotactic bands of Escherichia coli in motility buffer both with and without serine have been made. The purpose is to test the applicability of the phenomenological model proposed by Keller and Segel (J. Theor. Biol. 1971. 30:235) and to determine the motility (mu) and chemotactic (delta) coefficients of the bacteria. We extend the previous analytical solution of the simplified Keller-Segel model by taking into account the substrate diffusion which turns out to be significant in the case of oxygen. We demonstrate that unique sets of values of mu and delta can be obtained for various samples at different stages of migration by comparing the numerical solution of the model equation and the experimental data. The rapid-scanning technique also reveals a hitherto unobserved time-dependent fine structure in the bacterial band. We give a qualitative argument to show that the fine structure is an example of the dissipative structure that arises from a nonlinear coupling between the bacterial density and the oxygen concentration gradient. Implications for a further study of the dissipative structure in testing the Keller-Segel model of chemotaxis are briefly discussed.     

Observations on the hydrodynamics and swimming motions of mammalian spermatozoa

An asymptotic solution of the Stokes Flow equations for a self-propelling filament is presented. An explicit expression for the propulsive velocity is obtained for the case of an infinite filament undergoing small amplitude sinusoidal motions. The asymptotic solution is then used to obtain drag coefficients to be used in a simpler approximate analysis which can be applied to experimentally observed motions.     

Elastic properties of an intact and ACL-ruptured knee joint: measurement, mathematical modelling, and haptic rendering

An analytical, dynamic model of the human knee joint has been developed to simulate the unloaded knee joint behaviour in 6 degrees of freedom. It is based on extensive robot-based measurements of the elastic properties of a human cadaver knee joint. The measured data are compared with data from the literature to ensure that a proper database for modelling is used. The analytical modelling of the passive elastic joint properties is done with Local Linear Model Trees. The deduced knee joint model incorporates passive elastic properties of the internal knee joint structures, passive elastic muscle forces, damping forces, gravitational forces, and external forces. There are two sets of parameters, one simulating the movement of the intact knee joint, and a second simulating the knee joint with ruptured anterior cruciate ligament. The dynamic model can be easily processed in real-time. It is implemented in the haptic display of the Munich Knee Joint Simulator (MKS), which enables a person to move a plastic leg driven by a robot manipulator and feel the simulated knee joint force. Orthopaedic physicians judged the performance of the dynamic knee joint model by executing physical knee joint tests at the MKS.     

NMR spin exchange kinetics at equilibrium in membrane transport and enzyme systems

A set of differential equations is formulated to describe the rapid exchange (time scale, approximately 0.01 to approximately 10 s) of a labelled solute across the membranes of cells in suspension. The labelling is achieved with nuclear magnetic resonance by exposure of the system to a high intensity radio-frequency pulse, and the excited nuclei relax to the equilibrium state with a short half life. An analytical expression for the decay of the magnetic resonance signal is presented; the solution involves the determination of eigenvalues, of an array of Laplace-Carson transformed differential equations, by use of the general solution of a quartic polynomial. Simulations of the behaviour of the exchange system using various conditions of cell number, rate constants and nuclear magnetic relaxation times are presented. The marked concentration dependence of the extent of reaction at a given time has not previously been reported for nuclear magnetic resonance exchange systems and is a feature anticipated from the known saturability of several membrane transport systems including glucose transport into human erythrocytes. The theory is readily generalized to other model systems by appropriate reinterpretation of the physical meaning of various parameters; the general form of the solution holds in many biological contexts other than membrane transport and includes equilibrium enzyme kinetics.     

Description and error evaluation of an in vitro knee joint testing system

An experimental system for the analysis of knee joint biomechanics is presented. The system provides for the simultaneous recording of ligament forces using buckle transducers and three-dimensional joint motion using an instrumented spatial linkage, as in vitro specimens are subjected to a variety of external loads by a pneumatic loading apparatus with associated force transducers. The system components are described, and results of an evaluation of system errors and accuracy are presented. The experimental setup has been successfully used in the analysis of normal knee ligament mechanics, as well as surgical reconstructions of the anterior cruciate ligament. The system can also be adapted to test other human or animal in vitro joints.     

Analysis of a diffusion-limited hollow fiber reactor for the measurement of effective substrate diffusivities

Mathematical analyses of a diffusion-limited hollow fiber reactor for the measurement of effective substrate diffusivities are presented. An analytical solution to the mathematical model with a first order substrate consumption rate is used to show that the procedure of Webster and Shuler(1) is incorrect. A rigorous analysis that requires numerical solution is also outlined for any form of the substrate consumption rate. These analyses allow for more accurate estimations of effective substrate diffusivities since they should be used in conjunction with integral reactor behavior.     

