Quantitative characterization of run-and-tumble statistics in bulk bacterial suspensions.

We introduce a numerical method to extract the parameters of run-and-tumble dynamics from experimental measurements of the intermediate scattering function. We show that proceeding in Laplace space is unpractical and employ instead renewal processes to work directly in real time. We first validate our approach against data produced using agent-based simulations. This allows us to identify the length and time scales required for an accurate measurement of the motility parameters, including tumbling frequency and swim speed. We compare different models for the run-and-tumble dynamics by accounting for speed variability at the single-cell and population level, respectively. Finally, we apply our approach to experimental data on wild-type Escherichia coli obtained using differential dynamic microscopy.

Characterization and Control of the Run-and-Tumble Dynamics of Escherichia Coli.

We characterize the full spatiotemporal gait of populations of swimming Escherichia coli using renewal processes to analyze the measurements of intermediate scattering functions. This allows us to demonstrate quantitatively how the persistence length of an engineered strain can be controlled by a chemical inducer and to report a controlled transition from perpetual tumbling to smooth swimming. For wild-type E. coli, we measure simultaneously the microscopic motility parameters and the large-scale effective diffusivity, hence quantitatively bridging for the first time small-scale directed swimming and macroscopic diffusion.

Hydrodynamically induced helical particle drift due to patterned surfaces.

Advances in microfabrication enable the tailoring of surfaces to achieve optimal sorting, mixing, and focusing of complex particulate suspensions in microfluidic devices. Corrugated surfaces have proved to be a powerful tool to manipulate particle motion for a variety of applications, yet the fundamental physical mechanism underlying the hydrodynamic coupling of the suspended particles and surface topography has remained elusive. Here, we study the hydrodynamic interactions between sedimenting spherical particles and nearby corrugated surfaces, whose corrugations are tilted with respect to gravity. Our experiments show three-dimensional, helical particle trajectories with an overall drift along the corrugations, which agree quantitatively with our analytical perturbation theory. The theoretical predictions reveal that the interaction of the disturbance flows, induced by the particle motion, with the corrugations generates locally a transverse anisotropy of the pressure field, which explains the helical dynamics and particle drift. We demonstrate that this dynamical behavior is generic for various surface shapes, including rectangular, sinusoidal, and triangular corrugations, and we identify surface characteristics that produce an optimal particle drift. Our findings reveal a universal feature inherent to particle transport near patterned surfaces and provide fundamental insights for future microfluidic applications that aim to enhance the focusing or sorting of particulate suspensions.

A geometric criterion for the optimal spreading of active polymers in porous media.

Efficient navigation through disordered, porous environments poses a major challenge for swimming microorganisms and future synthetic cargo-carriers. We perform Brownian dynamics simulations of active stiff polymers undergoing run-reverse dynamics, and so mimic bacterial swimming, in porous media. In accord with experiments of Escherichia coli, the polymer dynamics are characterized by trapping phases interrupted by directed hopping motion through the pores. Our findings show that the spreading of active agents in porous media can be optimized by tuning their run lengths, which we rationalize using a coarse-grained model. More significantly, we discover a geometric criterion for the optimal spreading, which emerges when their run lengths are comparable to the longest straight path available in the porous medium. Our criterion unifies results for porous media with disparate pore sizes and shapes and for run-and-tumble polymers. It thus provides a fundamental principle for optimal transport of active agents in densely-packed biological and environmental settings.

Two-dimensional Brownian motion of anisotropic dimers.

We study the two-dimensional motion of colloidal dimers by single-particle tracking and compare the experimental observations obtained by bright-field microscopy to theoretical predictions for anisotropic diffusion. The comparison is based on the mean-square displacements in the laboratory and particle frame as well as generalizations of the self-intermediate scattering functions, which provide insights into the rotational dynamics of the dimer. The diffusional anisotropy leads to a measurable translational-rotational coupling that becomes most prominent by aligning the coordinate system with the initial orientation of the particles. In particular, we find a splitting of the time-dependent diffusion coefficients parallel and perpendicular to the long axis of the dimer which decays over the orientational relaxation time. Deviations of the self-intermediate scattering functions from pure exponential relaxation are small but can be resolved experimentally. The theoretical predictions and experimental results agree quantitatively.

Microswimmers near corrugated, periodic surfaces.

We explore hydrodynamic interactions between microswimmers and corrugated, or rough, surfaces, as found often in biological systems and microfluidic devices. Using the Lorentz reciprocal theorem for viscous flows we derive exact expressions for the roughness-induced velocities up to first order in the surface-height fluctuations and provide solutions for the translational and angular velocities valid for arbitrary surface shapes. We apply our theoretical predictions to elucidate the impact of a periodic, wavy surface on the velocities of microswimmers modeled in terms of a superposition of Stokes singularities. Our findings, valid in the framework of a far-field analysis, show that the roughness-induced velocities vary non-monotonically with the wavelength of the surface. For wavelengths comparable to the swimmer-surface distance a pusher can experience a repulsive contribution due to the reflection of flow fields at the edge of a surface cavity, which decreases the overall attraction to the wall.

