Using covariant Lyapunov vectors to quantify high-dimensional chaos with a conservation law

We explore the high-dimensional chaos of a one-dimensional lattice of diffusively coupled tent maps using the covariant Lyapunov vectors (CLVs). We investigate the connection between the dynamics of the maps in the physical space and the dynamics of the covariant Lyapunov vectors and covariant Lyapunov exponents that describe the direction and growth (or decay) of small perturbations in the tangent space. We explore the tangent space splitting into physical and transient modes and find that the splitting persists for all of the conditions we explore. In general, the leading CLVs are highly localized in space and the CLVs become less localized with increasing Lyapunov index. We consider the dynamics with a conservation law whose strength is controlled by a parameter that can be continuously varied. Our results indicate that a conservation law delocalizes the spatial variation of the CLVs. We find that when a conservation law is present, the leading CLVs are entangled with fewer of their neighboring CLVs than in the absence of a conservation law.

Overview and recent advances in the targeting of medulloblastoma cancer stem cells

Introduction: Medulloblastoma, an embryonal small round blue cell tumor primarily arising in the posterior fossa, is the most common malignancy of the central nervous system in children and requires intensive multi-modality therapy for cure. Overall 5-year survival is approximately 75% in children with primary disease, but outcomes for relapsed disease are very poor. Recent advances have identified molecular subgroups with excellent prognosis, with 5-year overall survival rates >90%, and subgroups with very poor prognosis with overall survival rates <50%. Molecular subtyping has allowed for more sophisticated risk stratification of patients, but new treatments for the highest risk patients have not yet improved outcomes. Targeting cancer stem cells may improve outcomes, and several candidate targets and novel drugs are under investigation.Areas covered: We discuss medulloblastoma epidemiology, biology, treatment modalities, risk stratification, and molecular subgroup analysis, links between subgroup and developmental biology, cancer stem cell biology in medulloblastoma including previously described cancer stem cell markers and proposed targeted treatments in the current literature.Expert opinion: The understanding of cancer stem cells in medulloblastoma will advance therapies targeting the most treatment-resistant cells within the tumor and therefore reduce the incidence of treatment refractory and relapsed disease.

Clinical and Neuroimaging Features of Magnetic Resonance-Guided Stereotactic Laser Ablation for Newly Diagnosed and Recurrent Pediatric Brain Tumors: A Single Institutional Series

OBJECTIVE

We describe our single-institutional experience with magnetic resonance-guided stereotactic laser ablation (SLA) for the treatment of newly diagnosed and recurrent pediatric brain tumors.

METHODS

Eighteen consecutive ablation procedures were performed in 17 patients from March 2016-April 2020. Patient demographics, indications, procedures, neuroimaging features, and outcomes were reviewed retrospectively.

RESULTS

Seventeen patients (mean age of 11.4 years, 11 boys, 6 girls) underwent SLA with a mean follow-up of 24 months (range: 3-45 months). Tumor histologies included pilocytic astrocytoma (n = 5), ganglioglioma (n = 3), low-grade glioma not otherwise specified (n = 4), glioblastoma (n = 2), meningioma (n = 1), medulloblastoma (n = 1), and metastatic malignant peripheral nerve sheath tumor (n = 1). SLA was first-line therapy in 10 patients. Mean procedure duration including anesthesia time was 328 minutes (range: 244-529 minutes), and mean postoperative length of stay was 1.5 days (range 1-5 days). The complication rate was 29%, which included 3 patients who experienced postoperative motor changes, which resolved within several weeks of surgery, 1 patient with self-limited intraoperative bradycardia and hypotension, and 1 patient who died postoperatively due to intracranial hemorrhage from a distant lesion. Twelve of 17 patients had a neuroimaging response after SLA (4 complete responses, 8 partial responses, 1 stable disease). Percentage of tumor shrinkage from baseline ranged from 33%-100% (mean 75%). Patients with low-grade glioma exhibited the best responses to SLA (range 3%-100% decrease; mean 90%; 36% complete response rate).

CONCLUSIONS

SLA is a minimally invasive modality for the treatment of newly diagnosed and recurrent low-grade pediatric brain tumors. Low-grade glioma exhibited the best responses. Identification of ideal candidates for SLA, mitigation of perioperative complications, and demonstration of long-term outcomes need to be better defined in a clinical trial setting.

Characterization of G-CSF receptor expression in medulloblastoma

Background

Identifying mechanisms of medulloblastoma recurrence is a key to improving patient survival, and targeting treatment-resistant subpopulations within tumors could reduce disease recurrence. Expression of the granulocyte colony-stimulating factor receptor (G-CSF-R, CD114) is a potential marker of cancer stem cells, and therefore we hypothesized that a subpopulation of medulloblastoma cells would also express CD114 and would demonstrate chemoresistance and responsiveness to G-CSF.

Methods

Prevalence of CD114-positive (CD114+) cells in medulloblastoma cell lines, patient-derived xenograft (PDX) tumors, and primary patient tumor samples were assessed by flow cytometry. Growth rates, chemoresistance, and responses to G-CSF of CD114+ and CD114-negative (CD114−) cells were characterized in vitro using continuous live cell imaging and flow cytometry. Gene expression profiles were compared between CD114+ and CD114− medulloblastoma cells using quantitative RT-PCR.

