Uncovering specific mechanisms across cell types in dynamical models.

Ordinary differential equations are frequently employed for mathematical modeling of biological systems. The identification of mechanisms that are specific to certain cell types is crucial for building useful models and to gain insights into the underlying biological processes. Regularization techniques have been proposed and applied to identify mechanisms specific to two cell types, e.g., healthy and cancer cells, including the LASSO (least absolute shrinkage and selection operator). However, when analyzing more than two cell types, these approaches are not consistent, and require the selection of a reference cell type, which can affect the results. To make the regularization approach applicable to identifying cell-type specific mechanisms in any number of cell types, we propose to incorporate the clustered LASSO into the framework of ordinary differential equation modeling by penalizing the pairwise differences of the logarithmized fold-change parameters encoding a specific mechanism in different cell types. The symmetry introduced by this approach renders the results independent of the reference cell type. We discuss the necessary adaptations of state-of-the-art numerical optimization techniques and the process of model selection for this method. We assess the performance with realistic biological models and synthetic data, and demonstrate that it outperforms existing approaches. Finally, we also exemplify its application to published biological models including experimental data, and link the results to independent biological measurements.

Detecting frequency modulation in stochastic time-series data.

We propose a statistical test to identify nonstationary frequency-modulated stochastic processes from time-series data. Our method uses the instantaneous phase as a discriminatory statistics with reliable critical values derived from surrogate data. We simulated an oscillatory second-order autoregressive process to evaluate the size and power of the test. We found that the test we propose is able to correctly identify more than 99% of nonstationary data when the frequency of the simulated data is doubled after the first half of the time series. Our method is easily interpretable, computationally cheap, and does not require choosing hyperparameters that are dependent on the data.

PEtab-Interoperable specification of parameter estimation problems in systems biology.

Reproducibility and reusability of the results of data-based modeling studies are essential. Yet, there has been-so far-no broadly supported format for the specification of parameter estimation problems in systems biology. Here, we introduce PEtab, a format which facilitates the specification of parameter estimation problems using Systems Biology Markup Language (SBML) models and a set of tab-separated value files describing the observation model and experimental data as well as parameters to be estimated. We already implemented PEtab support into eight well-established model simulation and parameter estimation toolboxes with hundreds of users in total. We provide a Python library for validation and modification of a PEtab problem and currently 20 example parameter estimation problems based on recent studies.

Estimating chain length for time delays in dynamical systems using profile likelihood.

MOTIVATION: Apparent time delays in partly observed, biochemical reaction networks can be modelled by lumping a more complex reaction into a series of linear reactions often referred to as the linear chain trick. Since most delays in biochemical reactions are no true, hard delays but a consequence of complex unobserved processes, this approach often more closely represents the true system compared with delay differential equations. In this paper, we address the question of how to select the optimal number of additional equations, i.e. the chain length (CL). RESULTS: We derive a criterion based on parameter identifiability to infer CLs and compare this method to choosing the model with a CL that leads to the best fit in a maximum likelihood sense, which corresponds to optimizing the Bayesian information criterion. We evaluate performance with simulated data as well as with measured biological data for a model of JAK2/STAT5 signalling and access the influence of different model structures and data characteristics. Our analysis revealed that the proposed method features a superior performance when applied to biological models and data compared with choosing the model that maximizes the likelihood. AVAILABILITY AND IMPLEMENTATION: Models and data used for simulations are available at https://github.com/Data2Dynamics/d2d and http://jeti.uni-freiburg.de/PNAS_Swameye_Data. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Marginally compact fractal trees with semiflexibility.

We study marginally compact macromolecular trees that are created by means of two different fractal generators. In doing so, we assume Gaussian statistics for the vectors connecting nodes of the trees. Moreover, we introduce bond-bond correlations that make the trees locally semiflexible. The symmetry of the structures allows an iterative construction of full sets of eigenmodes (notwithstanding the additional interactions that are present due to semiflexibility constraints), enabling us to get physical insights about the trees' behavior and to consider larger structures. Due to the local stiffness, the self-contact density gets drastically reduced.