Crowding-Enhanced Diffusion: An Exact Theory for Highly Entangled Self-Propelled Stiff Filaments.

We study a strongly interacting crowded system of self-propelled stiff filaments by event-driven Brownian dynamics simulations and an analytical theory to elucidate the intricate interplay of crowding and self-propulsion. We find a remarkable increase of the effective diffusivity upon increasing the filament number density by more than one order of magnitude. This counterintuitive "crowded is faster" behavior can be rationalized by extending the concept of a confining tube pioneered by Doi and Edwards for highly entangled, crowded, passive to active systems. We predict a scaling theory for the effective diffusivity as a function of the Péclet number and the filament number density. Subsequently, we show that an exact expression derived for a single self-propelled filament with motility parameters as input can predict the nontrivial spatiotemporal dynamics over the entire range of length and timescales. In particular, our theory captures short-time diffusion, directed swimming motion at intermediate times, and the transition to complete orientational relaxation at long times.

Frequency-dependent higher-order Stokes singularities near a planar elastic boundary: Implications for the hydrodynamics of an active microswimmer near an elastic interface.

The emerging field of self-driven active particles in fluid environments has recently created significant interest in the biophysics and bioengineering communities owing to their promising future for biomedical and technological applications. These microswimmers move autonomously through aqueous media, where under realistic situations they encounter a plethora of external stimuli and confining surfaces with peculiar elastic properties. Based on a far-field hydrodynamic model, we present an analytical theory to describe the physical interaction and hydrodynamic couplings between a self-propelled active microswimmer and an elastic interface that features resistance toward shear and bending. We model the active agent as a superposition of higher-order Stokes singularities and elucidate the associated translational and rotational velocities induced by the nearby elastic boundary. Our results show that the velocities can be decomposed in shear and bending related contributions which approach the velocities of active agents close to a no-slip rigid wall in the steady limit. The transient dynamics predict that contributions to the velocities of the microswimmer due to bending resistance are generally more pronounced than those due to shear resistance. Bending can enhance (suppress) the velocities resulting from higher-order singularities whereas the shear related contribution decreases (increases) the velocities. Most prominently, we find that near an elastic interface of only energetic resistance toward shear deformation, such as that of an elastic capsule designed for drug delivery, a swimming bacterium undergoes rotation of the same sense as observed near a no-slip wall. In contrast to that, near an interface of only energetic resistance toward bending, such as that of a fluid vesicle or liposome, we find a reversed sense of rotation. Our results provide insight into the control and guidance of artificial and synthetic self-propelling active microswimmers near elastic confinements.

Alternative Conversion Methods for Transition Probabilities in State-Transition Models: Validity and Impact on Comparative Effectiveness and Cost-Effectiveness.

Background. In state-transition models (STMs), decision problems are conceptualized using health states and transitions among those health states after predefined time cycles. The naive, commonly applied method (C) for cycle length conversion transforms all transition probabilities separately. In STMs with more than 2 health states, this method is not accurate. Therefore, we aim to describe and compare the performance of method C with that of alternative matrix transformation methods. Design. We compare 2 alternative matrix transformation methods (Eigenvalue method [E], Schure-Padé method [SP]) to method C applied in an STM of 3 different treatment strategies for women with breast cancer. We convert the given annual transition matrix into a monthly-cycle matrix and evaluate induced transformation errors for the transition matrices and the long-term outcomes: life years, quality-adjusted life-years, costs and incremental cost-effectiveness ratios, and the performance related to the decisions. In addition, we applied these transformation methods to randomly generated annual transition matrices with 4, 7, 10, and 20 health states. Results. In theory, there is no generally applicable correct transformation method. Based on our simulations, SP resulted in the smallest transformation-induced discrepancies for generated annual transition matrices for 2 treatment strategies. E showed slightly smaller discrepancies than SP in the strategy, where one of the direct transitions between health states was excluded. For long-term outcomes, the largest discrepancy occurred for estimated costs applying method C. For higher dimensional models, E performs best. Conclusions. In our modeling examples, matrix transformations (E, SP) perform better than transforming all transition probabilities separately (C). Transition probabilities based on alternative conversion methods should therefore be applied in sensitivity analyses.

Elastic behavior of a semiflexible polymer in 3D subject to compression and stretching forces.

