Kinetic Trajectories Research Articles

Kinetic Trajectories of Glucose Uptake in Single Cancer Cells Reveal a Drug-Induced Cell-State Change Within Hours of Drug Treatment.

The development of drug resistance is a nearly universal phenomenon in patients with glioblastoma multiforme (GBM) brain tumors. Upon treatment, GBM cancer cells may initially undergo a drug-induced cell-state change to a drug-tolerant, slow-cycling state. The kinetics of that process are not well understood, in part due to the heterogeneity of GBM tumors and tumor models, which can confound the interpretation of kinetic data. Here, we resolve drug-adaptation kinetics in a patient-derived in vitro GBM tumor model characterized by the epithelial growth factor receptor (EGFR) variant(v)III oncogene treated with an EGFR inhibitor. We use radiolabeled 18F-fluorodeoxyglucose (FDG) to monitor the glucose uptake trajectories of single GBM cancer cells over a 12 h period of drug treatment. Autocorrelation analysis of the single-cell glucose uptake trajectories reveals evidence of a drug-induced cell-state change from a high- to low-glycolytic phenotype after 5-7 h of drug treatment. Information theoretic analysis of a bulk transcriptome kinetic series of the GBM tumor model delineated the underlying molecular mechanisms driving the cellular state change, including a shift from a stem-like mesenchymal state to a more differentiated, slow-cycling astrocyte-like state. Our results demonstrate that complex drug-induced cancer cell-state changes of cancer cells can be captured via measurements of single cell metabolic trajectories and reveal the extremely facile nature of drug adaptation.

Reconstruction of proximal hamstring ruptures restores joint biomechanics during various walking conditions.

We aimed to examine the functional outcome in different walking conditions in elderly adults who underwent surgical repair after a non-contact hamstring injury. Our objective was to compare lower limb kinematics and kinetics over the entire gait cycle between the injured and contralateral leg in overground and level and uphill treadmill walking. 12 patients (mean ± SD, age: 65 ± 9 years; body mass index: 30 ± 6 kg/m2) walked at self-selected speed in overground (0% slope) and treadmill conditions (0% and 10% slope). We measured spatiotemporal parameters, joint angles (normalised to gait cycle) and joint moments (normalised to stance phase) of the hip, knee and ankle. Data between sides were compared using paired sample t-tests (p < 0.05) and continuous 95% confidence intervals of the paired difference between trajectories. Patients walked at an average speed of 1.31 ± 0.26 m/second overground and 0.92 ± 0.31 m/second on the treadmill. Spatiotemporal parameters were comparable between the injured and contralateral leg (p > 0.05). Joint kinematic and joint kinetic trajectories were comparable between sides for all walking conditions. Refixation of the proximal hamstring tendons resulted in comparable ambulatory mechanics at least 1 year after surgery in the injured leg and the contralateral leg, which were all within the range of normative values reported in the literature. These results complement our previous findings on hamstring repair in terms of clinical outcomes and muscle strength and support that surgical repair achieves good functional outcomes in terms of ambulation in an elderly population. clinicaltrials.gov (NCT04867746).

Acute effects of robot-assisted body weight unloading on biomechanical movement patterns during overground walking

Body weight unloading (BWU) is used in rehabilitation/training settings to reduce kinetic requirements, however different BWU methods may be unequally capable of preserving biomechanical movement patterns. Biomechanical analysis of both kinetic and kinematic movement trajectories rather than discrete variables has not previously been performed to describe the effect of BWU on gait patterns during horizontal walking. The aim of the present study was to investigate how robot-assisted BWU producing an dynamic unloading force on the body centre of mass, affects kinematic, kinetic, and spatiotemporal gait parameters in healthy young adults by use of time-continuous analysis. Twenty participants walked overground in a 3-D motion-capture lab at 0, 10, 20, 30, 40, and 50 % BWU at a self-selected speed. Vertical and anterior-posterior ground reaction forces (GRFs) and lower limb internal joint moments were obtained during the stance phase, while joint angles were obtained during entire strides. Time-continuous data were analysed using Statistical Parametric Mapping (SPM) and discrete data using conventional statistics to compare different BWU conditions by means of One-Way Repeated Measures Anova. With increasing BWU, corresponding reductions were observed for GRFs, internal joint moments, joint angles, walking speed, stride/step length and cadence. Observed effects were partially caused by decreased walking speed and increased BWU. While amplitude reductions were observed for kinetic and kinematic variables, trajectory shapes were largely preserved. In conclusion, dynamic robot-assisted BWU enables reduced kinetic requirements without distorting biomechanically normal gait patterns during overground walking in young healthy adults.

