Benchmarks for identification of ordinary differential equations from time series data

Motivation: In recent years, the biological literature has seen a significant increase of reported methods for identifying both structure and parameters of ordinary differential equations (ODEs) from time series data. A natural way to evaluate the performance of such methods is to try them on a sufficient number of realistic test cases. However, weak practices in specifying identification problems and lack of commonly accepted benchmark problems makes it difficult to evaluate and compare different methods

Input estimation for drug discovery using optimal control and Markov chain Monte Carlo approaches

Input estimation is employed in cases where it is desirable to recover the form of an input function which cannot be directly observed and for which there is no model for the generating process. In pharmacokinetic and pharmacodynamic modelling, input estimation in linear systems (deconvolution) is well established, while the nonlinear case is largely unexplored. In this paper, a rigorous definition of the input-estimation problem is given, and the choices involved in terms of modelling assumptions and estimation algorithms are discussed. In particular, the paper covers Maximum a Posteriori estimates using techniques from optimal control theory, and full Bayesian estimation using Markov Chain Monte Carlo (MCMC) approaches. These techniques are implemented using the optimisation software CasADi, and applied to two example problems: one where the oral absorption rate and bioavailability of the drug eflornithine are estimated using pharmacokinetic data from rats, and one where energy intake is estimated from body-mass measurements of mice exposed to monoclonal antibodies targeting the fibroblast growth factor receptor (FGFR) 1c. The results from the analysis are used to highlight the strengths and weaknesses of the methods used when applied to sparsely sampled data. The presented methods for optimal control are fast and robust, and can be recommended for use in drug discovery. The MCMC-based methods can have long running times and require more expertise from the user. The rigorous definition together with the illustrative examples and suggestions for software serve as a highly promising starting point for application of input-estimation methods to problems in drug discovery

Hybrid Modelling for Stroke Care: Review and suggestions of new approaches for risk assessment and simulation of scenarios

Stroke is an example of a complex and multi-factorial disease involving multiple organs, timescales, and disease mechanisms. To deal with this complexity, and to realize Precision Medicine of stroke, mathematical models are needed. Such approaches include: 1) machine learning, 2) bioinformatic network models, and 3) mechanistic models. Since these three approaches have complementary strengths and weaknesses, a hybrid modelling approach combining them would be the most beneficial. However, no concrete approach ready to be implemented for a specific disease has been presented to date. In this paper, we both review the strengths and weaknesses of the three approaches, and propose a roadmap for hybrid modelling in the case of stroke care. We focus on two main tasks needed for the clinical setting: a) For stroke risk calculation, we propose a new two-step approach, where non-linear mixed effects models and bioinformatic network models yield biomarkers which are used as input to a machine learning model and b) For simulation of care scenarios, we propose a new four-step approach, which revolves around iterations between simulations of the mechanistic models and imputations of non-modelled or non-measured variables. We illustrate and discuss the different approaches in the context of Precision Medicine for stroke

Input estimation for extended-release formulations exemplified with exenatide

Estimating the in vivo absorption profile of a drug is essential when developing extended-release medications. Such estimates can be obtained by measuring plasma concentrations over time and inferring the absorption from a model of the drug’s pharmacokinetics. Of particular interest is to predict the bioavailability—the fraction of the drug that is absorbed and enters the systemic circulation. This paper presents a framework for addressing this class of estimation problems and gives advice on the choice of method. In parametric methods, a model is constructed for the absorption process, which can be difficult when the absorption has a complicated profile. Here, we place emphasis on non-parametric methods that avoid making strong assumptions about the absorption. A modern estimation method that can address very general input-estimation problems has previously been presented. In this method, the absorption profile is modeled as a stochastic process, which is estimated using Markov chain Monte Carlo techniques. The applicability of this method for extended-release formulation development is evaluated by analyzing a dataset of Bydureon, an injectable extended-release suspension formulation of exenatide, a GLP-1 receptor agonist for treating diabetes. This drug is known to have non-linear pharmacokinetics. Its plasma concentration profile exhibits multiple peaks, something that can make parametric modeling challenging, but poses no major difficulties for non-parametric methods. The method is also validated on synthetic data, exploring the effects of sampling and noise on the accuracy of the estimates

Unraveling the Pharmacokinetic Interaction of Ticagrelor and MEDI2452 (Ticagrelor Antidote) by Mathematical Modeling