Results

CD114+ cells were identifiable in medulloblastoma cell lines, PDX tumors, and primary patient tumors and have slower growth rates than CD114− or mixed populations. G-CSF accelerates the growth of CD114+ cells, and CD114+ cells are more chemoresistant. The CD114+ population is enriched when G-CSF treatment follows chemotherapy. The CD114+ population also has higher expression of the CSF3R, NRP-1, TWIST1, and MYCN genes.

Conclusions

Our data demonstrate that a subpopulation of CD114+ medulloblastoma cells exists in cell lines and tumors, which may evade traditional chemotherapy and respond to exogenous G-CSF. These properties invite further investigation into the role of G-CSF in medulloblastoma therapy and methods to specifically target these cells.

Propagating fronts in fluids with solutal feedback

We numerically study the propagation of reacting fronts in a shallow and horizontal layer of fluid with solutal feedback and in the presence of a thermally driven flow field of counterrotating convection rolls. We solve the Boussinesq equations along with a reaction-convection-diffusion equation for the concentration field where the products of the nonlinear autocatalytic reaction are less dense than the reactants. For small values of the solutal Rayleigh number the characteristic fluid velocity scales linearly, and the front velocity and mixing length scale quadratically, with increasing solutal Rayleigh number. For small solutal Rayleigh numbers the front geometry is described by a curve that is nearly antisymmetric about the horizontal midplane. For large values of the solutal Rayleigh number the characteristic fluid velocity, the front velocity, and the mixing length exhibit square-root scaling and the front shape collapses onto an asymmetric self-similar curve. In the presence of counterrotating convection rolls, the mixing length decreases while the front velocity increases. The complexity of the front geometry increases when both the solutal and convective contributions are significant and the dynamics can exhibit chemical oscillations in time for certain parameter values. Last, we discuss the spatiotemporal features of the complex fronts that form over a range of solutal and thermal driving.

The multikinase inhibitor RXDX-105 is effective against neuroblastoma in vitro and in vivo

Neuroblastoma is the most common extracranial solid tumor of childhood and accounts for 15% of all pediatric cancer-related deaths. New therapies are needed to improve outcomes for children with high-risk and relapsed tumors. Inhibitors of the RET kinase and the RAS-MAPK pathway have previously been shown to be effective against neuroblastoma, suggesting that combined inhibition may have increased efficacy. RXDX-105 is a small molecule inhibitor of multiple kinases, including the RET and BRAF kinases. We found that treatment of neuroblastoma cells with RXDX-105 resulted in a significant decrease in cell viability and proliferation in vitro and in tumor growth and tumor vascularity in vivo. Treatment with RXDX-105 inhibited RET phosphorylation and phosphorylation of the MEK and ERK kinases in neuroblastoma cells and xenograft tumors, and RXDX-105 treatment induced both apoptosis and cell cycle arrest. RXDX-105 also showed enhanced efficacy in combination with 13-cis-retinoic acid, which is currently a component of maintenance therapy for children with high-risk neuroblastoma. Our results demonstrate that RXDX-105 shows promise as a novel therapeutic agent for children with high-risk and relapsed neuroblastoma.

Correlations between the leading Lyapunov vector and pattern defects for chaotic Rayleigh-Bénard convection

We probe the effectiveness of using topological defects to characterize the leading Lyapunov vector for a high-dimensional chaotic convective flow field. This is accomplished using large-scale parallel numerical simulations of Rayleigh-Bénard convection for experimentally accessible conditions. We quantify the statistical correlations between the spatiotemporal dynamics of the leading Lyapunov vector and different measures of the flow field pattern's topology and dynamics. We use a range of pattern diagnostics to describe the flow field structures which includes many of the traditional diagnostics used to describe convection as well as some diagnostics tailored to capture the dynamics of the patterns. We use the ideas of precision and recall to build a statistical description of each pattern diagnostic's ability to describe the spatial variation of the leading Lyapunov vector. The precision of a diagnostic indicates the probability that it will locate a region where the Lyapunov vector is larger than a threshold value. The recall of a diagnostic indicates its ability to locate all of the possible spatial regions where the Lyapunov vector is above threshold. By varying the threshold used for the Lyapunov vector magnitude, we generate precision-recall curves which we use to quantify the complex relationship between the pattern diagnostics and the spatiotemporally varying magnitude of the leading Lyapunov vector. We find that pattern diagnostics which include information regarding the flow history outperform pattern diagnostics that do not. In particular, an emerging target defect has the highest precision of all of the pattern diagnostics we have explored.

Erratum: Exploring spiral defect chaos in generalized Swift-Hohenberg models with mean flow [Phys. Rev. E 84, 046215 (2011)]

This corrects the article DOI: 10.1103/PhysRevE.84.046215.