Identification of Motor Control Objectives in Human Locomotion via Multi-Objective Inverse Optimal Control

Abstract Predictive simulations of human motion are a precious resource for a deeper understanding of the motor control policies encoded by the central nervous system. They also have profound implications for the design and control of assistive and rehabilitation devices, for ergonomics, as well as for surgical planning. However, the potential of state-of-the-art predictive approaches is not fully realized yet, making it difficult to draw convincing conclusions about the actual optimality principles underlying human walking. In the present study, we propose a novel formulation of a bilevel, inverse optimal control strategy based on a full-body three-dimensional neuromusculoskeletal model. In the lower level, prediction of walking is formulated as a principled multi-objective optimal control problem based on a weighted Chebyshev metric, whereas the contributions of candidate control objectives are systematically and efficiently identified in the upper level. Our framework has proved to be effective in determining the contributions of the selected objectives and in reproducing salient features of human locomotion. Nonetheless, some deviations from the experimental kinematic and kinetic trajectories have emerged, suggesting directions for future research. The proposed framework can serve as an inverse optimal control platform for testing multiple optimality criteria, with the ultimate goal of learning the control objectives that best explain observed human motion.2

Finite-State Impedance and Direct Myoelectric Control for Robotic Ankle Prostheses: Comparing Their Performance and Exploring Their Combination.

Non-volitional control, such as finite-state machine (FSM) impedance control, does not directly incorporate user intent signals, while volitional control, like direct myoelectric control (DMC), relies on these signals. This paper compares the performance, capabilities, and perception of FSM impedance control to DMC on a robotic prosthesis for subjects with and without transtibial amputation. It then explores, using the same metrics, the feasibility and performance of the combination of FSM impedance control and DMC across the full gait cycle, termed Hybrid Volitional Control (HVC). After calibration and acclimation with each controller, subjects walked for two minutes, explored the control capabilities, and completed a questionnaire. FSM impedance control produced larger average peak torque (1.15 Nm/kg) and power (2.05 W/kg) than DMC (0.88 Nm/kg and 0.94 W/kg). The discrete FSM, however, caused non-standard kinetic and kinematic trajectories, while DMC yielded trajectories qualitatively more similar to able-bodied biomechanics. While walking with HVC, all subjects successfully achieved ankle push-off and were able to modulate the magnitude of push-off via the volitional input. Unexpectedly, however, HVC behaved either more similarly to FSM impedance control or to DMC alone, rather than in combination. Both DMC and HVC, but not FSM impedance control, allowed subjects to achieve unique activities such as tip-toe standing, foot tapping, side-stepping, and backward walking. Able-bodied subject (N=6) preferences were split amongst the controllers, while all transtibial subjects (N=3) preferred DMC. Desired performance and ease of use showed the highest correlations with overall satisfaction (0.81 and 0.82, respectively).

A reduced-order closed-loop hybrid dynamic model for design and development of lower limb prostheses.

This manuscript presents a simplified dynamic human-prosthesis model and simulation framework for the purpose of designing and developing lower limb prosthesis hardware and controllers. The objective was to provide an offline design tool to verify the closed-loop behavior of the prosthesis with the human, in order to avoid relying solely on limiting kinematic and kinetic reference trajectories of (able-bodied) subjects and associated static or inverse dynamic analyses, while not having to resort to complete neuromusculoskeletal models of the human that require extensive optimizations to run. The presented approach employs a reduced-order model that includes only the prosthetic limb and trunk in a multi-body dynamic model. External forces are applied to the trunk during stance phase of the intact leg to represent its presence. Walking is realized by employing the well-known spring-loaded inverted pendulum model, which is shown to generate realistic dynamics on the prosthesis while maintaining a stable and modifiable gait. This simple approach is inspired from the rationale that the human is adaptive, and from the desire to facilitate modifications or inclusions of additional user actions. The presented framework is validated with two use cases, featuring a commercial and research knee prosthesis in combination with a passive ankle prosthesis, performing a continuous sequence of standing still, walking at different velocities and stopping.

