Low-cost arabinose induced genetic circuit for protein production: Modeling.

A low-cost reagent-producing genetic circuit was designed during this work. Its functioning is based on a positive feedback loop induced by a small amount of arabinose, allowing users to obtain reactants in a safe, constant, and controlled manner. The design-only approach to the project allows us to work in different kinds of computational models, thus, an ODE-based model was thoroughly developed and a cellular automata-based one was experimented with. Working on the ODE model, equilibrium states and system stability were studied. Circuit properties were also focused on one of which was a high concentration of interest protein produced by low inductor inputs. As a result, a mathematical expression capable of describing the quantity of produced reagent was obtained. In addition, the cellular automata model offers a new perspective, given its differences from the ODE model e.g. this type of model is a stochastic analysis and describes each cell individually instead of describing the whole cellular population.

Modelling Oscillatory Patterns in the Bovine Estrous Cycle with Boolean Delay Equations

Boolean delay equations (BDEs), with their relatively simple and intuitive mode of modelling, have been used in many research areas including, for example, climate dynamics and earthquake propagation. Their application to biological systems has been scarce and limited to the molecular level. Here, we derive and present two BDE models. One is directly derived from a previously published ordinary differential equation (ODE) model for the bovine estrous cycle, whereas the second model includes a modification of a particular biological mechanism. We not only compare the simulation results from the BDE models with the trajectories of the ODE model, but also validate the BDE models with two additional numerical experiments. One experiment induces a switch in the oscillatory pattern upon changes in the model parameters, and the other simulates the administration of a hormone that is known to shift the estrous cycle in time. The models presented here are the first BDE models for hormonal oscillators, and the first BDE models for drug administration. Even though automatic parameter estimation still remains challenging, our results support the role of BDEs as a framework for the systematic modelling of complex biological oscillators.

Effect of Human Mobility On The Spatial Spread of Airborne Diseases: An Epidemic Model With Indirect Transmission

We extended a class of coupled PDE-ODE models for studying the spatial spread of airborne diseases by incorporating human mobility. Human populations are modeled with patches, and a Lagrangian perspective is used to keep track of individuals’ places of residence. The movement of pathogens in the air is modeled with linear diffusion and coupled to the SIR dynamics of each human population through an integral of the density of pathogen around the population patch. In the limit of fast diffusion pathogens, the method of matched asymptotic analysis is used to reduce the coupled PDE-ODE model to a nonlinear system of ODEs for the average density of pathogens in the air. The reduced system of ODEs is used to derive the basic reproduction number and the final size relation for the model. Numerical simulations of the full PDE-ODE model and the reduced system of ODEs are used to assess the impact of human mobility, together with the diffusion of pathogens on the dynamics of the disease. Results from the two models are consistent and show that human mobility significantly affects disease dynamics. In addition, we show that an increase in the diffusion rate of pathogen leads to a smaller epidemic.

Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip Experiment

The present work is motivated by the development of a mathematical model mimicking the mechanisms observed in lab-on-chip experiments, made to reproduce on microfluidic chips the in vivo reality. Here we consider the Cancer-on-Chip experiment where tumor cells are treated with chemotherapy drug and secrete chemical signals in the environment attracting multiple immune cell species. The in silico model here proposed goes towards the construction of a “digital twin” of the experimental immune cells in the chip environment to better understand the complex mechanisms of immunosurveillance. To this aim, we develop a tumor-immune microfluidic hybrid PDE–ODE model to describe the concentration of chemicals in the Cancer-on-Chip environment and immune cells migration. The development of a trustable simulation algorithm, able to reproduce the immunocompetent dynamics observed in the chip, requires an efficient tool for the calibration of the model parameters. In this respect, the present paper represents a first methodological work to test the feasibility and the soundness of the calibration technique here proposed, based on a multidimensional spline interpolation technique for the time-varying velocity field surfaces obtained from cell trajectories.

Critical role of DNA unwinding and Cas9 conformational changes in modelling off-target effects

CRISPR-Cas9 off-target effects interfere with the ability to accurately perform genetic edits. To predict off-target effects CRISPR-Cas9 researchers perform high throughput guide RNA mismatch and bulge experiments and then use the data to fit thermodynamic binding models. While impactful from an engineering perspective such models are not based on the experimentally observed target interrogation process and thus incorrectly measure the energetic effects mismatches have on the system. In this work we convert an experimentally deduced qualitive model of target interrogation to a linear ODE model and demonstrate that the mismatch tolerance patterns observed in experiments do not need to be caused by differences in energetic penalties of mismatches but rather are emergent effects of the timing and coordination of target DNA unwinding and Cas9 conformational changes.

