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Concept: Mathematical model


Myxococcus xanthus cells self-organize into periodic bands of traveling waves, termed ripples, during multicellular fruiting body development and predation on other bacteria. To investigate the mechanistic basis of rippling behavior and its physiological role during predation by this Gram-negative soil bacterium, we have used an approach that combines mathematical modeling with experimental observations. Specifically, we developed an agent-based model (ABM) to simulate rippling behavior that employs a new signaling mechanism to trigger cellular reversals. The ABM has demonstrated that three ingredients are sufficient to generate rippling behavior: (i) side-to-side signaling between two cells that causes one of the cells to reverse, (ii) a minimal refractory time period after each reversal during which cells cannot reverse again, and (iii) physical interactions that cause the cells to locally align. To explain why rippling behavior appears as a consequence of the presence of prey, we postulate that prey-associated macromolecules indirectly induce ripples by stimulating side-to-side contact-mediated signaling. In parallel to the simulations, M. xanthus predatory rippling behavior was experimentally observed and analyzed using time-lapse microscopy. A formalized relationship between the wavelength, reversal time, and cell velocity has been predicted by the simulations and confirmed by the experimental data. Furthermore, the results suggest that the physiological role of rippling behavior during M. xanthus predation is to increase the rate of spreading over prey cells due to increased side-to-side contact-mediated signaling and to allow predatory cells to remain on the prey longer as a result of more periodic cell motility.

Concepts: Simulation, Operations research, Biological pest control, Mathematical model, Predation, Causality, Bacteria


Many mathematical models have investigated the impact of expanding access to antiretroviral therapy (ART) on new HIV infections. Comparing results and conclusions across models is challenging because models have addressed slightly different questions and have reported different outcome metrics. This study compares the predictions of several mathematical models simulating the same ART intervention programmes to determine the extent to which models agree about the epidemiological impact of expanded ART.

Concepts: Africa, Mathematical model, South Africa, Protease inhibitor, Infectious disease, Antiretroviral drug, AIDS, HIV


Focal degradation of extracellular matrix (ECM) is the first step in the invasion of cancer cells. MT1-MMP is a potent membrane proteinase employed by aggressive cancer cells. In our previous study, we reported that MT1-MMP was preferentially located at membrane protrusions called invadopodia, where MT1-MMP underwent quick turnover. Our computer simulation and experiments showed that this quick turnover was essential for the degradation of ECM at invadopodia (Hoshino, D., et al., (2012) PLoS Comp. Biol., 8: e1002479). Here we report on characterization and analysis of the ECM-degrading activity of MT1-MMP, aiming at elucidating a possible reason for its repetitive insertion in the ECM degradation. First, in our computational model, we found a very narrow transient peak in the activity of MT1-MMP followed by steady state activity. This transient activity was due to the inhibition by TIMP-2, and the steady state activity of MT1-MMP decreased dramatically at higher TIMP-2 concentrations. Second, we evaluated the role of the narrow transient activity in the ECM degradation. When the transient activity was forcibly suppressed in computer simulations, the ECM degradation was heavily suppressed, indicating the essential role of this transient peak in the ECM degradation. Third, we compared continuous and pulsatile turnover of MT1-MMP in the ECM degradation at invadopodia. The pulsatile insertion showed basically consistent results with the continuous insertion in the ECM degradation, and the ECM degrading efficacy depended heavily on the transient activity of MT1-MMP in both models. Unexpectedly, however, low-frequency/high-concentration insertion of MT1-MMP was more effective in ECM degradation than high-frequency/low-concentration pulsatile insertion even if the time-averaged amount of inserted MT1-MMP was the same. The present analysis and characterization of ECM degradation by MT1-MMP together with our previous report indicate a dynamic nature of MT1-MMP at invadopodia and the importance of its transient peak in the degradation of the ECM.