Effects of temperature on the structures and dynamics of a binary complex plasma

In the paper, the effects of temperature on the structure and dynamics of a binary complex plasma system are investigated through two-dimensional (2D) Langevin dynamics simulation. Two kinds of dust particles with different masses are considered in the binary complex system. The particle distribution, Voronoi structure diagram and pair correlation function are used to characterize the system structure. The evolution process of kinetic energy, speed and trajectories of binary particles as time under different system temperatures are used to study the dynamical characteristics of the system. It shows that binary particles with different masses have the trend to separately distribute themselves with a boundary, which is very clear at the lower temperature. There is an optimum temperature, which can produce the separation distribution with fewest small particles mixing in the region of large particles. The dynamical investigation shows that small particles firstly reach the system center and then they are pushed out by large particles. The kinetic energy has a radial distribution, showing a drastic change around the boundary of the binary particles. The investigations indicate that the structures and dynamics of the binary complex plasma can be affected by system temperature.

RAFFT: Efficient prediction of RNA folding pathways using the fast Fourier transform.

We propose a novel heuristic to predict RNA secondary structure formation pathways that has two components: (i) a folding algorithm and (ii) a kinetic ansatz. This heuristic is inspired by the kinetic partitioning mechanism, by which molecules follow alternative folding pathways to their native structure, some much faster than others. Similarly, our algorithm RAFFT starts by generating an ensemble of concurrent folding pathways ending in multiple metastable structures, which is in contrast with traditional thermodynamic approaches that find single structures with minimal free energies. When we constrained the algorithm to predict only 50 structures per sequence, near-native structures were found for RNA molecules of length ≤ 200 nucleotides. Our heuristic has been tested on the coronavirus frameshifting stimulation element (CFSE): an ensemble of 68 distinct structures allowed us to produce complete folding kinetic trajectories, whereas known methods require evaluating millions of sub-optimal structures to achieve this result. Thanks to the fast Fourier transform on which RAFFT (RNA folding Algorithm wih Fast Fourier Transform) is based, these computations are efficient, with complexity [Formula: see text].

The numerical simulation of the generation of lower-band VLF chorus using a quasi-broadband Vlasov Hybrid Simulation code

In this paper, we perform the numerical modelling of lower-band VLF chorus in the earth’s magnetosphere. Assuming parallel propagation the 1d3v code has one spatial dimension z along the ambient magnetic field, which has a parabolic z dependence about the equator. The method used is Vlasov Hybrid Simulation (VHS) also known in the literature as the method of Kinetic Phase Point Trajectories (Nunn in Computer Physics Comms 60:1–25, 1990, J Computational Phys 108(1):180–196, 1993; Kazeminezhad et al. in Phys Rev E67:026704, 2003). The method is straightforward and easy to program, and robust against distribution function filamentation. Importantly, VHS does not invoke unphysical smoothing of the distribution function. Previous versions of the VLF/VHS code had a narrow bandwidth ~ 100 Hz, which enabled simulation of a wide variety of discrete triggered emissions. The present quasi-broadband VHS code has a bandwidth of ~ 3000 Hz, which is far more realistic for the simulation of chorus in its entirety. Further, the quasi-broadband code does not require artificial saturation, and does not need to employ matched filtering to accommodate large spatial frequency gradients. The aim of this paper which has been achieved is to produce VLF chorus Vlasov simulations employing a systematic variety of triggering input signals, namely key down, single pulse, PLHR, and broadband hiss.Graphical

Radial kinetic nonholonomic trajectories are Riemannian geodesics!

Nonholonomic mechanics describes the motion of systems constrained by nonintegrable constraints. One of its most remarkable properties is that the derivation of the nonholonomic equations is not variational in nature. However, in this paper, we prove (Theorem 1.1) that for kinetic nonholonomic systems, the solutions starting from a fixed point q are true geodesics for a family of Riemannian metrics on the image submanifold {{mathcal {M}}}^{nh}_q of the nonholonomic exponential map. This implies a surprising result: the kinetic nonholonomic trajectories with starting point q, for sufficiently small times, minimize length in {{mathcal {M}}}^{nh}_q!

Individuality decoded by running patterns: Movement characteristics that determine the uniqueness of human running.

Human gait is as unique to an individual as is their fingerprint. It remains unknown, however, what gait characteristics differentiate well between individuals that could define the uniqueness of human gait. The purpose of this work was to determine the gait characteristics that were most relevant for a neural network to identify individuals based on their running patterns. An artificial neural network was trained to recognize kinetic and kinematic movement trajectories of overground running from 50 healthy novice runners (males and females). Using layer-wise relevance propagation, the contribution of each variable to the classification result of the neural network was determined. It was found that gait characteristics of the coronal and transverse plane as well as medio-lateral ground reaction forces provided more information for subject identification than gait characteristics of the sagittal plane and ground reaction forces in vertical or anterior-posterior direction. Additionally, gait characteristics during the early stance were more relevant for gait recognition than those of the mid and late stance phase. It was concluded that the uniqueness of human gait is predominantly encoded in movements of the coronal and transverse plane during early stance.

