Joachim Almquist

Kinetic models in industrial biotechnology - Improving cell factory performance

An increasing number of industrial bioprocesses capitalize on living cells by using them as cell factories that convert sugars into chemicals. These processes range from the production of bulk chemicals in yeasts and bacteria to the synthesis of therapeutic proteins in mammalian cell lines. One of the tools in the continuous search for improved performance of such production systems is the development and application of mathematical models. To be of value for industrial biotechnology, mathematical models should be able to assist in the rational design of cell factory properties or in the production processes in which they are utilized. Kinetic models are particularly suitable towards this end because they are capable of representing the complex biochemistry of cells in a more complete way compared to most other types of models. They can, at least in principle, be used to in detail understand, predict, and evaluate the effects of adding, removing, or modifying molecular components of a cell factory and for supporting the design of the bioreactor or fermentation process. However, several challenges still remain before kinetic modeling will reach the degree of maturity required for routine application in industry. Here we review the current status of kinetic cell factory modeling. Emphasis is on modeling methodology concepts, including model network structure, kinetic rate expressions, parameter estimation, optimization methods, identifiability analysis, model reduction, and model validation, but several applications of kinetic models for the improvement of cell factories are also discussed.

Bridging the gaps in systems biology

Abstract Systems biology aims at creating mathematical models, i.e., computational reconstructions of biological systems and processes that will result in a new level of understanding—the elucidation of the basic and presumably conserved “design” and “engineering” principles of biomolecular systems. Thus, systems biology will move biology from a phenomenological to a predictive science. Mathematical modeling of biological networks and processes has already greatly improved our understanding of many cellular processes. However, given the massive amount of qualitative and quantitative data currently produced and number of burning questions in health care and biotechnology needed to be solved is still in its early phases. The field requires novel approaches for abstraction, for modeling bioprocesses that follow different biochemical and biophysical rules, and for combining different modules into larger models that still allow realistic simulation with the computational power available today. We have identified and discussed currently most prominent problems in systems biology: (1) how to bridge different scales of modeling abstraction, (2) how to bridge the gap between topological and mechanistic modeling, and (3) how to bridge the wet and dry laboratory gap. The future success of systems biology largely depends on bridging the recognized gaps.

Yeast AMP-activated protein kinase monitors glucose concentration changes and absolute glucose levels

Background: Little is known about the signaling dynamics of AMP-activated protein kinase. Results: We define the dynamics of yeast AMPK signaling under different glucose concentrations. Conclusion: The Snf1-Mig1 signaling system monitors glucose concentration changes and absolute glucose levels to adjust the metabolism to a wide range of conditions. Significance: This description of AMPK signaling dynamics will stimulate studies defining the integration of signaling and metabolism. Analysis of the time-dependent behavior of a signaling system can provide insight into its dynamic properties. We employed the nucleocytoplasmic shuttling of the transcriptional repressor Mig1 as readout to characterize Snf1-Mig1 dynamics in single yeast cells. Mig1 binds to promoters of target genes and mediates glucose repression. Mig1 is predominantly located in the nucleus when glucose is abundant. Upon glucose depletion, Mig1 is phosphorylated by the yeast AMP-activated kinase Snf1 and exported into the cytoplasm. We used a three-channel microfluidic device to establish a high degree of control over the glucose concentration exposed to cells. Following regimes of glucose up- and downshifts, we observed a very rapid response reaching a new steady state within less than 1 min, different glucose threshold concentrations depending on glucose up- or downshifts, a graded profile with increased cell-to-cell variation at threshold glucose concentrations, and biphasic behavior with a transient translocation of Mig1 upon the shift from high to intermediate glucose concentrations. Fluorescence loss in photobleaching and fluorescence recovery after photobleaching data demonstrate that Mig1 shuttles constantly between the nucleus and cytoplasm, although with different rates, depending on the presence of glucose. Taken together, our data suggest that the Snf1-Mig1 system has the ability to monitor glucose concentration changes as well as absolute glucose levels. The sensitivity over a wide range of glucose levels and different glucose concentration-dependent response profiles are likely determined by the close integration of signaling with the metabolism and may provide for a highly flexible and fast adaptation to an altered nutritional status.

Mixed Effects Modeling Using Stochastic Differential Equations: Illustrated by Pharmacokinetic Data of Nicotinic Acid in Obese Zucker Rats

Inclusion of stochastic differential equations in mixed effects models provides means to quantify and distinguish three sources of variability in data. In addition to the two commonly encountered sources, measurement error and interindividual variability, we also consider uncertainty in the dynamical model itself. To this end, we extend the ordinary differential equation setting used in nonlinear mixed effects models to include stochastic differential equations. The approximate population likelihood is derived using the first-order conditional estimation with interaction method and extended Kalman filtering. To illustrate the application of the stochastic differential mixed effects model, two pharmacokinetic models are considered. First, we use a stochastic one-compartmental model with first-order input and nonlinear elimination to generate synthetic data in a simulated study. We show that by using the proposed method, the three sources of variability can be successfully separated. If the stochastic part is neglected, the parameter estimates become biased, and the measurement error variance is significantly overestimated. Second, we consider an extension to a stochastic pharmacokinetic model in a preclinical study of nicotinic acid kinetics in obese Zucker rats. The parameter estimates are compared between a deterministic and a stochastic NiAc disposition model, respectively. Discrepancies between model predictions and observations, previously described as measurement noise only, are now separated into a comparatively lower level of measurement noise and a significant uncertainty in model dynamics. These examples demonstrate that stochastic differential mixed effects models are useful tools for identifying incomplete or inaccurate model dynamics and for reducing potential bias in parameter estimates due to such model deficiencies.