Concepts: AnyLogic, Cell membrane, Monte Carlo method, Mathematical model, Thermodynamics, Computer graphics, Computational science, Computer simulation


Computer modeling, simulation and optimization are powerful tools that have seen increased use in biomechanics research. Dynamic optimizations can be categorized as either data-tracking or predictive problems. The data-tracking approach has been used extensively to address human movement problems of clinical relevance. The predictive approach also holds great promise, but has seen limited use in clinical applications. Enhanced software tools would facilitate the application of predictive musculoskeletal simulations to clinically-relevant research. The open-source software OpenSim provides tools for generating tracking simulations but not predictive simulations. However, OpenSim includes an extensive application programming interface that permits extending its capabilities with scripting languages such as MATLAB. In the work presented here, we combine the computational tools provided by MATLAB with the musculoskeletal modeling capabilities of OpenSim to create a framework for generating predictive simulations of musculoskeletal movement based on direct collocation optimal control techniques. In many cases, the direct collocation approach can be used to solve optimal control problems considerably faster than traditional shooting methods. Cyclical and discrete movement problems were solved using a simple 1 degree of freedom musculoskeletal model and a model of the human lower limb, respectively. The problems could be solved in reasonable amounts of time (several seconds to 1-2 hours) using the open-source IPOPT solver. The problems could also be solved using the fmincon solver that is included with MATLAB, but the computation times were excessively long for all but the smallest of problems. The performance advantage for IPOPT was derived primarily by exploiting sparsity in the constraints Jacobian. The framework presented here provides a powerful and flexible approach for generating optimal control simulations of musculoskeletal movement using OpenSim and MATLAB. This should allow researchers to more readily use predictive simulation as a tool to address clinical conditions that limit human mobility.

Concepts: How to Solve It, Optimization, Mathematical model, Computer program, Computer simulation, Operations research, Optimal control, Application programming interface


Using a database with the mitochondrial DNA (mtDNA) of 513 Neolithic individuals, we quantify the space-time variation of the frequency of haplogroup K, previously proposed as a relevant Neolithic marker. We compare these data to simulations, based on a mathematical model in which a Neolithic population spreads from Syria to Anatolia and Europe, possibly interbreeding with Mesolithic individuals (who lack haplogroup K) and/or teaching farming to them. Both the data and the simulations show that the percentage of haplogroup K (%K) decreases with increasing distance from Syria and that, in each region, the %K tends to decrease with increasing time after the arrival of farming. Both the model and the data display a local minimum of the genetic cline, and for the same Neolithic regional culture (Sweden). Comparing the observed ancient cline of haplogroup K to the simulation results reveals that about 98% of farmers were not involved in interbreeding neither acculturation (cultural diffusion). Therefore, cultural diffusion involved only a tiny fraction (about 2%) of farmers and, in this sense, the most relevant process in the spread of the Neolithic in Europe was demic diffusion (i.e., the dispersal of farmers), as opposed to cultural diffusion (i.e., the incorporation of hunter-gatherers).

Concepts: Neolithic Revolution, Simulation, Optimization, Mitochondrial DNA, Mitochondrion, Mathematical model, Neolithic, DNA


The desktop slot exhaust hood has been widely used, but it is calculated by empirical formula. Axial velocity change rule of desktop slot exhaust hood can effectively provide the basis of the wind speed needed in order to control the poison. According to gas motion mathematical model, the geometry model and boundary conditions of desktop slot exhaust hood was established, and the influence of the hood sizes to axial velocity were analyzed by Fluent simulation. The changes of relationship between the axial velocity(V) and the distance from the hood mouth (L), the short edge of the hood mouth(a), the long edge of the hood mouth(b), the equivalent diameter of the hood mouth(d) and the square root of the hood mouth area(√A) were comparative analyzed by dimensionless processing. The result is the V/V0with L/d have better change rule. The axial velocity change rule of different axial velocity were also analyzed using V/V0with L/d change rule, and the change rule of V/V0with L/d of desktop slot exhaust hood was obtained, which was verified by experiment.

Concepts: Square root, Economics, Mathematical model, Geometry, Empiricism, Science, Wind, Mathematics


The extent to which leaf-lobing influences the interception of direct solar radiation by individual plants was studied by means of computer simulations. The morphology, size and orientation ofAmbrosia artemisiifolia L. leaves were measured and used to construct a prototypeAmbrosia plant upon which a computer simulation was based. The leaf geometries of this simulation were then varied, and daily integrated irradiances (DII) were calculated for each variant plant simulation. Data indicate that lobedAmbrosia leaves do not confer an advantage to light-interception based upon values of DII. Simulated plants identical in all respects to the prototype, but with simple, elliptic leaves, had equivalent DII values to the prototype. Simulations with leaves in which gaps between lobes were “filledin” had reduced light-interception efficiencies compared to the prototype and to a simulation with elliptic-leaves. Lightinterception was maximized when leaves on distal nodes wereAmbrosia-like and leaves on proximal nodes were elliptic. The data are interpreted to indicate that lobingperse is not functionally advantageous to light-interception; however, gradients of leaf-lobing along the length of shoots may be very significant in terms of overall light interception.