Velocity and geometry of propagating fronts in complex convective flow fields

We numerically study the propagation of reacting fronts through three-dimensional flow fields composed of convection rolls that include time-independent cellular flow, spatiotemporally chaotic flow, and weakly turbulent flow. We quantify the asymptotic front velocity and determine its scaling with system parameters including the local angle of the convection rolls relative to the direction of front propagation. For cellular flow fields, the orientation of the convection rolls has a significant effect upon the front velocity and the front geometry remains relatively smooth. However, for chaotic and weakly turbulent flow fields, the front velocity depends upon the geometric complexity of the wrinkled front interface and does not depend significantly upon the local orientation of the convection rolls. Using the box counting dimension we find that the front interface is fractal for chaotic and weakly turbulent flows with a dimension that increases with flow complexity.

Severe Neuropathic Pain With Concomitant Administration of Vincristine and Posaconazole

Vincristine is a chemotherapeutic agent with a potential toxicity of sensorimotor peripheral neuropathy. Patients receiving chemotherapy are in an immunocompromised state and may require antifungal agents. Triazole antifungals are known inhibitors of cytochrome P450 (CYP) enzymes. Vincristine is a known CYP3A4 and CYP3A5 substrate, and concomitant administration with fluconazole or voriconazole has been reported to increase vincristine toxicity and peripheral neuropathy, but there is limited literature on posaconazole in this regard. This 5-year-old girl with pre-B-cell acute lymphoblastic leukemia received vincristine while receiving posaconazole for a mucormycosis infection and developed unexpectedly severe peripheral neuropathy. After recovery, the child continued on mucormycosis prophylaxis with posaconazole with instructions to hold for 2 days before and on the day of vincristine administration. This case illustrates the potentiating effect that posaconazole had on vincristine-associated neurotoxicity, and our approach to mitigating that negative interaction.

Chaotic Rayleigh-Bénard convection with finite sidewalls

We explore the role of finite sidewalls on chaotic Rayleigh-Bénard convection. We use large-scale parallel spectral-element numerical simulations for the precise conditions of experiment for cylindrical convection domains. We solve the Boussinesq equations for thermal convection and the conjugate heat transfer problem for the energy transfer at the solid sidewalls of the cylindrical domain. The solid sidewall of the convection domain has finite values of thickness, thermal conductivity, and thermal diffusivity. We compute the Lyapunov vectors and exponents for the entire fluid-solid coupled problem. We quantify the chaotic dynamics of convection over a range of thermal sidewall boundary conditions. We find that the dynamics become less chaotic as the thermal conductivity of the sidewalls increases as measured by the value of the fractal dimension of the dynamics. The thermal conductivity of the sidewall is a stabilizing influence; the heat transfer between the fluid and solid regions is always in the direction to reduce the fluid motion near the sidewalls. Although the heat interaction for strongly conducting sidewalls is only about 1% of the heat transfer through the fluid layer, it is sufficient to reduce the fractal dimension of the dynamics by approximately 25% in our computations.

Spatiotemporal dynamics of the covariant Lyapunov vectors of chaotic convection

We explore the spatiotemporal dynamics of the spectrum of covariant Lyapunov vectors for chaotic Rayleigh-Bénard convection. We use the inverse participation ratio to quantify the amount of spatial localization of the covariant Lyapunov vectors. The covariant Lyapunov vectors are found to be spatially localized at times when the instantaneous covariant Lyapunov exponents are large. The spatial localization of the Lyapunov vectors often occurs near defect structures in the fluid flow field. There is an overall trend of decreasing spatial localization of the Lyapunov vectors with increasing index of the vector. The spatial localization of the covariant Lyapunov vectors with positive Lyapunov exponents decreases an order of magnitude faster with increasing vector index than all of the remaining vectors that we have computed. We find that a weighted covariant Lyapunov vector is useful for the visualization and interpretation of the significant connections between the Lyapunov vectors and the flow field patterns.

Challenges of assessing response to therapy in non-Hodgkin's lymphoma of the bone

A 17-year-old male adolescent was diagnosed with diffuse large B cell lymphoma arising from the right humeral head. The lymphoma was found to be isolated to the bone, with a very small extraosseous component. After completion of a standard chemotherapy regimen, the Positron Emission Tomography-Computed Tomography (PET-CT) became PET negative but the CT and MRI appeared mostly unchanged in appearance, suggesting refractory disease. Repeat biopsy confirmed that no lymphoma remained, and he was in complete remission. Three months after completion of therapy, MRI continued to be abnormal. This case illustrates the unique challenges posed by the imaging characteristics of bone lymphoma, both during and after therapy. Biopsy is definitive but causes additional morbidity and may not be necessary. Imaging is done routinely to assess response to therapy, as with this patient, but in lymphomas of the bone imaging can be misleading and can lead to unnecessary procedures or follow-up imaging.

Abstract OT2-06-03: METAMORPH: METAstatic markers of recurrent tumor PHenotype for breast cancer

Up to 30% of patients diagnosed with breast cancer will develop recurrent disease within their lifetime, and currently this form of the disease is incurable. There are unmet needs to better understand underlying metastatic biology, identify new therapeutic targets and develop better methods for monitoring changes in disease, both to monitor response and elucidate resistance mechanisms. To address these needs, the METAMORPH Study encompasses a comprehensive approach that combines serial molecular tissue profiling at the RNA and DNA level with circulating markers (DTCs, CTCs, plasma tumor DNA), and ongoing assessment of therapeutic response.