ORDINARY DIFFERENTIAL EQUATIONS WITH MACHINE LEARNING FOR PREDICTION OF SMART COMPOSITE FRACTURE TOUGHNESS

This work in on the development of an ordinary differential equation (ODE) model coupled with statistical methods for the prediction of fracture toughness of a magnetostrictive, piezoelectric smart self-sensing Fiber Reinforced Polymer (FRP) composite. The smart composite with sensing properties encompasses Terfenol-D alloy nanoparticles and Single Walled Carbon NanoTubes (SWCNT). To explore various configurations the of nanoparticle constituents’ effect on fracture toughness within the FRP composite, the ODE model developed within a finite element analysis (FEA) environment is considered to attain fracture observations across the solution space. The acquired FEA data is then used to feed the machine-learning (ML) algorithms to obtain composite fracture toughness predictions. A comparison and development of artificial neural networks (ANN), decision trees and support vector machines (SVM) models for FRP smart self-sensing composite fracture toughness prediction is done. Qualitative results stating if the sample has fractured or not and quantitative data giving the fracture toughness and strain energy release rate for the smart self-sensing FRP composites is attained. A comparison of all predictions from the developed models for both fracture toughness is corroborated with literature data.

Generation of multicellular spatiotemporal models of population dynamics from ordinary differential equations, with applications in viral infection

Background The biophysics of an organism span multiple scales from subcellular to organismal and include processes characterized by spatial properties, such as the diffusion of molecules, cell migration, and flow of intravenous fluids. Mathematical biology seeks to explain biophysical processes in mathematical terms at, and across, all relevant spatial and temporal scales, through the generation of representative models. While non-spatial, ordinary differential equation (ODE) models are often used and readily calibrated to experimental data, they do not explicitly represent the spatial and stochastic features of a biological system, limiting their insights and applications. However, spatial models describing biological systems with spatial information are mathematically complex and computationally expensive, which limits the ability to calibrate and deploy them and highlights the need for simpler methods able to model the spatial features of biological systems. Results In this work, we develop a formal method for deriving cell-based, spatial, multicellular models from ODE models of population dynamics in biological systems, and vice versa. We provide examples of generating spatiotemporal, multicellular models from ODE models of viral infection and immune response. In these models, the determinants of agreement of spatial and non-spatial models are the degree of spatial heterogeneity in viral production and rates of extracellular viral diffusion and decay. We show how ODE model parameters can implicitly represent spatial parameters, and cell-based spatial models can generate uncertain predictions through sensitivity to stochastic cellular events, which is not a feature of ODE models. Using our method, we can test ODE models in a multicellular, spatial context and translate information to and from non-spatial and spatial models, which help to employ spatiotemporal multicellular models using calibrated ODE model parameters. We additionally investigate objects and processes implicitly represented by ODE model terms and parameters and improve the reproducibility of spatial, stochastic models. Conclusion We developed and demonstrate a method for generating spatiotemporal, multicellular models from non-spatial population dynamics models of multicellular systems. We envision employing our method to generate new ODE model terms from spatiotemporal and multicellular models, recast popular ODE models on a cellular basis, and generate better models for critical applications where spatial and stochastic features affect outcomes.

State Estimation and Slug Control of the Subsea Multiphase Pipeline

The simulation and control of the severe slugging flow in the subsea multiphase pipeline is the focus of research in the production and exploitation of oil companies. Severe slug flow results in severe fluctuations of pressure and flow rate at both the wells end and the receiving host processing facilities, causing safety and shutdown risks. To prevent the severe slugging flow regime in multiphase transport pipelines, an Ordinary Differential Equation (ODE) model is established by using the mass conservation law for individual phases in the pipeline and the riser sections. Then, the proposed model is compared to the results from the OLGA simulation. A comparative study of different slugging flow control solutions is conducted. Unscented Kalman Filter (UKF), Wavelet Neural Network (WNN) and UKF&WNN are used for state estimation and combined with PI controller. The UKF and WNN are good nonlinear filters. However, when the nominal choke opening is increased, they work unsatisfying. The UKF&WNN observer shows slightly better results than UKF and WNN when the system has high input disturbance.

Identifiability analysis for models of the translation kinetics after mRNA transfection

Mechanistic models are a powerful tool to gain insights into biological processes. The parameters of such models, e.g. kinetic rate constants, usually cannot be measured directly but need to be inferred from experimental data. In this article, we study dynamical models of the translation kinetics after mRNA transfection and analyze their parameter identifiability. Previous studies have considered ordinary differential equation (ODE) models of the process, and here we formulate a stochastic differential equation (SDE) model. For both model types, we consider structural identifiability based on the model equations and practical identifiability based on simulated as well as experimental data and find that the SDE model provides better parameter identifiability than the ODE model. Moreover, our analysis shows that even for those parameters of the ODE model that are considered to be identifiable, the obtained estimates are sometimes unreliable. Overall, our study clearly demonstrates the relevance of considering different modeling approaches and that stochastic models can provide more reliable and informative results.