Universal Gorban's Entropies: Geometric Case Study.

Recently, A.N. Gorban presented a rich family of universal Lyapunov functions for any linear or non-linear reaction network with detailed or complex balance. Two main elements of the construction algorithm are partial equilibria of reactions and convex envelopes of families of functions. These new functions aimed to resolve “the mystery” about the difference between the rich family of Lyapunov functions (f-divergences) for linear kinetics and a limited collection of Lyapunov functions for non-linear networks in thermodynamic conditions. The lack of examples did not allow to evaluate the difference between Gorban’s entropies and the classical Boltzmann–Gibbs–Shannon entropy despite obvious difference in their construction. In this paper, Gorban’s results are briefly reviewed, and these functions are analysed and compared for several mechanisms of chemical reactions. The level sets and dynamics along the kinetic trajectories are analysed. The most pronounced difference between the new and classical thermodynamic Lyapunov functions was found far from the partial equilibria, whereas when some fast elementary reactions became close to equilibrium then this difference decreased and vanished in partial equilibria.

Dynamic Flux Analysis: An Experimental Approach of Fluxomics.

Metabolic flux analysis represents an essential perspective to understand cellular physiology and offers quantitative information to guide pathway engineering. A valuable approach for experimental elucidation of metabolic flux is dynamic flux analysis, which estimates the relative or absolute flow rates through a series of metabolic intermediates in a given pathway. It is based on kinetic isotope labeling experiments, liquid chromatography-mass spectrometry (LC-MS), and computational analysis that relate kinetic isotope trajectories of metabolites to pathway activity. Herein, we illustrate the mathematic principles underlying the dynamic flux analysis and mainly focus on describing the experimental procedures for data generation. This protocol is exemplified using cyanobacterial metabolism as an example, for which reliable labeling data for central carbon metabolites can be acquired quantitatively. This protocol is applicable to other microbial systems as well and can be readily adapted to address different metabolic processes.

KineCluE: A kinetic cluster expansion code to compute transport coefficients beyond the dilute limit

This paper introduces the KineCluE code that implements the self-consistent mean-field theory for clusters of finite size. Transport coefficients are obtained as a sum over cluster contributions, each being individually computed with KineCluE. This method allows for the calculation of these coefficients beyond the infinitely dilute limit, and it is an important step in bridging the gap between dilute and concentrated approaches. Inside a finite volume of space containing the components of a given cluster, all kinetic trajectories are accounted for in an exact manner. The code, written in Python, adapts to a wide variety of systems, with various crystallographic structures (possibly under strain), defects and solute amount and types, and various jump mechanisms, including collective ones. The code also features a set of useful tools, such as the sensitivity study routine that allows for the identification of the most important jump frequencies to get accurate transport coefficients with minimum computational cost.

Research on the Effect of Tree Barriers on Rockfall Using a Three-Dimensional Discontinuous Deformation Analysis Method

On rockfall slopes, trees can play a natural and efficient protective role in preventing the occurrence of rockfall disasters. This paper presents a study on the tree barrier effect on rockfall based on a three-dimensional discontinuous deformation analysis (3D DDA) method. The tree barrier effect on rockfall is studied considering the 3D spatial effect of rockfall movement and the 3D spatial distribution of trees. The basic movement forms and collision modes of rockfall related to the tree barrier are classified, and the impact factors of tree arrangements on rockfall are proposed. The contact mechanism employed in the 3D DDA method is illustrated, and the accuracy of the 3D DDA rockfall simulation is verified by comparing with the results obtained from laboratory experiments. Numerical examples are conducted to study the effect of the tree barrier on rockfall, and general laws are derived by analyzing the variation of kinetic energies and motion trajectories of moving blocks. The results show that the 3D DDA method can effectively predict the 3D motion behaviors of rockfall and assess the tree barrier effect. Furthermore, a reasonable arrangement of trees or a combination of protective facilities and trees can prevent or mitigate the rockfall hazards.

