Robustness of glycolysis in yeast to internal and external noise

Generalized Structural Kinetic Modeling: A Survey and Guide

Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional dynamical models of complex systems are rarely mathematically tractable and their numerical exploration suffers both from computational and data limitations. Here we review generalized modeling, an alternative approach for formulating dynamical models to gain insights into dynamics and bifurcations of uncertain systems. We argue that this approach deals elegantly with the uncertainties that exist in real world data and enables analytical insight or highly efficient numerical investigation. We provide a survey of recent successes of generalized modeling and a guide to the application of this modeling approach in future studies such as complex integrative ecological models.

In silico Determination of Some Conditions Leading to Glycolytic Oscillations and Their Interference With Some Other Processes in E. coli Cells

Autonomous oscillations of species levels in the glycolysis express the self-control of this essential cellular pathway belonging to the central carbon metabolism (CCM), and this phenomenon takes place in a large number of bacteria. Oscillations of glycolytic intermediates in living cells occur according to the environmental conditions and to the cell characteristics, especially the adenosine triphosphate (ATP) recovery system. Determining the conditions that lead to the occurrence and maintenance of the glycolytic oscillations can present immediate practical applications. Such a model-based analysis allows in silico (model-based) design of genetically modified microorganisms (GMO) with certain characteristics of interest for the biosynthesis industry, medicine, etc. Based on our kinetic model validated in previous works, this paper aims to in silico identify operating parameters and cell factors leading to the occurrence of stable glycolytic oscillations in the Escherichia coli cells. As long as most of the glycolytic intermediates are involved in various cellular metabolic pathways belonging to the CCM, evaluation of the dynamics and average level of its intermediates is of high importance for further applicative analyses. As an example, by using a lumped kinetic model for tryptophan (TRP) synthesis from literature, and its own kinetic model for the oscillatory glycolysis, this paper highlights the influence of glycolytic oscillations on the oscillatory TRP synthesis through the PEP (phosphoenolpyruvate) glycolytic node shared by the two oscillatory processes. The numerical analysis allows further TRP production maximization in a fed-batch bioreactor (FBR).

Mathematical model of chaotic oscillations and oscillatory entrainment in glycolysis originated from periodic substrate supply

We study the influence of periodic influx on a character of glycolytic oscillations within the forced Selkov system. We demonstrate that such a simple system demonstrates a rich variety of dynamical regimes (domains of entrainment of different order (Arnold tongues), quasiperiodic oscillations, and chaos), which can be qualitatively collated with the known experimental data. We determine detailed dynamical regimes exploring the map of Lyapunov characteristic exponents obtained in numerical simulations of the Selkov system with periodic influx. In addition, a special study of the chaotic regime and the scenario of its origin in this system was evaluated and discussed.

Impact of correlated noise in an energy depot model

Based on the depot model of the motion of active Brownian particles (ABPs), the impact of cross-correlated multiplicative and additive noises has been investigated. Using a nonlinear Langevin approach, we discuss a new mechanism for the transport of ABPs in which the energy originates from correlated noise. It is shown that the correlation between two types of noise breaks the symmetry of the potential to generate motion of the ABPs with a net velocity. The absolute maximum value of the mean velocity depends on correlated noise or multiplicative noise, whereas a monotonic decrease in the mean velocity occurs with additive noise. In the case of no correlation, the ABPs undergo pure diffusion with zero mean velocity, whereas in the case of perfect correlation, the ABPs undergo pure drift with zero diffusion. This shows that the energy stemming from correlated noise is primarily converted to kinetic energy of the intrawell motion and is eventually dissipated in drift motion. A physical explanation of the mechanisms for noise-driven transport of ABPs is derived from the effective potential of the Fokker-Planck equation.

An integrated multidisciplinary model describing initiation of cancer and the Warburg hypothesis

Background

In this paper we propose a chemical physics mechanism for the initiation of the glycolytic switch commonly known as the Warburg hypothesis, whereby glycolytic activity terminating in lactate continues even in well-oxygenated cells. We show that this may result in cancer via mitotic failure, recasting the current conception of the Warburg effect as a metabolic dysregulation consequent to cancer, to a biophysical defect that may contribute to cancer initiation.

Model

Our model is based on analogs of thermodynamic concepts that tie non-equilibrium fluid dynamics ultimately to metabolic imbalance, disrupted microtubule dynamics, and finally, genomic instability, from which cancers can arise. Specifically, we discuss how an analog of non-equilibrium Rayleigh-Benard convection can result in glycolytic oscillations and cause a cell to become locked into a higher-entropy state characteristic of cancer.

Conclusions

A quantitative model is presented that attributes the well-known Warburg effect to a biophysical mechanism driven by a convective disturbance in the cell. Contrary to current understanding, this effect may precipitate cancer development, rather than follow from it, providing new insights into carcinogenesis, cancer treatment, and prevention.

The stubborn roots of metabolic cycles

Efforts to catalogue the structure of metabolic networks have generated highly detailed, genome-scale atlases of biochemical reactions in the cell. Unfortunately, these atlases fall short of capturing the kinetic details of metabolic reactions, instead offering only topological information from which to make predictions. As a result, studies frequently consider the extent to which the topological structure of a metabolic network determines its dynamic behaviour, irrespective of kinetic details. Here, we study a class of metabolic networks known as non-autocatalytic metabolic cycles, and analytically prove an open conjecture regarding the stability of their steady states. Importantly, our results are invariant to the choice of kinetic parameters, rate laws, equilibrium fluxes and metabolite concentrations. Unexpectedly, our proof exposes an elementary but apparently open problem of locating the roots of a sum of two polynomials S = P + Q, when the roots of the summand polynomials P and Q are known. We derive two new results named the Stubborn Roots Theorems, which provide sufficient conditions under which the roots of S remain qualitatively identical to the roots of P. Our study illustrates how complementary feedback, from classical fields such as dynamical systems to biology and vice versa, can expose fundamental and potentially overlooked questions.