Using sensitivity equations for computing gradients of the FOCE and FOCEI approximations to the population likelihood

The first order conditional estimation (FOCE) method is still one of the parameter estimation workhorses for nonlinear mixed effects (NLME) modeling used in population pharmacokinetics and pharmacodynamics. However, because this method involves two nested levels of optimizations, with respect to the empirical Bayes estimates and the population parameters, FOCE may be numerically unstable and have long run times, issues which are most apparent for models requiring numerical integration of differential equations. We propose an alternative implementation of the FOCE method, and the related FOCEI, for parameter estimation in NLME models. Instead of obtaining the gradients needed for the two levels of quasi-Newton optimizations from the standard finite difference approximation, gradients are computed using so called sensitivity equations. The advantages of this approach were demonstrated using different versions of a pharmacokinetic model defined by nonlinear differential equations. We show that both the accuracy and precision of gradients can be improved extensively, which will increase the chances of a successfully converging parameter estimation. We also show that the proposed approach can lead to markedly reduced computational times. The accumulated effect of the novel gradient computations ranged from a 10-fold decrease in run times for the least complex model when comparing to forward finite differences, to a substantial 100-fold decrease for the most complex model when comparing to central finite differences. Considering the use of finite differences in for instance NONMEM and Phoenix NLME, our results suggests that significant improvements in the execution of FOCE are possible and that the approach of sensitivity equations should be carefully considered for both levels of optimization.

A Nonlinear Mixed Effects Approach for Modeling the Cell-To-Cell Variability of Mig1 Dynamics in Yeast

The last decade has seen a rapid development of experimental techniques that allow data collection from individual cells. These techniques have enabled the discovery and characterization of variability within a population of genetically identical cells. Nonlinear mixed effects (NLME) modeling is an established framework for studying variability between individuals in a population, frequently used in pharmacokinetics and pharmacodynamics, but its potential for studies of cell-to-cell variability in molecular cell biology is yet to be exploited. Here we take advantage of this novel application of NLME modeling to study cell-to-cell variability in the dynamic behavior of the yeast transcription repressor Mig1. In particular, we investigate a recently discovered phenomenon where Mig1 during a short and transient period exits the nucleus when cells experience a shift from high to intermediate levels of extracellular glucose. A phenomenological model based on ordinary differential equations describing the transient dynamics of nuclear Mig1 is introduced, and according to the NLME methodology the parameters of this model are in turn modeled by a multivariate probability distribution. Using time-lapse microscopy data from nearly 200 cells, we estimate this parameter distribution according to the approach of maximizing the population likelihood. Based on the estimated distribution, parameter values for individual cells are furthermore characterized and the resulting Mig1 dynamics are compared to the single cell times-series data. The proposed NLME framework is also compared to the intuitive but limited standard two-stage (STS) approach. We demonstrate that the latter may overestimate variabilities by up to almost five fold. Finally, Monte Carlo simulations of the inferred population model are used to predict the distribution of key characteristics of the Mig1 transient response. We find that with decreasing levels of post-shift glucose, the transient response of Mig1 tend to be faster, more extended, and displays an increased cell-to-cell variability.

Joint feedback analysis modeling of nonesterified fatty acids in obese zucker rats and normal Sprague-Dawley rats after different routes of administration of nicotinic acid

Data were pooled from several studies on nicotinic acid (NiAc) intervention of fatty acid turnover in normal Sprague–Dawley and obese Zucker rats in order to perform a joint PKPD of data from more than 100 normal Sprague–Dawley and obese Zucker rats, exposed to several administration routes and rates. To describe the difference in pharmacodynamic parameters between obese and normal rats, we modified a previously published nonlinear mixed effects model describing tolerance and oscillatory rebound effects of NiAc on nonesterified fatty acids plasma concentrations. An important conclusion is that planning of experiments and dose scheduling cannot rely on pilot studies on normal animals alone. The obese rats have a less-pronounced concentration–response relationship and need higher doses to exhibit desired response. The relative level of fatty acid rebound after cessation of NiAc administration was also quantified in the two rat populations. Building joint normal-disease models with scaling parameter(s) to characterize the “degree of disease” can be a useful tool when designing informative experiments on diseased animals, particularly in the preclinical screen. Data were analyzed using nonlinear mixed effects modeling, for the optimization, we used an improved method for calculating the gradient than the usually adopted finite difference approximation.

Hemostatic effects of the ticagrelor antidote MEDI2452 in pigs treated with ticagrelor on a background of aspirin

Essentials MEDI2452 is a specific antidote of the platelet P2Y12 receptor antagonist ticagrelor. Hemostatic effects of MEDI2452 were evaluated in pigs treated with ticagrelor and aspirin. MEDI2452 eliminated free ticagrelor within 5 min and gradually normalized platelet aggregation. Improvements in blood pressure (significant) and in blood‐loss and survival (non‐significant) were observed.

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.

Modeling of free fatty acid dynamics : insulin and nicotinic acid resistance under acute and chronic treatments

Nicotinic acid (NiAc) is a potent inhibitor of adipose tissue lipolysis. Acute administration results in a rapid reduction of plasma free fatty acid (FFA) concentrations. Sustained NiAc exposure is associated with tolerance development (drug resistance) and complete adaptation (FFA returning to pretreatment levels). We conducted a meta-analysis on a rich pre-clinical data set of the NiAc–FFA interaction to establish the acute and chronic exposure-response relations from a macro perspective. The data were analyzed using a nonlinear mixed-effects framework. We also developed a new turnover model that describes the adaptation seen in plasma FFA concentrations in lean Sprague–Dawley and obese Zucker rats following acute and chronic NiAc exposure. The adaptive mechanisms within the system were described using integral control systems and dynamic efficacies in the traditional