Loss of control biomechanics of the human arm-elbow system

An experimental study was conducted to determine whether external disturbance oscillations, such as those that could be created by hand held tools, alter the dynamic response characteristics of the human arm-muscle system. A special arm-test frame was used to induce external sinusoidal torque oscillations of various amplitudes and frequencies, while the reaction force and angular displacement were monitored. Two different output variable frequency responses were determined using input/output cross-spectrum analysis. The angular displacement of the test frame and a component of hand reaction force were the output variables used, while the test frame torque was the input. Test results from one subject are presented in this paper. Changes in the magnitude and phase angle of the frequency responses were observed for different frequencies of the disturbance torque. These changes indicate that the stability margin and response amplitude of the human arm-muscle system do change as a function of the frequency and amplitude of external disturbance oscillations. This suggests that at certain operating frequencies hand held tools can induce large reaction amplitudes or even loss of control.     

The primate median eminence

A pressure device has been used to obtain information about the forces involved in the maintenance of the aggregated state of melanophores of the angelfish, Pterophyllum scalare. Single aggregated melanophores of isolated scales were submitted to mechanical compression with forces ranging from 50-320 mup. As a function of the gradually increasing force melanophores disperse their pigment, the degree of dispersion being proportional to the intensity of the force. When microtubules are destroyed by treatment with 0.3 mM vinblastine in KCl solution, pigment dispersion in response to the external force is similar to that observed in KCl alone. After changing the medium to NaCl solution, melanin granules remain concentrated in the cell center; the force-induced melanosome dispersion, however, is significantly enhanced. Distinctly lower forces are required to produce an expansion equivalent to that observed in KCl solution. When the medium is changed to vinblastine-KCl again, the dispersion in response to the external force resembles that obtained before NaCl treatment. Removal of Ca++ and Mg++ ions by treatment with 2 mM EDTA or EGTA in Ringer's solution containing 0.1 mM adrenalin produces a remarkable enhancement of melanosome dispersion in response to increasing external force. This effect of EDTA or EGTA is completely reversible. When the medium is changed to normal Ca++-Ringer's, the force/dispersion curve resembles that obtained before EDTA or EGTA treatment. It is concluded that a state of equilibrium exists between the external force and an opposing force produced by the melanophore. The differences in the opposing force under different experimental conditions may be due to a "contractile component". This component seems to be independent of microtubules, as indicated by vinblastine experiments. It "contracts" under aggregating stimulus and "relaxes" under dispersing stimulus. From the data presented in this paper, the order of magnitude of the pressure developed by the contractile component in the completely aggregated state was calculated as between 5-7 p/cm2 in the relaxed state and about 20 p/cm2 during contraction. These values are comparable to those observed in other nonmuscular cells.     

Mass spectrometric approaches using electrospray ionization charge states and hydrogen-deuterium exchange for determining protein structures and their conformational changes

Electrospray ionization (ESI) mass spectrometry (MS) is a powerful analytical tool for elucidating structural details of proteins in solution especially when coupled with amide hydrogen/deuterium (H/D) exchange analysis. ESI charge-state distributions and the envelopes of charges they form from proteins can provide an abundance of information on solution conformations that is not readily available through other biophysical techniques such as near ultraviolet circular dichroism (CD) and tryptophan fluorescence. The most compelling reason for the use of ESI-MS over nuclear magnetic resonance (NMR) for measuring H/D after exchange is that larger proteins and lesser amounts of samples can be studied. In addition, MS can provide structural details on transient or folding intermediates that may not be accessible by CD, fluorescence, and NMR because these techniques measure the average properties of large populations of proteins in solution. Correlations between measured H/D and calculated parameters that are often available from crystallographic data can be used to extend the range of structural details obtained on proteins. Molecular dynamics and energy minimization by simulation techniques such as assisted model building with energy refinement (AMBER) force field can be very useful in providing structural models of proteins that rationalize the experimental H/D exchange results. Charge-state envelopes and H/D exchange information from ESI-MS data used complementarily with NMR and CD data provides the most powerful approach available to understanding the structures and dynamics of proteins in solution.     

A Mathematical Model of the Human Circadian System and Its Application to Jet Lag

A mathematical model of the circadian system is described that is appropriate for application to jet lag. The core of the model is a van der Pol equation with an external force. Approximate solutions of this equation in which the external force is composed of a constant and an oscillating term are investigated. They lead to analytical expressions for the amplitude and period of free-running rhythms and for the frequency limits of the entrainment region. The free-running period increases quadratically with stiffness. Both period and amplitude depend on the value of the constant external force. The width of the range of entrainment is mostly determined by the external force, whereas the relative position of this range follows the intrinsic period of the oscillator. Experiments with forced and spontaneous internal desynchronization were evaluated using these analytical expressions, and estimates were obtained for the intrinsic period of the oscillator, its stiffness, and the external force. A knowledge of these model parameters is essential for predictions about circadian dynamics, and there are practical implications for the assessment of the adaptation after rapid transmeridian travel.     