METAMORPH is a prospective cohort study of women with suspected or confirmed recurrent breast cancer and accessible tumor by standard clinical biopsy, who are enrolled at the University of Pennsylvania prior to starting a new therapy for recurrent metastatic disease. The aims of this trial are to (1) evaluate the mechanisms through which recurrent breast cancer are genetically distinct from the primary tumor, (2) evaluate the circulating tumor biomarker trajectory of recurrent disease, (3) elucidate “escape pathways” of progressing tumors that emerge during the selective pressure of therapy, and (4) explore clinical utility of tumor and blood testing. The study protocol integrates research aims into clinical care, including a standardized approach to disease assessment and biopsy, pathologic confirmation of histology and receptor subtype, panel-based CLIA-approved genomic profiling, collection of research specimens, and standardized reporting of results, which are returned to patients and physicians. Patients are followed for treatment and outcome, and serial samples are collected at progression. A companion protocol, COMET, provides education about genomic testing and assesses patient understanding and impact of results. To date, 155 patients have enrolled, 142 (92%) have been biopsied, 120 (77%) have had sufficient DNA for molecular profiling and 109 (70%) have had genomic panel testing. Accrual is ongoing, with an initial target of 300 patients. Multiple sites within the UPHS Health System are enrolling. Contact information: angela.demichele@uphs.upenn.edu.

Key words: Metastatic disease, tumor profiling.

Citation Format: DeMichele A, Soucier-Ernst DJ, Clark C, Shih N, Stavropoulos W, Maxwell KN, Feldman M, Lierbamen D, Morrissette JJD, Paul MR, Pan T-C, Wang J, Belka GK, Chen Y, Yee S, Carpenter E, Fox K, Matro J, Clark A, Shah P, Domchek S, Bradbury A, Chodosh L. METAMORPH: METAstatic markers of recurrent tumor PHenotype for breast cancer [abstract]. In: Proceedings of the 2017 San Antonio Breast Cancer Symposium; 2017 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2018;78(4 Suppl):Abstract nr OT2-06-03.

Abstract PD8-04: Evolutionary history and genomic landscape of metastatic breast cancer

Background: The majority of deaths from breast cancer are due to distant metastatic disease. Despite this, few systematic genomic analyses have been performed on metastatic tumors. This results from the relative difficulty of performing biopsies on metastatic tumors, as well as the uncertainty regarding genomic determinism, according to which the majority of actionable mutations present in metastases can be discovered in the primary tumor.

Methods: “METAMORPH” is an ongoing prospective cohort study of women with suspected or confirmed recurrent breast cancer enrolled prior to starting a new therapy for recurrent metastatic disease. Biopsies of metastatic lesions were performed under radiologic guidance, and archival primary tumors were subsequently obtained. WES and sWGS were performed to determine coding mutations and aberrant copy-number in metastatic tumors from 67 patients, 33 of which were assayed with corresponding matched primary tumors.

Results: Using Bayesian approaches, we find that cancers fit one of two patterns: canonical linear evolution (whereby the metastatic tumor arises from one or more advanced primary tumor subclones) vs. branched evolution (whereby both primary and metastatic tumors develop mutations that go on to become clonal within their respective tumors after the time of dissemination). In cases where tumors show evidence of branched evolution or small subclone dissemination, we expect that a large proportion of mutations may not be represented in both the primary and corresponding metastatic tumors. Indeed, primary-metastatic tumor pairs show substantial discordance at the genomic level, sharing only ˜30% of mutations and ˜28% of copy-number alterations on average. Furthermore, we find that metastatic tumors have decreased clonal heterogeneity, suggesting a history of selection. Indeed, we find clinically relevant mutations that are present exclusively in the primary or the corresponding recurrent metastatic tumor, as well as genes that are recurrently altered in metastatic tumors, such as amplification of SRC-1, loss of genes encoding CDK inhibitors, and alterations in JAK1/2/3.Finally, compared to the primary tumors from which they arose, metastatic tumors exhibit increased frequencies of alterations in several discrete pathways, including those involving the extracellular matrix as well as PI3K/AKT/mTOR, estrogen, and HER2 signaling.

Conclusions: The low degree of genomic concordance between primary and metastatic tumors due to evolutionary distance, as well as the presence of activating and targetable mutations specifically in metastatic tumors, suggests that there is value in comprehensively characterizing metastatic tumors to inform patient treatment and identify novel targets underlying breast cancer progression.

Citation Format: Paul MR, Pan T-C, Pant D, Belka GK, Chen Y, Shih N, Lieberman D, Morrissette JJD, Soucier-Ernst D, Clark C, Stavropoulos W, Maxwell K, Feldman M, DeMichele A, Chodosh LA. Evolutionary history and genomic landscape of metastatic breast cancer [abstract]. In: Proceedings of the 2017 San Antonio Breast Cancer Symposium; 2017 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2018;78(4 Suppl):Abstract nr PD8-04.