The dynamics of hybrid metabolic-genetic oscillators

The synthetic construction of intracellular circuits is frequently hindered by a poor knowledge of appropriate kinetics and precise rate parameters. Here, we use generalized modeling (GM) to study the dynamical behavior of topological models of a family of hybrid metabolic-genetic circuits known as "metabolators." Under mild assumptions on the kinetics, we use GM to analytically prove that all explicit kinetic models which are topologically analogous to one such circuit, the "core metabolator," cannot undergo Hopf bifurcations. Then, we examine more detailed models of the metabolator. Inspired by the experimental observation of a Hopf bifurcation in a synthetically constructed circuit related to the core metabolator, we apply GM to identify the critical components of the synthetically constructed metabolator which must be reintroduced in order to recover the Hopf bifurcation. Next, we study the dynamics of a re-wired version of the core metabolator, dubbed the "reverse" metabolator, and show that it exhibits a substantially richer set of dynamical behaviors, including both local and global oscillations. Prompted by the observation of relaxation oscillations in the reverse metabolator, we study the role that a separation of genetic and metabolic time scales may play in its dynamics, and find that widely separated time scales promote stability in the circuit. Our results illustrate a generic pipeline for vetting the potential success of a circuit design, simply by studying the dynamics of the corresponding generalized model.

Glycolytic oscillations in a model of a lactic acid bacterium metabolism

Glycolytic oscillations in yeast have been extensively studied. It is still unclear, if these oscillations are caused by the allosteric enzyme phosphofructokinase or the stoichiometry of glycolysis which contains an autocatalysis with respect to ATP. Bacterial glycolysis shows a different stoichiometry, however, also containing a stoichiometric autocatalysis. For Escherichia coli, the regulation of the enzyme phosphofructokinase is also assumed to be a major reason for oscillations to occur. We investigated glycolytic oscillations in a quantitative kinetic model for Streptococcus pyogenes set-up on the basis of experimental data. We found oscillations within physiologically feasible parameter ranges. We investigated the origin of these oscillations and conclude that, again, both the stoichiometry of the system, as well as its allosterically regulated enzymes can give rise to these oscillations. For the analysis we employed established and new optimization methods for finding oscillatory regimes and present these in the context of this study.

Resilience to leaking--dynamic systems modeling of information security

Leaking of confidential material is a major threat to information security within organizations and to society as a whole. This insight has gained traction in the political realm since the activities of Wikileaks, which hopes to attack ‘unjust’ systems or ‘conspiracies’. Eventually, such threats to information security rely on a biologistic argument on the benefits and drawbacks that uncontrolled leaking might pose for ‘just’ and ‘unjust’ entities. Such biological metaphors are almost exclusively based on the economic advantage of participants. Here, I introduce a mathematical model of the complex dynamics implied by leaking. The complex interactions of adversaries are modeled by coupled logistic equations including network effects of econo-communication networks. The modeling shows, that there might arise situations where the leaking envisioned and encouraged by Wikileaks and the like can strengthen the defending entity (the ‘conspiracy’). In particular, the only severe impact leaking can have on an organization seems to originate in the exploitation of leaks by another entity the organization competes with. Therefore, the model suggests that leaks can be used as a `tactical mean’ in direct adversary relations, but do not necessarily increase public benefit and societal immunization to ‘conspiracies’. Furthermore, within the model the exploitation of the (open) competition between entities seems to be a more promising approach to control malicious organizations : divide-et-impera policies triumph here.

Desynchronisation of glycolytic oscillations in yeast cell populations

Glycolytic oscillations of intact yeast cells of the strain Saccharomyces carlsbergensis were investigated at both the levels of cell populations and of individual cells. Individual cells showed glycolytic oscillations even at very low cell densities (e.g. 1.010⁵ cells/ml). By contrast, the collective behaviour on the population level was cell density-dependent: at high cell densities it is oscillatory, but below the threshold density of 1.010⁶ cells/ml the collective dynamics becomes quiescent. We demonstrate that the transition in the collective dynamics is caused by the desynchronisation of the oscillations of individual cells. This is characteristic for a Kuramoto transition. Spatially resolved measurements at low cell densities revealed that even cells that adhere to their neighbours oscillated with their own, independent frequencies and phases.

Engineering glyceraldehyde-3-phosphate dehydrogenase for switching control of glycolysis in Escherichia coli

Glycolysis has evolved to be a highly robust mechanism for maintaining the cellular metabolism of living organisms. However, relevant modifications of glycolytic activity are required to intentionally modulate cellular phenotypes. Here, we designed a platform that allows switching control of glycolysis in Escherichia coli in response to an environmental signal, in this case, temperature. This system functions by regulating the expression of gapA, which encodes glyceraldehyde-3-phosphate dehydrogenase (GAPDH), one of the key glycolytic enzymes. Because a very low level of gapA expression is capable of maintaining cellular physiology, we also modified GAPDH through directed evolution to provide sensitive regulation of glycolytic activity. The switching control of glycolysis was successfully demonstrated by regulating the expression of engineered gapA through changes in temperature. This system offers potential control over the cell's central carbon-metabolism switch, providing the ability to perform reprogrammed tasks with desired timing depending on environmental signals.