A Mathematical Model of the Human Circadian System and Its Application to Jet Lag

A mathematical model of the circadian system is described that is appropriate for application to jet lag. The core of the model is a van der Pol equation with an external force. Approximate solutions of this equation in which the external force is composed of a constant and an oscillating term are investigated. They lead to analytical expressions for the amplitude and period of free-running rhythms and for the frequency limits of the entrainment region. The free-running period increases quadratically with stiffness. Both period and amplitude depend on the value of the constant external force. The width of the range of entrainment is mostly determined by the external force, whereas the relative position of this range follows the intrinsic period of the oscillator. Experiments with forced and spontaneous internal desynchronization were evaluated using these analytical expressions, and estimates were obtained for the intrinsic period of the oscillator, its stiffness, and the external force. A knowledge of these model parameters is essential for predictions about circadian dynamics, and there are practical implications for the assessment of the adaptation after rapid transmeridian travel.     

Catch-Bond Behavior of Bacteria Binding by Slip Bonds

It is shown that multipili-adhering bacteria expressing helix-like pili binding by slip bonds can show catch-bond behavior. When exposed to an external force, such bacteria can mediate adhesion to their hosts by either of two limiting means: sequential or simultaneous pili force exposure (referring to when the pili mediate force in a sequential or simultaneous manner, respectively). As the force is increased, the pili can transition from sequential to simultaneous pili force exposure. Since the latter mode of adhesion gives rise to a significantly longer bacterial adhesion lifetime than the former, this results in a prolongation of the lifetime, which shows up as a catch-bond behavior. The properties and conditions of this effect were theoretically investigated and assessed in some detail for dual-pili-adhering bacteria, by both analytical means and simulations. The results indicate that the adhesion lifetime of such bacteria can be prolonged by more than an order of magnitude. This implies that the adhesion properties of multibinding systems cannot be directly conveyed to the individual adhesion-receptor bonds.     

Quantitation of the förster energy transfer for two-dimensional systems: I. Lateral phase separation in unilamellar vesicles formed by binary phospholipid mixtures

An analytical solution is presented for the rate of energy transfer in unilamellar vesicles formed by binary mixtures of phospholipids showing lateral phase separation. The analytical approach developed here is mainly based on geometrical considerations and therefore, is formally different for lateral phase separation phenomena taking place in the gel and in the liquid crystalline states of the lipid system. The rate of energy transfer among donor and acceptor molecules attached to chemically different phospholipids is mathematically correlated to the average cluster size of the less-rich component of the binary mixture, thus allowing its calculation from experimental measurements. Moreover, the equations derived here permit the calculation of the average cluster size as a function of the concentration of each lipid component within certain ranges, and this can be used to improve our knowledge of the thermodynamics of these processes.     

Protein tagging and detection with engineered self-assembling fragments of green fluorescent protein

Existing protein tagging and detection methods are powerful but have drawbacks. Split protein tags can perturb protein solubility or may not work in living cells. Green fluorescent protein (GFP) fusions can misfold or exhibit altered processing. Fluorogenic biarsenical FLaSH or ReASH substrates overcome many of these limitations but require a polycysteine tag motif, a reducing environment and cell transfection or permeabilization. An ideal protein tag would be genetically encoded, would work both in vivo and in vitro, would provide a sensitive analytical signal and would not require external chemical reagents or substrates. One way to accomplish this might be with a split GFP, but the GFP fragments reported thus far are large and fold poorly, require chemical ligation or fused interacting partners to force their association, or require coexpression or co-refolding to produce detectable folded and fluorescent GFP. We have engineered soluble, self-associating fragments of GFP that can be used to tag and detect either soluble or insoluble proteins in living cells or cell lysates. The split GFP system is simple and does not change fusion protein solubility.     

Dynamics of the Coiled-Coil Unfolding Transition of Myosin Rod Probed by Dissipation Force Spectrum

The motor protein myosin II plays a crucial role in muscle contraction. The mechanical properties of its coiled-coil region, the myosin rod, are important for effective force transduction during muscle function. Previous studies have investigated the static elastic response of the myosin rod. However, analogous to the study of macroscopic complex fluids, how myosin will respond to physiological time-dependent loads can only be understood from its viscoelastic response. Here, we apply atomic force microscopy using a magnetically driven oscillating cantilever to measure the dissipative properties of single myosin rods that provide unique dynamical information about the coiled-coil structure as a function of force. We find that the friction constant of the single myosin rod has a highly nontrivial variation with force; in particular, the single-molecule friction constant is reduced dramatically and increases again as it passes through the coiled-uncoiled transition. This is a direct indication of a large free-energy barrier to uncoiling, which may be related to a fine-tuned dynamic mechanosignaling response to large and unexpected physiological loads. Further, from the critical force at which the minimum in friction occurs we determine the asymmetry of the bistable landscape that controls uncoiling of the coiled coil. This work highlights the sensitivity of the dissipative signal in force unfolding to dynamic molecular structure that is hidden to the elastic signal.