Treatment of immune thrombocytopenic purpura associated with cytomegalovirus infection in a child with pre-B cell acute lymphoblastic leukaemia after central nervous system relapse

A 13-year-old male patient with a history of pre-B cell acute lymphoblastic leukaemia (ALL) with isolated central nervous system relapse on maintenance chemotherapy presented with severe thrombocytopenia refractory to platelet transfusions. The patient showed only modest responses to two courses of intravenous immunoglobulin and steroids. He was found to be positive for cytomegalovirus (CMV) with modest viral load. His thrombocytopenia normalised with rituximab therapy and CMV treatment supporting the diagnosis of CMV-associated immune thrombocytopenic purpura (ITP). Following treatment, the patient continued to have a stable platelet count well above the threshold for transfusions. He continued to be intermittently treated for CMV when viral loads became detectable. This report discusses the unique management considerations of ITP in a patient undergoing therapy for ALL with a review of previously reported cases and discusses the possibility of CMV viraemia as a modulating factor.

Covariant Lyapunov vectors of chaotic Rayleigh-Bénard convection

We explore numerically the high-dimensional spatiotemporal chaos of Rayleigh-Bénard convection using covariant Lyapunov vectors. We integrate the three-dimensional and time-dependent Boussinesq equations for a convection layer in a shallow square box geometry with an aspect ratio of 16 for very long times and for a range of Rayleigh numbers. We simultaneously integrate many copies of the tangent space equations in order to compute the covariant Lyapunov vectors. The dynamics explored has fractal dimensions of 20≲D_{λ}≲50, and we compute on the order of 150 covariant Lyapunov vectors. We use the covariant Lyapunov vectors to quantify the degree of hyperbolicity of the dynamics and the degree of Oseledets splitting and to explore the temporal and spatial dynamics of the Lyapunov vectors. Our results indicate that the chaotic dynamics of Rayleigh-Bénard convection is nonhyperbolic for all of the Rayleigh numbers we have explored. Our results yield that the entire spectrum of covariant Lyapunov vectors that we have computed are tangled as indicated by near tangencies with neighboring vectors. A closer look at the spatiotemporal features of the Lyapunov vectors suggests contributions from structures at two different length scales with differing amounts of localization.

Nanomechanical motion of Escherichia coli adhered to a surface

Nanomechanical motion of bacteria adhered to a chemically functionalized silicon surface is studied by means of a microcantilever. A non-specific binding agent is used to attach Escherichia coli (E. coli) to the surface of a silicon microcantilever. The microcantilever is kept in a liquid medium, and its nanomechanical fluctuations are monitored using an optical displacement transducer. The motion of the bacteria couples efficiently to the microcantilever well below its resonance frequency, causing a measurable increase in the microcantilever fluctuations. In the time domain, the fluctuations exhibit large-amplitude low-frequency oscillations. In corresponding frequency-domain measurements, it is observed that the mechanical energy is focused at low frequencies with a 1/f^α -type power law. A basic physical model is used for explaining the observed spectral distribution of the mechanical energy. These results lay the groundwork for understanding the motion of microorganisms adhered to surfaces and for developing micromechanical sensors for bacteria.

Front propagation in a chaotic flow field

We investigate numerically the dynamics of a propagating front in the presence of a spatiotemporally chaotic flow field. The flow field is the three-dimensional time-dependent state of spiral defect chaos generated by Rayleigh-Bénard convection in a spatially extended domain. Using large-scale parallel numerical simulations, we simultaneously solve the Boussinesq equations and a reaction-advection-diffusion equation with a Fischer-Kolmogorov-Petrovskii-Piskunov reaction for the transport of the scalar species in a large-aspect-ratio cylindrical domain for experimentally accessible conditions. We explore the front dynamics and geometry in the low-Damköhler-number regime, where the effect of the flow field is significant. Our results show that the chaotic flow field enhances the front propagation when compared with a purely cellular flow field. We quantify this enhancement by computing the spreading rate of the reaction products for a range of parameters. We use our results to quantify the complexity of the three-dimensional front geometry for a range of chaotic flow conditions.

Coupled motion of microscale and nanoscale elastic objects in a viscous fluid

We study the coupled dynamics of two closely spaced micron or nanoscale elastic objects immersed in a viscous fluid. The dynamics of the elastic objects are coupled through the motion of the surrounding viscous fluid. We consider two cases: (i) one object is driven externally by an imposed harmonic actuation force and the second object is passive and (ii) both objects are driven by a Brownian force to yield stochastic dynamics. Using a harmonic oscillator approximation for the elastic objects and the unsteady Stokes equations to describe the fluid dynamics, we develop analytical expressions for the amplitude and phase of the displacement of the oscillating objects. For the case of an imposed actuation we use an impulse in force to determine the resulting dynamics over all frequencies. For the Brownian-driven objects the stochastic dynamics are found using the fluctuation-dissipation theorem. We validate our theoretical expressions by comparison with results from finite-element numerical simulations of the complete fluid-solid interaction problem. Our results yield interesting features in the amplitude and phase of the displacement of the elastic objects due to the fluid motion. We find that the dynamics depend on the separation of the objects, a measure of the mass loading due to the fluid, and the frequency parameter which acts as a frequency-based Reynolds number. Our results are valid over the range of parameters typical of micron and nanoscale elastic objects in fluid. The range of dynamics found can be understood in terms of the interplay between the viscous and potential components of the fluid flow field described by the unsteady Stokes equation for an oscillating cylinder. For small values of the frequency parameter, typical of nanoscale elastic objects, the dynamics are overdamped due to the dominance of viscous forces over inertial forces. For moderate and large values of the frequency parameter, typical of micron-scale elastic objects, we find that the dynamics of the fluid-coupled objects exhibits an interesting mode splitting to yield a bimodal signature in the amplitude-frequency plots. We find that the mode splitting can be described using a normal mode analysis containing only potential fluid interactions between the cylinders.

