Analysis of electrophoretic mobility data for human erythrocytes according to sublayer models

An attempt was made to analyze the electrophoretic mobility data of human erythrocytes in media of different pH values and ionic strengths through cell surface models in which the surface charge layer consists of several ion-penetrable sublayers with a uniform charge distribution in each sublayer. As a result, the three-sublayer model was found to explain the mobility data much better than the two-sublayer model in a wide range of ionic strength at all pH values studied.     

Deriving dispersal distances from genetic data.

Dispersal is one of the most important factors determining the genetic structure of a population, but good data on dispersal distances are rare because it is difficult to observe a large sample of dispersal events. However, genetic data contain unbiased information about the average dispersal distances in species with a strong sex bias in their dispersal rates. By plotting the genetic similarity between members of the philopatric sex against some measure of the distance between them, the resulting regression line can be used for estimating how far dispersing individuals of the opposite sex have moved before settling. Dispersers showing low genetic similarity to members of the opposite sex will on average have originated from further away. Applying this method to a microsatellite dataset from lions (Panthera leo) shows that their average dispersal distance is 1.3 home ranges with a 95% confidence interval of 0.4-3.0 home ranges. These results are consistent with direct observations of dispersal from our study population and others. In this case, direct observations of dispersal distance were not detectably biased by a failure to detect long-range dispersal, which is thought to be a common problem in the estimation of dispersal distance.     

Deriving quantitative conclusions from microarray expression data

MOTIVATION: The last few years have seen the development of DNA microarray technology that allows simultaneous measurement of the expression levels of thousands of genes. While many methods have been developed to analyze such data, most have been visualization-based. Methods that yield quantitative conclusions have been diverse and complex. RESULTS: We present two straightforward methods for identifying specific genes whose expression is linked with a phenotype or outcome variable as well as for systematically predicting sample class membership: (1) a conservative, permutation-based approach to identifying differentially expressed genes; (2) an augmentation of K-nearest-neighbor pattern classification. Our analyses replicate the quantitative conclusions of Golub et al. (1999; Science, 286, 531-537) on leukemia data, with better classification results, using far simpler methods. With the breast tumor data of Perou et al. (2000; Nature, 406, 747-752), the methods lend rigorous quantitative support to the conclusions of the original paper. In the case of the lymphoma data in Alizadeh et al. (2000; Nature, 403, 503-511), our analyses only partially support the conclusions of the original authors. AVAILABILITY: The software and supplementary information are available freely to researchers at academic and non-profit institutions at http://cc.ucsf.edu/jain/public     

Deriving biomedical diagnostics from NMR spectroscopic data

Biomedical spectroscopic experiments generate large volumes of data. For accurate, robust diagnostic tools the data must be analyzed for only a few characteristic observations per subject, and a large number of subjects must be studied. We describe here two of the current data analytic approaches applied to this problem: SIMCA (principal component analysis, partial least squares), and the statistical classification strategy (SCS). We demonstrate the application of the SCS by three examples of its use in analyzing ¹H NMR spectra: screening for colon cancer, characterization of thyroid cancer, and distinguishing cancer from cholangitis in the biliary tract.     

Intra-specific niche partitioning obscures the importance of fine-scale habitat data in species distribution models

Geographic information systems (GIS) allow researchers to make cost-effective, spatially explicit predictions of species’ distributions across broad geographic areas. However, there has been little research on whether using fine-scale habitat data collected in the field could produce more robust models of species’ distributions. Here we used radio-telemetry data collected on a declining species, the North American wood turtle (Glyptemys insculpta), to test whether fine-scale habitat variables were better predictors of occurrence than land-cover and topography variables measured in a GIS. Patterns of male and female occurrence were similar in the spring; however, females used a much wider array of land-cover types and topographic positions in the summer and early fall, making it difficult for GIS-based models to accurately predict female occurrence at this time of year. Males on the other hand consistently selected flat, low-elevation, riparian areas throughout the year, and this consistency in turn led to the development of a strong GIS-based model. These results demonstrate the importance of taking a more sex-specific and temporally dynamic view of the environmental niche.     

