Extensive regulation of metabolism and growth during the cell division cycle

Yeast cells grown in culture can spontaneously synchronize their respiration, metabolism, gene expression and cell division. Such metabolic oscillations in synchronized cultures reflect single-cell oscillations, but the relationship between the oscillations in single cells and synchronized cultures is poorly understood. To understand this relationship and the coordination between metabolism and cell division, we collected and analyzed DNA-content, gene-expression and physiological data, at hundreds of time-points, from cultures metabolically-synchronized at different growth rates, carbon sources and biomass densities. The data enabled us to extend and generalize an ensemble-average-over-phases (EAP) model that connects the population-average gene-expression of asynchronous cultures to the gene-expression dynamics in the single-cells comprising the cultures. The extended model explains the carbon-source specific growth-rate responses of hundreds of genes. Our data demonstrate that for a given growth rate, the frequency of metabolic cycling in synchronized cultures increases with the biomass density. This observation underscores the difference between metabolic cycling in synchronized cultures and in single cells and suggests entraining of the single-cell cycle by a quorum-sensing mechanism. Constant levels of residual glucose during the metabolic cycling of synchronized cultures indicate that storage carbohydrates are required to fuel not only the G1/S transition of the division cycle but also the metabolic cycle. Despite the large variation in profiled conditions and in the time-scale of their dynamics, most genes preserve invariant dynamics of coordination with each other and with the rate of oxygen consumption. Similarly, the G1/S transition always occurs at the beginning, middle or end of the high oxygen consumption phases, analogous to observations in human and drosophila cells.Comment: 34 pages, 7 figure

Modelling of biological systems using multidimensional population balances

Biological systems are intrinsically heterogeneous and, consequently, their mathematical descriptions should account for this heterogeneity as it often influences the dynamic behaviour of the individual cells. For example, in the cell cycle dependent production ofproteins, it is necessary to account for the distribution of the individual cells with respect to their position in the cell cycle as this has a strong influence on protein production. A second notable example is the formation of cancerous cells. In this case, the failure of regulatory mechanisms results in the transition of somatic cells to their cancerous state. Therefore, in developing the corresponding mathematical model, it is necessary to consider both the different states of the cells as well as their regulation. In this regard, the population balance equation is the ideal mathematical framework to capture cell population heterogeneity as it elegantly takes into account the distribution of cell populations with respect to their intracellular state together with the phenomena of cell birth, division, differentiation and recombination. Recent developments in solution algorithms together with the exponential increase in computational abilities now permit the efficient solution of one-dimensional population balance models which attribute the heterogeneity of cell populations to differences in the age or mass of individual cells. The inherent complexity of biological systems implies that the differentiation of cells based on a single characteristic alone may not be sufficient to capture the underlying biological phenomena. Therefore, current research is focussing on the development of multi-dimensional population balances that consider the differentiation of cells based on multiple characteristics, most notably, the state of cells with respect to key intracellular metabolites. However, conventional numerical techniques are inefficient for the solution of the formulated population balance models and this warrants the development of novel, tailor-made algorithms. This thesis presents one such solution algorithm and demonstrates its application to the study of several biological systems. The algorithm developed herein employs a finite-volume technique to convert the partial-differential equation comprising the population balance model into a set of ordinary differential equations. A two-tier technique based on the solution technique for inhomogeneous differential equations is then developed to solve the system of ordinary differential equations. This approach has two main advantages: (a) the decomposition technique considerably reduces the stiffness of the system of equations enabling more efficient solution, and (b) semianalytical solutions for the integrals employed in the modelling of cell division and differentiation can be obtained further reducing computation times. Further improvements in solution efficiency are obtained by the formulation of a two-level discretisation algorithm. In this approach, processes such as cell growth which are more sensitive to the discretisation are solved using a fine grid whereas less sensitive processes such as cell' division - which are usually more computationally expensive - are solved using a coarse grid at a higher level. Thus, further improvements are obtained in the efficiency of the technique. The solution algorithm is applied to various multi-dimensional population balance models of biological systems. The technique is first demonstrated on models of oscillatory dynamics in yeast glycolysis, cell-cycle related oscillations in eukaryotes, and circadian oscillations in crayfish. A model of cell division and proliferation control in eukaryotes is an example of a second class of problems where extracellular phenomena influence the behaviour of cells. As a third case for demonstration, a hybrid model of biopolymer accumulation in bacteria is formulated. In this case, cybernetic modelling principles are used to account for intracellular competitions while the population balance framework takes into consideration the heterogeneity of the cell population. Another important aspect in the formulation ofmulti-dimensional population balances is the development of the intracellular models themselves. While research in the biological sciences is permitting the formulation of detailed dynamic models of various bioprocesses, the accurate estimation of the kinetic parameters in these models can be difficult due to the unavailability of sufficient experimental data. This can result in considerable parametric uncertainty as is demonstrated on a simple cybernetic' model of biopolymer accumulation in bacteria. However, it is shown that, via the use of systems engineering tools, experiments can be designed that permit the accurate estimation of all model parameters even when measurements pertaining to all modelled quantities are unavailable.Imperial Users onl