A cyanine dye-based fluorescent probe as indicator of copper clock reaction for tracing Cu2+-catalyzed oxidation of cysteine

Using cyanine dye-coupling 2-pyridylmethyl chelating unit as fluorescent probe, we successfully developed an indicator of copper clock reaction to monitor the process of cysteine (Cys) oxidation. During the monitoring assay, the fluorescent changes reflected three sequential reaction and binding behaviors including oxidation of Cys, oxidation of Cu(I) and binding between Cu(II) and the oxidation product cystine (Cys-Cys). Because the different kinetic trajectories were obtained when used Cys, GSH and Hcy as the substrates, respectively, a new strategy for distinguishing Cys from GSH and Hcy was further developed using the cyanine dye-coupling Cu(II) complex.

A probabilistic approach for the mean-field limit to the Cucker-Smale model with a singular communication

We present a probabilistic approach for derivation of the kinetic Cucker-Smale (C-S) equation from the particle C-S model with singular communication. For the system we are considering, it is impossible to validate effective description for certain special initial data, thus such a probabilistic approach is the best one can hope for. More precisely, we consider a system in which kinetic trajectories are deviated from a microscopic model and use a suitable probability measure to quantify the randomness in the initial data. We show that the set of bad initial data does in fact have small measure and that this small probability decays to zero algebraically, as \begin{document}$ N $\end{document} tends to infinity. For this, we introduce an appropriate cut-off in the communication weight. We also provide a relation between the order of the singularity and the order of the cut-off such that the machinery for deriving classical mean-field limits introduced in [ 3 ] can be applied to our setting.

Guiding kinetic trajectories between jammed and unjammed states in 2D colloidal nanocrystal-polymer assemblies with zwitterionic ligands.

Mesostructured matter composed of colloidal nanocrystals in solidified architectures abounds with broadly tunable catalytic, magnetic, optoelectronic, and energy storing properties. Less common are liquid-like assemblies of colloidal nanocrystals in a condensed phase, which may have different energy transduction behaviors owing to their dynamic character. Limiting investigations into dynamic colloidal nanocrystal architectures is the lack of schemes to control or redirect the tendency of the system to solidify. We show how to solidify and subsequently reconfigure colloidal nanocrystal assemblies dimensionally confined to a liquid-liquid interface. Our success in this regard hinged on the development of competitive chemistries anchoring or releasing the nanocrystals to or from the interface. With these chemistries, it was possible to control the kinetic trajectory between quasi-two-dimensional jammed (solid-like) and unjammed (liquid-like) states. In future schemes, it may be possible to leverage this control to direct the formation or destruction of explicit physical pathways for energy carriers to migrate in the system in response to an external field.

A further investigation about a simple model of the hunting behavior of some old locomotives

In a previous paper, a very rough model was proposed to investigate the unsatisfactory hunting behavior of some old locomotive prototypes, which prevented high speed service in the third decade of the last century. The first idea was to exploit nonlinear equations in order to investigate chaotic behavior, because large hunting oscillations, suddenly rising, were reported in the literature. The model was first suggested by the similarity between the usual piecewise linear tread taper and the Chua’s diode characteristic, and evolved in a circuit which was able to mimic, at least in some ways, the locomotive behavior. Although useless as design tool, because a careful a posteriori optimization is needed due to an insufficient number of parameters, the model seems to deserve further investigation. Here, some work is presented, to refine the previous analysis and to present a new version of the model, no longer limited to oscillation modes dominated by natural frequencies of body and bogies, and suitable to simulate kinetic trajectories, elastic or viscous links, and dampers.

Connecting the dots across time: reconstruction of single-cell signalling trajectories using time-stamped data.

Single-cell responses are shaped by the geometry of signalling kinetic trajectories carved in a multidimensional space spanned by signalling protein abundances. It is, however, challenging to assay a large number (more than 3) of signalling species in live-cell imaging, which makes it difficult to probe single-cell signalling kinetic trajectories in large dimensions. Flow and mass cytometry techniques can measure a large number (4 to more than 40) of signalling species but are unable to track single cells. Thus, cytometry experiments provide detailed time-stamped snapshots of single-cell signalling kinetics. Is it possible to use the time-stamped cytometry data to reconstruct single-cell signalling trajectories? Borrowing concepts of conserved and slow variables from non-equilibrium statistical physics we develop an approach to reconstruct signalling trajectories using snapshot data by creating new variables that remain invariant or vary slowly during the signalling kinetics. We apply this approach to reconstruct trajectories using snapshot data obtained from in silico simulations, live-cell imaging measurements, and, synthetic flow cytometry datasets. The application of invariants and slow variables to reconstruct trajectories provides a radically different way to track objects using snapshot data. The approach is likely to have implications for solving matching problems in a wide range of disciplines.