Estimating linear temporal trends from aggregated environmental monitoring data

Trend estimates are often used as part of environmental monitoring programs. These trends inform managers (e.g., are desired species increasing or undesired species decreasing?). Data collected from environmental monitoring programs is often aggregated (i.e., averaged), which confounds sampling and process variation. State-space models allow sampling variation and process variations to be separated. We used simulated time-series to compare linear trend estimations from three state-space models, a simple linear regression model, and an auto-regressive model. We also compared the performance of these five models to estimate trends from a long term monitoring program. We specifically estimated trends for two species of fish and four species of aquatic vegetation from the Upper Mississippi River system. We found that the simple linear regression had the best performance of all the given models because it was best able to recover parameters and had consistent numerical convergence. Conversely, the simple linear regression did the worst job estimating populations in a given year. The state-space models did not estimate trends well, but estimated population sizes best when the models converged. We found that a simple linear regression performed better than more complex autoregression and state-space models when used to analyze aggregated environmental monitoring data.     

Comparative phylogeographic inference with genome-wide data from aggregated population pairs

Comparing divergences across multiple sister population pairs has been a focus in phylogeography since its inception. Initial approaches used organelle genetic data and involved qualitative comparisons of phylogenetic patterns to evaluate hypotheses of shared and variable evolutionary responses. This endeavor has progressed with coalescent model-based statistical techniques and advances in next-generation sequencing, yet there remains a need for methods that can exploit aggregated genomic-scale data within a unified analytical framework. To this end, we introduce the aggregate joint site frequency spectrum (ajSFS) by validating its use within a hierarchical Bayesian framework through several in silico experiments. Subsequently, we applied our method against two published restriction site–associated DNA marker datasets consisting of eight local replicates of a lamprey species pair and six co-distributed passerine taxon pairs, respectively, with the aim of inferring variability in co-divergence and co-migration histories. We found that the lamprey population pairs exhibited temporal synchrony in both co-divergence and collective secondary contact times, yet an idiosyncratic pattern in secondary migration intensities. In contrast, the bird population pairs displayed thoroughly asynchronous co-divergence histories. Our results demonstrate that the ajSFS can be exploited for complex and flexible co-demographic inference, opening up new possibilities for comparative phylogeography and population genomic studies.     

Deriving enzymatic and taxonomic signatures of metagenomes from short read data

Background  

We propose a method for deriving enzymatic signatures from short read metagenomic data of unknown species. The short read data are converted to six pseudo-peptide candidates. We search for occurrences of Specific Peptides (SPs) on the latter. SPs are peptides that are indicative of enzymatic function as defined by the Enzyme Commission (EC) nomenclature. The number of SP hits on an ensemble of short reads is counted and then converted to estimates of numbers of enzymatic genes associated with different EC categories in the studied metagenome. Relative amounts of different EC categories define the enzymatic spectrum, without the need to perform genomic assemblies of short reads.     

Inferring the effective reproductive number from deterministic and semi-deterministic compartmental models using incidence and mobility data

The effective reproduction number (ℜ_t) is a theoretical indicator of the course of an infectious disease that allows policymakers to evaluate whether current or previous control efforts have been successful or whether additional interventions are necessary. This metric, however, cannot be directly observed and must be inferred from available data. One approach to obtaining such estimates is fitting compartmental models to incidence data. We can envision these dynamic models as the ensemble of structures that describe the disease’s natural history and individuals’ behavioural patterns. In the context of the response to the COVID-19 pandemic, the assumption of a constant transmission rate is rendered unrealistic, and it is critical to identify a mathematical formulation that accounts for changes in contact patterns. In this work, we leverage existing approaches to propose three complementary formulations that yield similar estimates for ℜ_t based on data from Ireland’s first COVID-19 wave. We describe these Data Generating Processes (DGP) in terms of State-Space models. Two (DGP1 and DGP2) correspond to stochastic process models whose transmission rate is modelled as Brownian motion processes (Geometric and Cox-Ingersoll-Ross). These DGPs share a measurement model that accounts for incidence and transmission rates, where mobility data is assumed as a proxy of the transmission rate. We perform inference on these structures using Iterated Filtering and the Particle Filter. The final DGP (DGP3) is built from a pool of deterministic models that describe the transmission rate as information delays. We calibrate this pool of models to incidence reports using Hamiltonian Monte Carlo. By following this complementary approach, we assess the tradeoffs associated with each formulation and reflect on the benefits/risks of incorporating proxy data into the inference process. We anticipate this work will help evaluate the implications of choosing a particular formulation for the dynamics and observation of the time-varying transmission rate.     

