Relative sea-level change in northeastern Florida (USA) during the last ~8.0 ka

An existing database of relative sea-level (RSL) reconstructions from the U.S. Atlantic coast lacked valid sea-level index points from Georgia and Florida. This region lies on the edge of the collapsing forebulge of the former Laurentide Ice Sheet making it an important location for understanding glacio-isostatic adjustment and the history of ice-sheet melt. To address the paucity of data, we reconstruct RSL in northeastern Florida (St. Marys) over the last ∼8.0 ka from samples of basal salt-marsh sediment that minimize the influence of compaction. The analogy between modern salt-marsh foraminifera and their fossil counterparts preserved in the sedimentary record was used to estimate paleomarsh surface elevation. Sample ages were determined by radiocarbon dating of identifiable and in-situ plant macrofossils. This approach yielded 25 new sea-level index points that constrain a ∼5.7 m rise in RSL during the last ∼8.0 ka. The record shows that no highstand in sea level occurred in this region over the period of the reconstruction. We compared the new reconstruction to Earth-ice models ICE 6G-C VM5a and ICE 6G-C VM6. There is good fit in the later part of the Holocene with VM5a and for a brief time in the earlier Holocene with VM6. However, there are discrepancies in model-reconstruction fit in the early to mid Holocene in northeastern Florida and elsewhere along the Atlantic coast at locations with early Holocene RSL reconstructions. The most pronounced feature of the new reconstruction is a slow down in the rate of RSL rise from approximately 5.0 to 3.0 ka. This trend may reflect a significant contribution from local-scale processes such as tidal-range change and/or change in base flow of the St. Marys River in response to paleoclimate changes. However, the spatial expression (local vs. regional) of this slow down is undetermined and corroborative records are needed to establish its geographical extent

Challenges in the calibration of large-scale ordinary differential equation models.

Mathematical models based on ordinary differential equations have been employed with great success to study complex biological systems. With soaring data availability, more and more models of increasing size are being developed. When working with these large-scale models, several challenges arise, such as high computation times or poor identifiability of model parameters. In this work, we review and illustrate the most common challenges using a published model of cellular metabolism. We summarize currently available methods to deal with some of these challenges while focusing on reproducibility and reusability of models, efficient and robust model simulation and parameter estimation

Evaluation of derivative-free optimizers for parameter estimation in systems biology.

Derivative-free optimization can be used to estimate parameters without computing derivatives. As there exist many methods, it is unclear which to use in practice. Here, we present two comparative studies of 18 state-of-the-art methods: Firstly, we evaluate them on a set of 466 classic optimization test problems of dimension 2 to 300. Secondly, we study their performance in parameter estimation on 8 ODE models of biological processes, comparing them to state-of-the-art derivative-based optimization. We observe that different problem features necessitate the use of different methods, for which we can give suggestions based on our findings. Our analysis suggests that classic test problems are not representative for problems in systems biology. For ODE models, we find that purely derivative-free methods are for most problems not reliable or at least inferior to derivative-based methods

Dirac mixture distributions for the approximation of mixed effects models.

Mixed effect modeling is widely used to study cell-to-cell and patient-to-patient variability. The population statistics of mixed effect models is usually approximated using Dirac mixture distributions obtained using Monte-Carlo, quasi Monte-Carlo, and sigma point methods. Here, we propose the use of a method based on the Cramér-von Mises Distance, which has been introduced in the context of filtering. We assess the accuracy of the different methods using several problems and provide the first scalability study for the Cramér-von Mises Distance method. Our results indicate that for a given number of points, the method based on the modified Cramér-von Mises Distance method tends to achieve a better approximation accuracy than Monte-Carlo and quasi Monte-Carlo methods. In contrast to sigma-point methods, the method based on the modified Cramér-von Mises Distance allows for a flexible number of points and a more accurate approximation for nonlinear problems

Optimization and profile calculation of ODE models using second order adjoint sensitivity analysis.

Motivation: Parameter estimation methods for ordinary differential equation (ODE) models of biological processes can exploit gradients and Hessians of objective functions to achieve convergence and computational efficiency. However, the computational complexity of established methods to evaluate the Hessian scales linearly with the number of state variables and quadratically with the number of parameters. This limits their application to low-dimensional problems. Results: We introduce second order adjoint sensitivity analysis for the computation of Hessians and a hybrid optimization-integration-based approach for profile likelihood computation. Second order adjoint sensitivity analysis scales linearly with the number of parameters and state variables. The Hessians are effectively exploited by the proposed profile likelihood computation approach. We evaluate our approaches on published biological models with real measurement data. Our study reveals an improved computational efficiency and robustness of optimization compared to established approaches, when using Hessians computed with adjoint sensitivity analysis. The hybrid computation method was more than 2-fold faster than the best competitor. Thus, the proposed methods and implemented algorithms allow for the improvement of parameter estimation for medium and large scale ODE models

Benchmarking of numerical integration methods for ODE models of biological systems.

Ordinary differential equation (ODE) models are a key tool to understand complex mechanisms in systems biology. These models are studied using various approaches, including stability and bifurcation analysis, but most frequently by numerical simulations. The number of required simulations is often large, e.g., when unknown parameters need to be inferred. This renders efficient and reliable numerical integration methods essential. However, these methods depend on various hyperparameters, which strongly impact the ODE solution. Despite this, and although hundreds of published ODE models are freely available in public databases, a thorough study that quantifies the impact of hyperparameters on the ODE solver in terms of accuracy and computation time is still missing. In this manuscript, we investigate which choices of algorithms and hyperparameters are generally favorable when dealing with ODE models arising from biological processes. To ensure a representative evaluation, we considered 142 published models. Our study provides evidence that most ODEs in computational biology are stiff, and we give guidelines for the choice of algorithms and hyperparameters. We anticipate that our results will help researchers in systems biology to choose appropriate numerical methods when dealing with ODE models

First report of the genetic background of Marfan syndrome in Polish patients

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