Bioconvection in spatially extended domains

We numerically explore gyrotactic bioconvection in large spatially extended domains of finite depth using parameter values from available experiments with the unicellular alga Chlamydomonas nivalis. We numerically integrate the three-dimensional, time-dependent continuum model of Pedley et al. [J. Fluid Mech. 195, 223 (1988)] using a high-order, parallel, spectral-element approach. We explore the long-time nonlinear patterns and dynamics found for layers with an aspect ratio of 10 over a range of Rayleigh numbers. Our results yield the pattern wavelength and pattern dynamics which we compare with available theory and experimental measurement. There is good agreement for the pattern wavelength at short times between numerics, experiment, and a linear stability analysis. At long times we find that the general sequence of patterns given by the nonlinear evolution of the governing equations correspond qualitatively to what has been described experimentally. However, at long times the patterns in numerics grow to larger wavelengths, in contrast to what is observed in experiment where the wavelength is found to decrease with time.

Length scale of a chaotic element in Rayleigh-Bénard convection

We describe an approach to quantify the length scale of a chaotic element of a Rayleigh-Bénard convection layer exhibiting spatiotemporal chaos. The length scale of a chaotic element is determined by simultaneously evolving the dynamics of two convection layers with a unidirectional coupling that involves only the time-varying values of the fluid velocity and temperature on the lateral boundaries of the domain. In our results we numerically simulate the full Boussinesq equations for the precise conditions of experiment. By varying the size of the boundary used for the coupling we identify a length scale that describes the size of a chaotic element. The length scale of the chaotic element is of the same order of magnitude, and exhibits similar trends, as the natural chaotic length scale that is based upon the fractal dimension.

Quantifying spatiotemporal chaos in Rayleigh-Bénard convection

Using large-scale parallel numerical simulations we explore spatiotemporal chaos in Rayleigh-Bénard convection in a cylindrical domain with experimentally relevant boundary conditions. We use the variation of the spectrum of Lyapunov exponents and the leading-order Lyapunov vector with system parameters to quantify states of high-dimensional chaos in fluid convection. We explore the relationship between the time dynamics of the spectrum of Lyapunov exponents and the pattern dynamics. For chaotic dynamics we find that all of the Lyapunov exponents are positively correlated with the leading-order Lyapunov exponent, and we quantify the details of their response to the dynamics of defects. The leading-order Lyapunov vector is used to identify topological features of the fluid patterns that contribute significantly to the chaotic dynamics. Our results show a transition from boundary-dominated dynamics to bulk-dominated dynamics as the system size is increased. The spectrum of Lyapunov exponents is used to compute the variation of the fractal dimension with system parameters to quantify how the underlying high-dimensional strange attractor accommodates a range of different chaotic dynamics.

Exploring spiral defect chaos in generalized Swift-Hohenberg models with mean flow

We explore the phenomenon of spiral defect chaos in two types of generalized Swift-Hohenberg model equations that include the effects of long-range drift velocity or mean flow. We use spatially extended domains and integrate the equations for very long times to study the pattern dynamics as the magnitude of the mean flow is varied. The magnitude of the mean flow is adjusted via a real and continuous parameter that accounts for the fluid boundary conditions on the horizontal surfaces in a convecting layer. For weak values of the mean flow, we find that the patterns exhibit a slow coarsening to a state dominated by large and very slowly moving target defects. For strong enough mean flow, we identify the existence of spatiotemporal chaos, which is indicated by a positive leading-order Lyapunov exponent. We compare the spatial features of the mean flow field with that of Rayleigh-Bénard convection and quantify their differences in the neighborhood of spiral defects.

Extensive chaos in the Lorenz-96 model

We explore the high-dimensional chaotic dynamics of the Lorenz-96 model by computing the variation of the fractal dimension with system parameters. The Lorenz-96 model is a continuous in time and discrete in space model first proposed by Lorenz to study fundamental issues regarding the forecasting of spatially extended chaotic systems such as the atmosphere. First, we explore the spatiotemporal chaos limit by increasing the system size while holding the magnitude of the external forcing constant. Second, we explore the strong driving limit by increasing the external forcing while holding the system size fixed. As the system size is increased for small values of the forcing we find dynamical states that alternate between periodic and chaotic dynamics. The windows of chaos are extensive, on average, with relative deviations from extensivity on the order of 20%. For intermediate values of the forcing we find chaotic dynamics for all system sizes past a critical value. The fractal dimension exhibits a maximum deviation from extensivity on the order of 5% for small changes in system size and the deviation from extensivity decreases nonmonotonically with increasing system size. The length scale describing the deviations from extensivity is consistent with the natural chaotic length scale in support of the suggestion that deviations from extensivity are due to the addition of chaotic degrees of freedom as the system size is increased. We find that each wavelength of the deviation from extensive chaos contains on the order of two chaotic degrees of freedom. As the forcing is increased, at constant system size, the dimension density grows monotonically and saturates at a value less than unity. We use this to quantify the decreasing size of chaotic degrees of freedom with increased forcing which we compare with spatial features of the patterns.

