Diffusing proteins on a fluctuating membrane: Analytical theory and simulations

Using analytical calculations and computer simulations we consider both the lateral diffusion of a membrane protein and the fluctuation spectrum of the membrane in which the protein is embedded. The membrane protein interacts with the membrane shape through its spontaneous curvature and bending rigidity. The lateral motion of the protein may be viewed as diffusion in an effective potential, hence, the effective mobility is always reduced compared to the case of free diffusion. Using a rigorous path-integral approach we derive an analytical expression for the effective diffusion coefficient for small ratios of temperature and bending rigidity, which is the biologically relevant limit. Simulations show very good quantitative agreement with our analytical result. The analysis of the correlation functions contributing to the diffusion coefficient shows that the correlations between the stochastic force of the protein and the response in the membrane shape are responsible for the reduction. Our quantitative analysis of the membrane height correlation spectrum shows an influence of the protein-membrane interaction causing a distinctly altered wave-vector dependence compared to a free membrane. Furthermore, the time correlations exhibit the two relevant timescales of the system: that of membrane fluctuations and that of lateral protein diffusion with the latter typically much longer than the former. We argue that the analysis of the long-time decay of membrane height correlations can thus provide a new means to determine the effective diffusion coefficient of proteins in the membrane.Comment: 12 pages, 8 figure

Lateral diffusion of a protein on a fluctuating membrane

Measurements of lateral diffusion of proteins in a membrane typically assume that the movement of the protein occurs in a flat plane. Real membranes, however, are subject to thermal fluctuations, leading to movement of an inclusion into the third dimension. We calculate the magnitude of this effect by projecting real three-dimensional diffusion onto an effective one on a flat plane. We consider both a protein that is free to diffuse in the membrane and one that also couples to the local curvature. For a freely diffusing inclusion the measured projected diffusion constant is up to 15% smaller than the actual value. Coupling to the curvature enhances diffusion significantly up to a factor of two.Comment: 6 pages, 4 figure

Diffusion of active tracers in fluctuating fields

The problem of a particle diffusion in a fluctuating scalar field is studied. In contrast to most studies of advection diffusion in random fields we analyze the case where the particle position is also coupled to the dynamics of the field. Physical realizations of this problem are numerous and range from the diffusion of proteins in fluctuating membranes and the diffusion of localized magnetic fields in spin systems. We present exact results for the diffusion constant of particles diffusing in dynamical Gaussian fields in the adiabatic limit where the field evolution is much faster than the particle diffusion. In addition we compute the diffusion constant perturbatively, in the weak coupling limit where the interaction of the particle with the field is small, using a Kubo-type relation. Finally we construct a simple toy model which can be solved exactly.Comment: 13 pages, 1 figur

Hybrid simulations of lateral diffusion in fluctuating membranes

In this paper we introduce a novel method to simulate lateral diffusion of inclusions in a fluctuating membrane. The regarded systems are governed by two dynamic processes: the height fluctuations of the membrane and the diffusion of the inclusion along the membrane. While membrane fluctuations can be expressed in terms of a dynamic equation which follows from the Helfrich Hamiltonian, the dynamics of the diffusing particle is described by a Langevin or Smoluchowski equation. In the latter equations, the curvature of the surface needs to be accounted for, which makes particle diffusion a function of membrane fluctuations. In our scheme these coupled dynamic equations, the membrane equation and the Langevin equation for the particle, are numerically integrated to simulate diffusion in a membrane. The simulations are used to study the ratio of the diffusion coefficient projected on a flat plane and the intramembrane diffusion coefficient for the case of free diffusion. We compare our results with recent analytical results that employ a preaveraging approximation and analyze the validity of this approximation. A detailed simulation study of the relevant correlation functions reveals a surprisingly large range where the approximation is applicable.Comment: 12 pages, 9 figures, accepted for publication in Phys. Rev.