We elucidate the elastic behavior of a wormlike chain in 3D under compression and provide exact solutions for the experimentally accessible force-extension relation in terms of generalized spheroidal wave functions. In striking contrast to the classical Euler buckling instability, the force-extension relation of a clamped semiflexible polymer exhibits a smooth crossover from an almost stretched to a buckled configuration. In particular, the associated susceptibility, which measures the strength of the response of the polymer to the applied force, displays a prominent peak in the vicinity of the critical Euler buckling force. For increasing persistence length, the force-extension relation and the susceptibility of semiflexible polymers approach the behavior of a classical rod, whereas thermal fluctuations permit more flexible polymers to resist the applied force. Furthermore, we find that semiflexible polymers confined to 2D can oppose the applied force more strongly than in 3D.

Probing the Spatiotemporal Dynamics of Catalytic Janus Particles with Single-Particle Tracking and Differential Dynamic Microscopy.

We demonstrate differential dynamic microscopy and particle tracking for the characterization of the spatiotemporal behavior of active Janus colloids in terms of the intermediate scattering function (ISF). We provide an analytical solution for the ISF of the paradigmatic active Brownian particle model and find striking agreement with experimental results from the smallest length scales, where translational diffusion and self-propulsion dominate, up to the largest ones, which probe effective diffusion due to rotational Brownian motion. At intermediate length scales, characteristic oscillations resolve the crossover between directed motion to orientational relaxation and allow us to discriminate active Brownian motion from other reorientation processes, e.g., run-and-tumble motion. A direct comparison to theoretical predictions reliably yields the rotational and translational diffusion coefficients of the particles, the mean and width of their speed distribution, and the temporal evolution of these parameters.

Bimodal probability density characterizes the elastic behavior of a semiflexible polymer in 2D under compression.

We explore the elastic behavior of a wormlike chain under compression in terms of exact solutions for the associated probability densities. Strikingly, the probability density for the end-to-end distance projected along the applied force exhibits a bimodal shape in the vicinity of the critical Euler buckling force of an elastic rod, reminiscent of the smeared discontinuous phase transition of a finite system. These two modes reflect the almost stretched and the S-shaped configuration of a clamped polymer induced by the compression. Moreover, we find a bimodal shape of the probability density for the transverse fluctuations of the free end of a cantilevered polymer as fingerprint of its semiflexibility. In contrast to clamped polymers, free polymers display a circularly symmetric probability density and their distributions are identical for compression and stretching forces.

Personalized treatment of women with early breast cancer: a risk-group specific cost-effectiveness analysis of adjuvant chemotherapy accounting for companion prognostic tests OncotypeDX and Adjuvant!Online.

BACKGROUND: Due to high survival rates and the relatively small benefit of adjuvant therapy, the application of personalized medicine (PM) through risk stratification is particularly beneficial in early breast cancer (BC) to avoid unnecessary harms from treatment. The new 21-gene assay (OncotypeDX, ODX) is a promising prognostic score for risk stratification that can be applied in conjunction with Adjuvant!Online (AO) to guide personalized chemotherapy decisions for early BC patients. Our goal was to evaluate risk-group specific cost effectiveness of adjuvant chemotherapy for women with early stage BC in Austria based on AO and ODX risk stratification. METHODS: A previously validated discrete event simulation model was applied to a hypothetical cohort of 50-year-old women over a lifetime horizon. We simulated twelve risk groups derived from the joint application of ODX and AO and included respective additional costs. The primary outcomes of interest were life-years gained, quality-adjusted life-years (QALYs), costs and incremental cost-effectiveness (ICER). The robustness of results and decisions derived were tested in sensitivity analyses. A cross-country comparison of results was performed. RESULTS: Chemotherapy is dominated (i.e., less effective and more costly) for patients with 1) low ODX risk independent of AO classification; and 2) low AO risk and intermediate ODX risk. For patients with an intermediate or high AO risk and an intermediate or high ODX risk, the ICER is below 15,000 EUR/QALY (potentially cost effective depending on the willingness-to-pay). Applying the AO risk classification alone would miss risk groups where chemotherapy is dominated and thus should not be considered. These results are sensitive to changes in the probabilities of distant recurrence but not to changes in the costs of chemotherapy or the ODX test. CONCLUSIONS: Based on our modeling study, chemotherapy is effective and cost effective for Austrian patients with an intermediate or high AO risk and an intermediate or high ODX risk. In other words, low ODX risk suggests chemotherapy should not be considered but low AO risk may benefit from chemotherapy if ODX risk is high. Our analysis suggests that risk-group specific cost-effectiveness analysis, which includes companion prognostic tests are essential in PM.

Intermediate scattering function of an anisotropic Brownian circle swimmer.