Stochastic dynamics of micron-scale doubly clamped beams in a viscous fluid

We study the stochastic dynamics of doubly clamped micron-scale beams in a viscous fluid driven by Brownian motion. We use a thermodynamic approach to compute the equilibrium fluctuations in beam displacement that requires only deterministic calculations. From calculations of the autocorrelations and noise spectra we quantify the beam dynamics by the quality factor and resonant frequency of the fundamental flexural mode over a wide range of experimentally accessible geometries. We consider beams with uniform rectangular cross section and explore the increased quality factor and resonant frequency as a baseline geometry is varied by increasing the width, increasing the thickness, and decreasing the length. The quality factor is nearly doubled by tripling either the width or the height of the beam. Much larger improvements are found by decreasing the beam length, however this is limited by the appearance of additional modes of fluid dissipation. Overall, the stochastic dynamics of the wider and thicker beams are well predicted by a two-dimensional approximate theory beyond what may be expected based upon the underlying assumptions, whereas the shorter beams require a more detailed analysis.

Extensive chaos in Rayleigh-Bénard convection

Using large-scale numerical calculations we explore spatiotemporal chaos in Rayleigh-Bénard convection for experimentally relevant conditions. We calculate the spectrum of Lyapunov exponents and the Lyapunov dimension describing the chaotic dynamics of the convective fluid layer at constant thermal driving over a range of finite system sizes. Our results reveal that the dynamics of fluid convection is truly chaotic for experimental conditions as illustrated by a positive leading-order Lyapunov exponent. We also find the chaos to be extensive over the range of finite-sized systems investigated as indicated by a linear scaling between the Lyapunov dimension of the chaotic attractor and the system size.

The kinetics of analyte capture on nanoscale sensors

This article presents a number of kinetic analyses related to binding processes relevant to capture of target analyte species in nanoscale cantilever-type devices designed to detect small concentrations of biomolecules. The overall analyte capture efficiency is a crucial measure of the ultimate sensitivity of such devices, and a detailed kinetic analysis tells us how rapidly such measurements may be made. We have analyzed the capture kinetics under a variety of conditions, including the possibility of so-called surface-enhanced ligand capture. One of the modalities studied requires ligand capture through a cross-linking mechanism, and it was found that this mode may provide a robust and sensitive approach to biomolecular detection. For the two modalities studied, we find that detection of specific biomolecules down to concentration levels of 1 nM or less appear to be quite feasible for the device configurations studied.

Rayleigh-Bénard convection in large-aspect-ratio domains

The coarsening and wave number selection of striped states growing from random initial conditions are studied in a nonrelaxational, spatially extended, and far-from-equilibrium system by performing large-scale numerical simulations of Rayleigh-Bénard convection in a large-aspect-ratio cylindrical domain with experimentally realistic boundaries. We find evidence that various measures of the coarsening dynamics scale in time with different power-law exponents, indicating that multiple length scales are required in describing the time dependent pattern evolution. The translational correlation length scales with time as t0.12, the orientational correlation length scales as t0.54, and the density of defects scale as t(-0.45). The final pattern evolves toward the wave number where isolated dislocations become motionless, suggesting a possible wave number selection mechanism for large-aspect-ratio convection.

Stochastic dynamics of nanoscale mechanical oscillators immersed in a viscous fluid

The stochastic response of nanoscale oscillators of arbitrary geometry immersed in a viscous fluid is studied. Using the fluctuation-dissipation theorem, it is shown that deterministic calculations of the governing fluid and solid equations can be used in a straightforward manner to directly calculate the stochastic response that would be measured in experiment. We use this approach to investigate the fluid coupled motion of single and multiple cantilevers with experimentally motivated geometries.

Traveling waves in rotating Rayleigh-Bénard convection: analysis of modes and mean flow

Numerical simulations of the Boussinesq equations with rotation for realistic no-slip boundary conditions and a finite annular domain are presented. These simulations reproduce traveling waves observed experimentally. Traveling waves are studied near threshold by using the complex Ginzburg-Landau equation (CGLE): a mode analysis enables the CGLE coefficients to be determined. The CGLE coefficients are compared with previous experimental and theoretical results. Mean flows are also computed and found to be more significant as the Prandtl number decreases (from sigma=6.4 to sigma=1). In addition, the mean flow around the outer radius of the annulus appears to be correlated with the mean flow around the inner radius.