Equivalence of aggregated Markov models of ion-channel gating

One cannot always distinguish different Markov models of ion-channel kinetics solely on the basis of steady-state kinetic data. If two generator (or transition) matrices are related by a similarity transformation that does not combine states with different conductances, then the models described by these generator matrices have the same observable steady-state statistics. This result suggests a procedure for expressing the model in a unique form, and sometimes reducing the number of parameters in a model. I apply the similarity transformation procedure to a number of simple models. When a model specifies the dependence of the rates of transition on an experimentally variable parameter such as the concentration of a ligand or the membrane potential, the class of equivalent models may be further restricted, but a model is not always uniquely determined even under these conditions. Voltage-step experiments produce non-stationary data that can also be used to distinguish models.     

Optimizing control programmes by integrating data from fine-scale space use by introduced predators

The control of introduced mammalian predators (IMP) through trapping campaigns relies on operator experience to deploy traps in sites with an expected high probability of IMP presence, where the maximum number of captures is anticipated. We tested the limitations of available information on fine-scale spatial use by feral cats modelled from remote data collection methods (small-resolution satellite imagery and GPS-telemetry) in an intensive control campaign conducted over 8 years in an ecologically sensitive area of New Zealand. We calculated dichotomous optimal/sub-optimal areas for cats and found that operators placed traps in or close to optimal areas. Over a continuous range of probabilities of cat use, trap sites were not principally placed in hot spots of cat use. Logistic regression revealed that the probability of cat use was significantly associated with the probability of capture. However, regressing catch-effort against the probability of cat use showed no association between sites of high probability of cat use and higher capture rates. The incorporation in the models of bait, trap type, and habitat suitability for rabbits, as variables of operator’s choice showed that rabbit suitability, and the combination of baits/traps were significant. Results suggest that trapping feral cats is a complex process that likely relies on variables of space, time, and individual cognition. However, control programmes could improve trap deployment by identifying sites of high probability of cat use to maximize capture probability, while traps in sub-optimal areas could be removed (cost reduction), reallocated to optimal areas, or used to “fence” core conservation areas.     

Rheology and ultrasound scattering from aggregated red cell suspensions in shear flow

The shear flow dynamics of reversible red cell aggregates in dense suspensions were investigated by ultrasound scattering, to study the shear disruption processes of Rayleigh clusters and examine the effective mean field approximation used in microrheological models. In a first section, a rheo-acoustical model, in the Rayleigh scattering regime, is proposed to describe the shear stress dependence of the low frequency scattered power in relation to structural parameters. The fractal scattering regime characterizing the anisotropic scattering from flocs of size larger than the ultrasound wavelength is further discussed. In the second section, we report flow-dependent changes in the low-frequency scattering coefficient in a plane-plane flow geometry to analyze the shear disruption processes of hardened or deformable red cell aggregates in neutral dextran polymer solution. Rheo-acoustical experiments are examined on the basis of the rheo-acoustical model and the effective medium approximation. The ability of ultrasound scattering technique to determine the critical disaggregation shear stress and to give quantitative information on particle surface adhesive energy is analyzed. Lastly, the shear-thinning behavior of weakly aggregated hardened or deformable red cells is described.     