Microswimmers exhibit noisy circular motion due to asymmetric propulsion mechanisms, their chiral body shape, or by hydrodynamic couplings in the vicinity of surfaces. Here, we employ the Brownian circle swimmer model and characterize theoretically the dynamics in terms of the directly measurable intermediate scattering function. We derive the associated Fokker-Planck equation for the conditional probabilities and provide an exact solution in terms of generalizations of the Mathieu functions. Different spatiotemporal regimes are identified reflecting the bare translational diffusion at large wavenumbers, the persistent circular motion at intermediate wavenumbers and an enhanced effective diffusion at small wavenumbers. In particular, the circular motion of the particle manifests itself in characteristic oscillations at a plateau of the intermediate scattering function for wavenumbers probing the radius.

Exact solution for the force-extension relation of a semiflexible polymer under compression.

Exact solutions for the elastic and thermodynamic properties for the wormlike chain model are elaborated in terms of Mathieu functions. The smearing of the classical Euler buckling instability for clamped polymers is analyzed for the force-extension relation. Interestingly, at strong compression forces the thermal fluctuations lead to larger elongations than for the elastic rod. The susceptibility defined as the derivative of the force-extension relation displays a prominent maximum at a force that approaches the critical Euler buckling force as the persistence length is increased. We also evaluate the excess entropy and heat capacity induced by the compression and find that they vary nonmonotonically with the load. These findings are corroborated by pseudo-Brownian simulations.

Intermediate scattering function of an anisotropic active Brownian particle.

Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.

Lessons Learned from a Cross-Model Validation between a Discrete Event Simulation Model and a Cohort State-Transition Model for Personalized Breast Cancer Treatment.

OBJECTIVES: Breast cancer is the most common malignancy among women in developed countries. We developed a model (the Oncotyrol breast cancer outcomes model) to evaluate the cost-effectiveness of a 21-gene assay when used in combination with Adjuvant! Online to support personalized decisions about the use of adjuvant chemotherapy. The goal of this study was to perform a cross-model validation. METHODS: The Oncotyrol model evaluates the 21-gene assay by simulating a hypothetical cohort of 50-year-old women over a lifetime horizon using discrete event simulation. Primary model outcomes were life-years, quality-adjusted life-years (QALYs), costs, and incremental cost-effectiveness ratios (ICERs). We followed the International Society for Pharmacoeconomics and Outcomes Research-Society for Medical Decision Making (ISPOR-SMDM) best practice recommendations for validation and compared modeling results of the Oncotyrol model with the state-transition model developed by the Toronto Health Economics and Technology Assessment (THETA) Collaborative. Both models were populated with Canadian THETA model parameters, and outputs were compared. RESULTS: The differences between the models varied among the different validation end points. The smallest relative differences were in costs, and the greatest were in QALYs. All relative differences were less than 1.2%. The cost-effectiveness plane showed that small differences in the model structure can lead to different sets of nondominated test-treatment strategies with different efficiency frontiers. We faced several challenges: distinguishing between differences in outcomes due to different modeling techniques and initial coding errors, defining meaningful differences, and selecting measures and statistics for comparison (means, distributions, multivariate outcomes). CONCLUSIONS: Cross-model validation was crucial to identify and correct coding errors and to explain differences in model outcomes. In our comparison, small differences in either QALYs or costs led to changes in ICERs because of changes in the set of dominated and nondominated strategies.

The ONCOTYROL Prostate Cancer Outcome and Policy Model: Effect of Prevalence Assumptions on the Benefit-Harm Balance of Screening.

BACKGROUND: The ONCOTYROL Prostate Cancer Outcome and Policy (PCOP) model is a state-transition microsimulation model evaluating the benefits and harms of prostate cancer (PCa) screening. The natural history and detection component of the original model was based on the 2003 version of the Erasmus MIcrosimulation SCreening ANalysis (MISCAN) model, which was not calibrated to prevalence data. Compared with data from autopsy studies, prevalence of latent PCa assumed by the original model is low, which may bias the model toward screening. Our objective was to recalibrate the original model to match prevalence data from autopsy studies as well and compare benefit-harm predictions of the 2 model versions differing in prevalence. METHODS: For recalibration, we reprogrammed the natural history and detection component of the PCOP model as a deterministic Markov state-transition cohort model in the statistical software package R. All parameters were implemented as variables or time-dependent functions and calibrated simultaneously in a single run. Observed data used as calibration targets included data from autopsy studies, cancer registries, and the European Randomized Study of Screening for Prostate Cancer. Compared models were identical except for calibrated parameters. RESULTS: We calibrated 46 parameters. Prevalence from autopsy studies could not be fitted using the original parameter set. Additional parameters, allowing for interruption of disease progression and age-dependent screening sensitivities, were needed. Recalibration to higher prevalence demonstrated a considerable increase of overdiagnosis and decline of screening sensitivity, which significantly worsened the benefit-harm balance of screening. CONCLUSIONS: Our calibration suggests that not all cancers are at risk of progression, and screening sensitivity may be lower at older ages. PCa screening models that use calibration to simulate disease progression in the unobservable latent phase are highly sensitive to prevalence assumptions.