The investigational ticagrelor-neutralizing antibody fragment, MEDI2452, is developed to rapidly and specifically reverse the antiplatelet effects of ticagrelor. However, the dynamic interaction of ticagrelor, the ticagrelor active metabolite (TAM), and MEDI2452, makes pharmacokinetic (PK) analysis nontrivial and mathematical modeling becomes essential to unravel the complex behavior of this system. We propose a mechanistic PK model, including a special observation model for post-sampling equilibration, which is validated and refined using mouse in vivo data from four studies of combined ticagrelor-MEDI2452 treatment. Model predictions of free ticagrelor and TAM plasma concentrations are subsequently used to drive a pharmacodynamic (PD) model that successfully describes platelet aggregation data. Furthermore, the model indicates that MEDI2452-bound ticagrelor is primarily eliminated together with MEDI2452 in the kidneys, and not recycled to the plasma, thereby providing a possible scenario for the extrapolation to humans. We anticipate the modeling work to improve PK and PD understanding, experimental design, and translational confidence

Dynamical modeling of collective behavior from pigeon flight data: flock cohesion and dispersion

Several models of flocking have been promoted based on simulations with qualitatively naturalistic behavior. In this paper we provide the first direct application of computational modeling methods to infer flocking behavior from experimental field data. We show that this approach is able to infer general rules for interaction, or lack of interaction, among members of a flock or, more generally, any community. Using experimental field measurements of homing pigeons in flight we demonstrate the existence of a basic distance dependent attraction/repulsion relationship and show that this rule is sufficient to explain collective behavior observed in nature. Positional data of individuals over time are used as input data to a computational algorithm capable of building complex nonlinear functions that can represent the system behavior. Topological nearest neighbor interactions are considered to characterize the components within this model. The efficacy of this method is demonstrated with simulated noisy data generated from the classical (two dimensional) Vicsek model. When applied to experimental data from homing pigeon flights we show that the more complex three dimensional models are capable of predicting and simulating trajectories, as well as exhibiting realistic collective dynamics. The simulations of the reconstructed models are used to extract properties of the collective behavior in pigeons, and how it is affected by changing the initial conditions of the system. Our results demonstrate that this approach may be applied to construct models capable of simulating trajectories and collective dynamics using experimental field measurements of herd movement. From these models, the behavior of the individual agents (animals) may be inferred

Diffusive molecular communication with a spheroidal receiver for organ-on-chip systems

Realistic models of the components and processes are required for molecular communication (MC) systems. In this paper, a spheroidal receiver structure is proposed for MC that is inspired by the 3D cell cultures known as spheroids being widely used in organ-on-chip systems. A simple diffusive MC system is considered where the spheroidal receiver and a point source transmitter are in an unbounded fluid environment. The spheroidal receiver is modeled as a porous medium for diffusive signaling molecules, then its boundary conditions and effective diffusion coefficient are characterized. It is revealed that the spheroid amplifies the diffusion signal, but also disperses the signal which reduces the information communication rate. Furthermore, we analytically formulate and derive the concentration Green’s function inside and outside the spheroid in terms of infinite series-forms that are confirmed by a particle-based simulator (PBS)

Spheroidal molecular communication via diffusion : signaling between homogeneous cell aggregates

Recent molecular communication (MC) research has integrated more detailed computational models to capture the dynamics of practical biophysical systems. This paper focuses on developing realistic models for MC transceivers inspired by spheroids – three-dimensional cell aggregates commonly used in organ-on-chip experimental systems. Potential applications that can be used or modeled with spheroids include nutrient transport in organ-on-chip systems, the release of biomarkers or reception of drug molecules by cancerous tumor sites, or transceiver nanomachines participating in information exchange. In this paper, a simple diffusive MC system is considered where a spheroidal transmitter and spheroidal receiver are in an unbounded fluid environment. These spheroidal antennas are modeled as porous media for diffusive signaling molecules, then their boundary conditions and effective diffusion coefficients are characterized. Furthermore, for either a point source or spheroidal transmitter, the Green’s function for concentration (GFC) outside and inside the receiving spheroid is analytically derived and formulated in terms of an infinite series and confirmed with a particle-based simulator (PBS). The provided GFCs enable computation of the transmitted and received signals in the proposed spheroidal communication system. This study shows that the porous structure of the receiving spheroid amplifies diffusion signals but also disperses them, thus there is a trade-off between porosity and information transmission rate. Furthermore, the results reveal that the porous arrangement of the transmitting spheroid not only disperses the received signal but also attenuates it in comparison to a point source transmitter. System performance is also evaluated in terms of the bit error rate (BER). Decreasing the porosity of the receiving spheroid is shown to enhance the system performance. Conversely, reducing the porosity of the transmitting spheroid can adversely affect system performance..

Network modeling of the transcriptional effects of copy number aberrations in glioblastoma

DNA copy number aberrations (CNAs) are a characteristic feature of cancer genomes. In this work, Rebecka Jörnsten, Sven Nelander and colleagues combine network modeling and experimental methods to analyze the systems-level effects of CNAs in glioblastoma