Brownian motion meets Riemann curvature

The general covariance of the diffusion equation is exploited in order to explore the curvature effects appearing on brownian motion over a d-dimensional curved manifold. We use the local frame defined by the so called Riemann normal coordinates to derive a general formula for the mean-square geodesic distance (MSD) at the short-time regime. This formula is written in terms of $O(d)$ invariants that depend on the Riemann curvature tensor. We study the n-dimensional sphere case to validate these results. We also show that the diffusion for positive constant curvature is slower than the diffusion in a plane space, while the diffusion for negative constant curvature turns out to be faster. Finally the two-dimensional case is emphasized, as it is relevant for the single particle diffusion on biomembranes.Comment: 16 pages and 3 figure

Reducing preventable adverse events in obstetrics by improving interprofessional communication skills - Results of an intervention study.

BACKGROUND: Progress in medicine involves the structured analysis and communication of errors. Comparability between the individual disciplines is only possible to a limited extent and obstetrics plays a special role: the expectation of a self-determined and joyful event meets with possibly serious complications in highly complex care situations. This must be managed by an interdisciplinary team with an increasingly condensed workload. Adverse events cannot be completely controlled. However, taking controllable risk factors into account and with a focused communication a reduction of preventable adverse events is possible. In the present study, the effect of interprofessional team training on preventable adverse events in an obstetric department was investigated. METHODS: The training consisted of a 4-h interdisciplinary training session based on psychological theories. Preventable adverse events were defined in six categories according to potential patterns of causation. 2,865 case records of a refence year (2018) and 2,846 case records of the year after the intervention (2020) were retrospectively evaluated. To determine the communication training effect, the identified preventable adverse events of 2018 and 2020 were compared according to categories and analyzed for obstetrically relevant controllable and uncontrollable risk factors. Questionnaires were used to identify improvements in self-reported perceptions and behaviors. RESULTS: The results show that preventable adverse events in obstetrics were significantly reduced after the intervention compared to the reference year before the intervention (13.35% in the year 2018 vs. 8.83% in 2020, p < 0.005). Moreover, obstetrically controllable risk factors show a significant reduction in the year after the communication training. The questionnaires revealed an increase in perceived patient safety (t(28) = 4.09, p < .001), perceived communication behavior (t(30) = -2.95, p = .006), and self-efficacy to cope with difficult situations (t(28) = -2.64, p = .013). CONCLUSIONS: This study shows that the communication training was able to reduce preventable adverse events and thus increase patient safety. In the future, regular trainings should be implemented alongside medical emergency trainings in obstetrics to improve patient safety. Additionally, this leads to the strengthening of human factors and ultimately also to the prevention of second victims. Further research should follow up implementing active control groups and a randomized-controlled trail study design. TRIAL REGISTRATION: The study was approved by the Ethics Committee of University Hospital  (protocol code 114/19-FSt/Sta, date of approval 29 May 2019), study registration: NCT03855735

Curvature-coupling dependence of membrane protein diffusion coefficients

We consider the lateral diffusion of a protein interacting with the curvature of the membrane. The interaction energy is minimized if the particle is at a membrane position with a certain curvature that agrees with the spontaneous curvature of the particle. We employ stochastic simulations that take into account both the thermal fluctuations of the membrane and the diffusive behavior of the particle. In this study we neglect the influence of the particle on the membrane dynamics, thus the membrane dynamics agrees with that of a freely fluctuating membrane. Overall, we find that this curvature-coupling substantially enhances the diffusion coefficient. We compare the ratio of the projected or measured diffusion coefficient and the free intramembrane diffusion coefficient, which is a parameter of the simulations, with analytical results that rely on several approximations. We find that the simulations always lead to a somewhat smaller diffusion coefficient than our analytical approach. A detailed study of the correlations of the forces acting on the particle indicates that the diffusing inclusion tries to follow favorable positions on the membrane, such that forces along the trajectory are on average smaller than they would be for random particle positions.Comment: 16 pages, 8 figure