Concepts: Fern, Plant morphology, Photosynthesis, Computer simulation, AnyLogic, Monte Carlo method, Mathematical model, Computer graphics


Ride-sharing services are transforming urban mobility by providing timely and convenient transportation to anybody, anywhere, and anytime. These services present enormous potential for positive societal impacts with respect to pollution, energy consumption, congestion, etc. Current mathematical models, however, do not fully address the potential of ride-sharing. Recently, a large-scale study highlighted some of the benefits of car pooling but was limited to static routes with two riders per vehicle (optimally) or three (with heuristics). We present a more general mathematical model for real-time high-capacity ride-sharing that (i) scales to large numbers of passengers and trips and (ii) dynamically generates optimal routes with respect to online demand and vehicle locations. The algorithm starts from a greedy assignment and improves it through a constrained optimization, quickly returning solutions of good quality and converging to the optimal assignment over time. We quantify experimentally the tradeoff between fleet size, capacity, waiting time, travel delay, and operational costs for low- to medium-capacity vehicles, such as taxis and van shuttles. The algorithm is validated with ∼3 million rides extracted from the New York City taxicab public dataset. Our experimental study considers ride-sharing with rider capacity of up to 10 simultaneous passengers per vehicle. The algorithm applies to fleets of autonomous vehicles and also incorporates rebalancing of idling vehicles to areas of high demand. This framework is general and can be used for many real-time multivehicle, multitask assignment problems.

Concepts: Engineering, Carpool, Transport, Optimization, Mathematics, Mathematical model, Operations research, Automobile


Cardiac arrhythmias and conduction disturbances are accompanied by structural remodelling of the specialised cardiomyocytes known collectively as the cardiac conduction system. Here, using contrast enhanced micro-computed tomography, we present, in attitudinally appropriate fashion, the first 3-dimensional representations of the cardiac conduction system within the intact human heart. We show that cardiomyocyte orientation can be extracted from these datasets at spatial resolutions approaching the single cell. These data show that commonly accepted anatomical representations are oversimplified. We have incorporated the high-resolution anatomical data into mathematical simulations of cardiac electrical depolarisation. The data presented should have multidisciplinary impact. Since the rate of depolarisation is dictated by cardiac microstructure, and the precise orientation of the cardiomyocytes, our data should improve the fidelity of mathematical models. By showing the precise 3-dimensional relationships between the cardiac conduction system and surrounding structures, we provide new insights relevant to valvar replacement surgery and ablation therapies. We also offer a practical method for investigation of remodelling in disease, and thus, virtual pathology and archiving. Such data presented as 3D images or 3D printed models, will inform discussions between medical teams and their patients, and aid the education of medical and surgical trainees.

Concepts: Image resolution, Cardiac electrophysiology, Engineering, Operations research, Mathematical model, Electrical conduction system of the heart, Medicine, Heart


Advances in Virtual Reality (VR) technologies allow the investigation of simulated moral actions in visually immersive environments. Using a robotic manipulandum and an interactive sculpture, we now also incorporate realistic haptic feedback into virtual moral simulations. In two experiments, we found that participants responded with greater utilitarian actions in virtual and haptic environments when compared to traditional questionnaire assessments of moral judgments. In experiment one, when incorporating a robotic manipulandum, we found that the physical power of simulated utilitarian responses (calculated as the product of force and speed) was predicted by individual levels of psychopathy. In experiment two, which integrated an interactive and life-like sculpture of a human into a VR simulation, greater utilitarian actions continued to be observed. Together, these results support a disparity between simulated moral action and moral judgment. Overall this research combines state-of-the-art virtual reality, robotic movement simulations, and realistic human sculptures, to enhance moral paradigms that are often contextually impoverished. As such, this combination provides a better assessment of simulated moral action, and illustrates the embodied nature of morally-relevant actions.

Concepts: Mathematical model, Morality, Haptic technology, Simulation123, Operations research, Simulated reality, Simulation, Virtual reality