Mean flow and spiral defect chaos in Rayleigh-Bénard convection

We describe a numerical procedure to construct a modified velocity field that does not have any mean flow. Using this procedure, we present two results. First, we show that, in the absence of the mean flow, spiral defect chaos collapses to a stationary pattern comprising textures of stripes with angular bends. The quenched patterns are characterized by mean wave numbers that approach those uniquely selected by focus-type singularities, which, in the absence of the mean flow, lie at the zigzag instability boundary. The quenched patterns also have larger correlation lengths and are comprised of rolls with less curvature. Secondly, we describe how the mean flow can contribute to the commonly observed phenomenon of rolls terminating perpendicularly into lateral walls. We show that, in the absence of the mean flow, rolls begin to terminate into lateral walls at an oblique angle. This obliqueness increases with the Rayleigh number.

Rayleigh-Bénard convection with a radial ramp in plate separation

Pattern formation in Rayleigh-Bénard convection in a large-aspect-ratio cylinder with a radial ramp in the plate separation is studied analytically and numerically by performing numerical simulations of the Boussinesq equations. A horizontal mean flow and a vertical large scale counterflow are quantified and used to understand the pattern wave number. Our results suggest that the mean flow, generated by amplitude gradients, plays an important role in the roll compression observed as the control parameter is increased. Near threshold, the mean flow has a quadrupole dependence with a single vortex in each quadrant while away from threshold the mean flow exhibits an octupole dependence with a counterrotating pair of vortices in each quadrant. This is confirmed analytically using the amplitude equation and Cross-Newell mean flow equation. By performing numerical experiments, the large scale counterflow is also found to aid in the roll compression away from threshold but to a much lesser degree. Our results yield an understanding of the pattern wave numbers observed in experiment away from threshold and suggest that near threshold the mean flow and large scale counterflow are not responsible for the observed shift to smaller than critical wave numbers.

Quantifying mosquito biting patterns on humans by DNA fingerprinting of bloodmeals

A major debate in infectious disease epidemiology concerns the relative importance of exposure and host factors, such as sex and acquired immunity, in determining observed age patterns of parasitic infection in endemic communities. Nonhomogeneous contact between hosts and vectors is also expected to increase the reproductive rate, and hence transmission, of mosquito-borne infections. Resolution of these questions for human parasitic diseases has been frustrated by the lack of a quantitative tool for quantifying the exposure rate of people in communities. Here, we show that the polymerase chain reaction (PCR) technique for amplifying and fingerprinting human DNA from mosquito bloodmeals can address this problem for mosquito-borne diseases. Analysis of parallel human and mosquito (resting Culex quinquefasciatus) samples from the same households in an urban endemic focus for bancroftian filariasis in South India demonstrates that a 9-locus radioactive short-tandem repeat system is able to identify the source of human DNA within the bloodmeals of nearly 80% of mosquitoes. The results show that a person's exposure rate, and hence the age and sex patterns of exposure to bites in an endemic community, can be successfully quantified by this method. Out of 276 bloodmeal PCR fingerprints, we also found that on average, 27% of the mosquitoes caught resting within individual households had fed on people outside the household. Additionally, 13% of mosquitoes biting within households contained blood from at least 2 people, with the rate of multiple feeding depending on the density of humans in the household. These complex vector feeding behaviors may partly account for the discrepancies in estimates of the infection rates of mosquito-borne diseases calculated parasitologically and entomologically, and they underline the potential of this tool for investigating the transmission dynamics of infection.

Power-law behavior of power spectra in low Prandtl number Rayleigh-Bénard convection

The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Bénard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains. The power law is found to arise from quasidiscontinuous changes in the slope of the time series of the heat transport associated with the nucleation of dislocation pairs and roll pinch-off events. For larger frequencies, the power spectra decay exponentially as expected for time continuous deterministic dynamics.

Local reduction of organ size in transgenic mice expressing a soluble insulin-like growth factor II/mannose-6-phosphate receptor

Genetic evidence suggests that the insulin-like growth factor II (IGF-II)/mannose-6-phosphate receptor (IGF2R) slows growth. A soluble form of IGF2R (sIGF2R) is produced by proteolytic cleavage of the intact cellular receptor and is found at high levels in fetal and neonatal plasma. To test the hypothesis that sIGF2R modulates organ size in vivo, we generated transgenic mice expressing a mouse Igf2r complementary DNA in which the transmembrane domain sequence was deleted. The transgene was driven by the keratin-10 promoter and was expressed at the highest levels in the skin and alimentary canal. Transgenics showed disproportionately reduced size of the alimentary canal, where the wet weight was decreased by 9-20% and the dry weight was decreased by 20-30%, whereas the water content per unit dry weight was not significantly changed. In addition, the circulating levels of IGF-II and the latent form of transforming growth factor-beta1 were increased by 58-77% and 56-140%, respectively, whereas plasma epidermal growth factor levels showed a 24-35% reduction. The serum and tissue activities of four lysosomal enzymes were not affected, with the exception of the colon in the line expressing the transgene at highest levels, where enzyme activities were decreased compared with control values. These results support a significant role for the sIGF2R in local modulation of organ size in vivo.