A Game-Based Learning Application to Help Learners to Practice Mathematical Patterns and Structures

Purpose: The purpose of this study is to develop a game-based mobile application to help learners practice mathematical patterns and structures. Method: The study followed a mixed-method research design and prototyping methodology to guide the study in developing the mobile application. An instrument based on the Octalysis framework was developed as an evaluation tool for the study. Results: The study developed a mobile application based on the Octalysis framework. The application has fully achieved all its intended features based on the rating provided by the students and IT experts. Conclusion: The study successfully developed a mobile learning application for mathematical patterns and structures. By incorporating GBL principles and the Octalysis framework, the app achieved its intended features and received positive evaluations from students and IT experts. This highlights the potential of the app in promoting mathematical learning. Recommendations: This study recommends that the application be further enhanced to include other topics. Incorporating other game-based principles and approaches like timed questions and the difficulty level is also worth pursuing. Actual testing for end-users is also needed to verify the application's effectiveness. Practical Implications: Successful development of a game-based mobile app for practicing mathematical patterns and structures can transform education technology by engaging learners and enhancing their experience. This study provides valuable insights for future researchers developing similar applications, highlighting the potential to revolutionize traditional approaches and create an interactive learning environment for improving mathematical abilities

Experimental investigations of sensor-based surface following performed by a mobile manipulator

We discuss a series of surface following experiments using a range finder mounted on the end of an arm that is mounted on a vehicle. The goal is to keep the range finder at a fixed distance from an unknown surface and to keep the orientation of the range finder perpendicular to the surface. During the experiments, the vehicle moves along a predefined trajectory while planning software determines the position and orientation of the arm. To keep the range finder perpendicular to the surface, the planning software calculates the surface normal for the unknown surface. We assume that the unknown surface is a cylinder (the surface depends on x and y but does not depend on z). To calculate the surface normal, the planning software must calculate the locations (x,y) of points on the surface in world coordinates. The calculation requires data on the position and orientation of the vehicle, the position and orientation of the arm, and the distance from the range finder to the surface. We discuss four series of experiments. During the first series of experiments, the calculated surface normal values had large high frequency random variations. A filter was used to produce an average value for the surface normal and we limited the rate of change in the yaw angle target for the arm. We performed the experiment for a variety of concave and convex surfaces. While the experiments were qualitative successes, the measured distance to the surface was significantly different than the target. The distance errors were systematic, low frequency, and had magnitudes up to 25 mm. During the second series of experiments, we reduced the variations in the calculated surface normal values. While reviewing the data collected while following the surface of a barrel, we found that the radius of the calculated surface was significantly different than the measured radius of the barrel

Электропривод клиновой задвижки, на основе ТРН-АД

В работе проведены исследования динамических режимов работы асинхронного электропривода клиновой задвижки. В процессе работы проводилось моделирование переходных процессов асинхронного двигателя в программной среде MATLAB Simulink. В результате работы была смоделирована система "тиристорный регулятор напряжения – асинхронный двигатель", реализованы режимы пуска и динамического торможения и проанализированы графики переходных процессов. Исследуемая система используется в качестве электропривода клиновой задвижки, устанавливаемой на магистральном нефтепроводе. Экономическая эффективность заключается в значительном повышении ресурса механизма и электрической части электропривода.In the work, the dynamic modes of operation of an asynchronous electric drive of a wedge gate valve are investigated. In the process of work, modeling of transient processes of an induction motor in the MATLAB Simulink software environment was carried out. As a result of the work, the system "thyristor voltage regulator - asynchronous motor" was simulated, the startup and dynamic braking modes were realized and the transient graphs were analyzed. The system under investigation is used as an electric drive of a wedge gate valve installed on a main oil pipeline. Economic efficiency consists in a significant increase in the life of the mechanism and the electrical part of the electric drive