Accurate state estimation from uncertain data and models: an application of data assimilation to mathematical models of human brain tumors

Background

Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this approach for making short-term (60-day) forecasts of the growth and spread of a malignant brain cancer (glioblastoma multiforme) in individual patient cases, where the observations are synthetic magnetic resonance images of a hypothetical tumor.

Results

We apply a modern state estimation algorithm (the Local Ensemble Transform Kalman Filter), previously developed for numerical weather prediction, to two different mathematical models of glioblastoma, taking into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging. The filter can accurately shadow the growth of a representative synthetic tumor for 360 days (six 60-day forecast/update cycles) in the presence of a moderate degree of systematic model error and measurement noise.

Conclusions

The mathematical methodology described here may prove useful for other modeling efforts in biology and oncology. An accurate forecast system for glioblastoma may prove useful in clinical settings for treatment planning and patient counseling.

Reviewers

This article was reviewed by Anthony Almudevar, Tomas Radivoyevitch, and Kristin Swanson (nominated by Georg Luebeck).     

Stability of discrete age-structured and aggregated delay-difference population models

Sufficiency conditions for local stability are derived for a class of density dependent Leslie matrix models. Four of the recruitment functions in common use in fisheries management are then considered. In two of these oscillating instability can never occur (Beverton and Holt and Cushing forms). In the other two (Deriso-Schnute and Shepherd forms) undamped oscillations are possible within the region of parameter space described here. An algorithm is developed for calculating necessary and sufficient local stability conditions for a simplified form of the general age-structured model. The complete spectrum of stability states (monotonic stability; monotonic instability; oscillating-stable; oscillating-unstable) and the bifurcation periods are given for selected examples of this model. The examples cover a large portion of the parameter space of interest in resource management. It is shown that in perfectly deterministic systems which are observed with error, oscillating instabilities may be missed, and such systems could be erroneously assumed to be stable.     

Deriving topological constraints from functional data for the design of reagentless fluorescent immunosensors

The possibility of obtaining, from any antibody, a fluorescent conjugate which responds to the binding of the antigen by a variation of fluorescence, would be of great interest in the micro- and nano-analytical sciences. This possibility was explored with antibody mAb4E11, which is directed against the dengue virus and for which no structural data is available. Three rules of design were developed to identify residues of the antibody to which a fluorophore could be chemically coupled, after changing them to cysteine by mutagenesis. (i) The target residue belonged to the hypervariable loops of the antibody. (ii) It was adjacent, along the amino acid sequence of the antibody, to a residue which was functionally important for the interaction with the antigen. (iii) It was not important in itself for the interaction with the antigen. Eight conjugates between a single chain variable fragment of mAb4E11 and an environment-sensitive fluorophore were constructed. Three of them showed an increase in their fluorescence intensity by 1.5-2.8-fold on antigen binding, without loss of affinity. This increase allowed the titration of the antigen in serum above a threshold concentration of 10nM. Experiments of quenching with potassium iodide suggested that the fluorescence variation was due to a shielding of the fluorescent group from the solvent by the binding of the antigen, and that therefore its mechanism is general.     

Bayesian fine-scale mapping of disease loci, by hidden Markov models

We present a new multilocus method for the fine-scale mapping of genes contributing to human diseases. The method is designed for use with multiple biallelic markers-in particular, single-nucleotide polymorphisms for which high-density genetic maps will soon be available. We model disease-marker association in a candidate region via a hidden Markov process and allow for correlation between linked marker loci. Using Markov-chain-Monte Carlo simulation methods, we obtain posterior distributions of model parameter estimates including disease-gene location and the age of the disease-predisposing mutation. In addition, we allow for heterogeneity in recombination rates, across the candidate region, to account for recombination hot and cold spots. We also obtain, for the ancestral marker haplotype, a posterior distribution that is unique to our method and that, unlike maximum-likelihood estimation, can properly account for uncertainty. We apply the method to data for cystic fibrosis and Huntington disease, for which mutations in disease genes have already been identified. The new method performs well compared with existing multi-locus mapping methods.