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

Clustering in Cell Cycle Dynamics with General Response/Signaling Feedback

Motivated by experimental and theoretical work on autonomous oscillations in yeast, we analyze ordinary differential equations models of large populations of cells with cell-cycle dependent feedback. We assume a particular type of feedback that we call Responsive/Signaling (RS), but do not specify a functional form of the feedback. We study the dynamics and emergent behaviour of solutions, particularly temporal clustering and stability of clustered solutions. We establish the existence of certain periodic clustered solutions as well as "uniform" solutions and add to the evidence that cell-cycle dependent feedback robustly leads to cell-cycle clustering. We highlight the fundamental differences in dynamics between systems with negative and positive feedback. For positive feedback systems the most important mechanism seems to be the stability of individual isolated clusters. On the other hand we find that in negative feedback systems, clusters must interact with each other to reinforce coherence. We conclude from various details of the mathematical analysis that negative feedback is most consistent with observations in yeast experiments.Comment: To appear in J. Theoretical Biology 292 (2012), 103-11

On the dynamics of the adenylate energy system: homeorhesis vs homeostasis.

Biochemical energy is the fundamental element that maintains both the adequate turnover of the biomolecular structures and the functional metabolic viability of unicellular organisms. The levels of ATP, ADP and AMP reflect roughly the energetic status of the cell, and a precise ratio relating them was proposed by Atkinson as the adenylate energy charge (AEC). Under growth-phase conditions, cells maintain the AEC within narrow physiological values, despite extremely large fluctuations in the adenine nucleotides concentration. Intensive experimental studies have shown that these AEC values are preserved in a wide variety of organisms, both eukaryotes and prokaryotes. Here, to understand some of the functional elements involved in the cellular energy status, we present a computational model conformed by some key essential parts of the adenylate energy system. Specifically, we have considered (I) the main synthesis process of ATP from ADP, (II) the main catalyzed phosphotransfer reaction for interconversion of ATP, ADP and AMP, (III) the enzymatic hydrolysis of ATP yielding ADP, and (IV) the enzymatic hydrolysis of ATP providing AMP. This leads to a dynamic metabolic model (with the form of a delayed differential system) in which the enzymatic rate equations and all the physiological kinetic parameters have been explicitly considered and experimentally tested in vitro. Our central hypothesis is that cells are characterized by changing energy dynamics (homeorhesis). The results show that the AEC presents stable transitions between steady states and periodic oscillations and, in agreement with experimental data these oscillations range within the narrow AEC window. Furthermore, the model shows sustained oscillations in the Gibbs free energy and in the total nucleotide pool. The present study provides a step forward towards the understanding of the fundamental principles and quantitative laws governing the adenylate energy system, which is a fundamental element for unveiling the dynamics of cellular life