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Physics predicts why and where biological cells are regulated

It can seem that cells make choices about behavior that is often hard to explain, but often mimic social interactions. Game theory, in particular, has been insightful for understanding the dynamics of populations of microbes. Unfortunately, an unintended consequence of applying social concepts such as game theory to cells is the use of language that frames our thinking. Bet hedging strategies, cooperators, cheaters, noncooperators, altruistic cells, etc. are common descriptions of cell behavior found in the literature. Who doesn’t think of a cancer cell as being a selfish cell – undergoing unlimited growth despite the fact that it will ultimately kill its host? But this anthropomorphic view doesn’t help us cure cancer, either. (Image courtesy of Nathan Johnson and Pacific Northwest National Laboratory).

In comparison, physics-based theories about life, which have been around for 100 years, have garnered little attention. Lotka proposed in 1922 that natural selection is about who can harvest the required energy for reproduction from the environment the fastest. We now know that biological cells are part of the same phenomena as hurricanes and tornadoes, called dissipative systems. As the lower atmosphere heats up in the summer due to radiation from the sun, winds form that move the hot air to the cooler upper atmosphere. Under normal conditions, the winds are relatively random – a gust here, a gust there and seemingly changing directions from moment to moment. But when the temperature difference between the upper and lower atmosphere becomes large enough, the winds become correlated in an attempt to reduce the temperature difference as quick as possible. Circular wind patterns form, with heat being taken from the hot lower atmosphere and dumped in the cooler upper atmosphere. When these circular winds rotate sideways, they become tornadoes.

From the viewpoint of physics, the atmosphere is trying to redistribute energy equally. The fastest way to do that is to have correlated motions (convection cells) to do that.

Biological cells serve the same purpose, but now the correlated processes are enabled by visible chemical structures. Sunlight comes to the cell in the form of high energy radiation, and that radiation is captured and turned into lower energy chemical compounds. The driving force again is the need to distribute energy equally in nature. Except now, those lower energy chemical compounds form the cell structures needed to capture the sunlight. The more sun that is captured by a cell, the more cells that can be produced – to capture more sunlight. This is the process of metabolism and growth.

The chemical compounds produced need to be in just the right proportions to form structures that can capture energy, however. This is where things can get out of control. If some compounds are produced in too great of a quantity, the energy-capturing structures can’t form. Cells regulate this process. Dysregulation can cause more than just cells not working well – it can cause cancer – unregulated growth to the detriment of the host. In our new study, we have shown that known sites of metabolic regulation in cells, enzyme regulation, can be predicted based on these very principles.

Read about the technical details in the article, Enzyme activities predicted by metabolite concentrations and solvent capacity in the cell, published in the Journal of The Royal Society Interface This work was paid for by the National Institute of Biomedical Imaging and Bioengineering and the U.S. Department of Energy, Office of Biological and Environmental Research.

On the Reunification of Chemical and Biochemical Thermodynamics

For 26 years, it has been assumed by some that the thermodynamics of open-system biochemical reactions must be executed by performing Legendre transformations on the terms involving the species whose concentrations are being held fixed. In contrast, standard nontransformed thermodynamics applies to chemical processes. However, it has recently been shown that such biochemical reactions may be accurately examined using either method. The papers that report this finding use the hydrolysis of ATP at fixed pH and pMg as an example. This biochemical process comprises 14 equilibrium reactions involving 17 chemical species. Consequently, the chemical and mathematical complexity is so high that the underlying principles leading to the equivalence of the two methods tend to become lost. Furthermore, the details of such an example are too complex for classroom presentation. This paper makes these principles abundantly clear by the thermodynamic examination of the simple case of a unimolecular isomerization conducted under both open and closed conditions. For the open system, the analysis is conducted using both Legendre-transformed and nontransformed methods. The results are shown to be identical provided that the chemical potentials of the terms on which the transform is performed are held constant. More importantly, the analysis makes the underlying reasons for the equivalence of the two methods very clear and shows when they will not be equivalent. The model is ideally suited for classroom presentation because of its chemical and mathematical simplicity.

Circadian Proteomic Analysis Uncovers Mechanisms of Post-Transcriptional Regulation in Metabolic Pathways

Transcriptional and translational feedback loops in fungi and animals drive circadian rhythms in transcript levels that provide output from the clock, but post-transcriptional mechanisms also contribute. To determine the extent and underlying source of this regulation, we applied newly developed analytical tools to a long-duration, deeply sampled, circadian proteomics time course comprising half of the proteome. We found a quarter of expressed proteins are clock regulated, but >40% of these do not arise from clock-regulated transcripts, and our analysis predicts that these protein rhythms arise from oscillations in translational rates. Our data highlighted the impact of the clock on metabolic regulation, with central carbon metabolism reflecting both transcriptional and post-transcriptional control and opposing metabolic pathways showing peak activities at different times of day. The transcription factor CSP-1 plays a role in this metabolic regulation, contributing to the rhythmicity and phase of clock-regulated proteins.


Comparison of Optimal Thermodynamic Models of the Tricarboxylic Acid Cycle from Heterotrophs, Cyanobacteria and Green Sulfur Bacteria

We have applied a new stochastic simulation approach to predict the metabolite levels, material flux and thermodynamic profiles of the oxidative TCA cycles found in E. coli and Synechococcus sp. PCC 7002, and in the reductive TCA cycle typical of chemolithoautotrophs and phototrophic green sulfur bacteria such as Chlorobaculum tepidum. The simulation approach is based on modeling states using statistical thermodynamics and employs an assumption similar to that used in transition state theory. The ability to evaluate the thermodynamics of metabolic pathways allows one to understand the relationship between coupling of energy and material gradients in the environment and the self-organization of stable biological systems, and it is shown that each cycle operates in the direction expected due to its environmental niche. The simulations predict changes in metabolite levels and flux in response to changes in cofactor concentrations that would be hard to predict without an elaborate model based on the law of mass action. In fact, we show that a thermodynamically unfavorable reaction can still have flux in the forward direction when it is part of a reaction network. The ability to predict metabolite levels, energy flow and material flux should be significant for understanding the dynamics of natural systems and for understanding principles for engineering organisms for production of specialty chemicals.

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Concepts, Challenges and Successes in Modeling Thermodynamics of Metabolism

The modeling of the chemical reactions involved in metabolism is a daunting task. Ideally, the modeling of metabolism would use kinetic simulations, but these simulations require knowledge of the thousands of rate constants involved in the reactions. The measurement of rate constants is very labor intensive, and hence rate constants for most enzymatic reactions are not available. Consequently, constraint-based flux modeling has been the method of choice because it does not require the use of the rate constants of the law of mass action. However, this convenience also limits the predictive power of constraint-based approaches in that the law of mass action is used only as a constraint, making it difficult to predict metabolite levels or energy requirements of pathways.
An alternative to both of these approaches is to model metabolism using simulations of states rather than simulations of reactions, in which the state is defined as the set of all metabolite counts or concentrations. While kinetic simulations model reactions based on the likelihood of the reaction derived from the law of mass action, states are modeled based on likelihood ratios of mass action. Both approaches provide information on the energy requirements of metabolic reactions and pathways. However, modeling states rather than reactions has the advantage that the parameters needed to model states (chemical potentials) are much easier to determine than the parameters needed to model reactions (rate constants). Herein we discuss recent results, assumptions and issues in using simulations of state to model metabolism.

Mathematical Modeling of Microbial Community Dynamics: A Methodological Review

Microorganisms in nature form diverse communities that dynamically change in structure and function in response to environmental variations. As a complex adaptive system, microbial communities show higher-order properties that are not present in individual microbes, but arise from their interactions. Predictive mathematical models not only help to understand the underlying principles of the dynamics and emergent properties of natural and synthetic microbial communities, but also provide key knowledge required for engineering them. In this article, we provide an overview of mathematical tools that include not only current mainstream approaches, but also less traditional approaches that, in our opinion, can be potentially useful. We discuss a broad range of methods ranging from low-resolution supra-organismal to high-resolution individual-based modeling. Particularly, we highlight the integrative approaches that synergistically combine disparate methods. In conclusion, we provide our outlook for the key aspects that should be further developed to move microbial community modeling towards greater predictive power.
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