Generalized Michaelis-Menten rate law with time-varying molecular concentrations.

The Michaelis-Menten (MM) rate law has been the dominant paradigm of modeling biochemical rate processes for over a century with applications in biochemistry, biophysics, cell biology, systems biology, and chemical engineering. The MM rate law and its remedied form stand on the assumption that the concentration of the complex of interacting molecules, at each moment, approaches an equilibrium (quasi-steady state) much faster than the molecular concentrations change. Yet, this assumption is not always justified. Here, we relax this quasi-steady state requirement and propose the generalized MM rate law for the interactions of molecules with active concentration changes over time. Our approach for time-varying molecular concentrations, termed the effective time-delay scheme (ETS), is based on rigorously estimated time-delay effects in molecular complex formation. With particularly marked improvements in protein-protein and protein-DNA interaction modeling, the ETS provides an analytical framework to interpret and predict rich transient or rhythmic dynamics (such as autogenously-regulated cellular adaptation and circadian protein turnover), which goes beyond the quasi-steady state assumption.

Backward simulation for inferring hidden biomolecular kinetic profiles.

Our backward simulation (BS) is an approach to infer the dynamics of individual components in ordinary differential equation (ODE) models, given the information on relatively downstream components or their sums. Here, we demonstrate the use of BS to infer protein synthesis rates with a given profile of protein concentrations over time in a circadian system. This protocol can also be applied to a wide range of problems with undetermined dynamics at the upstream levels. For complete details on the use and execution of this protocol, please refer to Lim et al. (2021).

Cost-effective circadian mechanism: rhythmic degradation of circadian proteins spontaneously emerges without rhythmic post-translational regulation.

Circadian protein oscillations are maintained by the lifelong repetition of protein production and degradation in daily balance. It comes at the cost of ever-replayed, futile protein synthesis each day. This biosynthetic cost with a given oscillatory protein profile is relievable by a rhythmic, not constant, degradation rate that selectively peaks at the right time of day but remains low elsewhere, saving much of the gross protein loss and of the replenishing protein synthesis. Here, our mathematical modeling reveals that the rhythmic degradation rate of proteins with circadian production spontaneously emerges under steady and limited activity of proteolytic mediators and does not necessarily require rhythmic post-translational regulation of previous focus. Additional (yet steady) post-translational modifications in a proteolytic pathway can further facilitate the degradation's rhythmicity in favor of the biosynthetic cost saving. Our work is supported by animal and plant circadian data, offering a generic mechanism for potentially widespread, time-dependent protein turnover.

Publisher Correction: Large-scale metabolic interaction network of the mouse and human gut microbiota.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Large-scale metabolic interaction network of the mouse and human gut microbiota.

The role of our gut microbiota in health and disease is largely attributed to the collective metabolic activities of the inhabitant microbes. A system-level framework of the microbial community structure, mediated through metabolite transport, would provide important insights into the complex microbe-microbe and host-microbe chemical interactions. This framework, if adaptable to both mouse and human systems, would be useful for mechanistic interpretations of the vast amounts of experimental data from gut microbiomes in murine animal models, whether humanized or not. Here, we constructed a literature-curated, interspecies network of the mammalian gut microbiota for mouse and human hosts, called NJC19. This network is an extensive data resource, encompassing 838 microbial species (766 bacteria, 53 archaea, and 19 eukaryotes) and 6 host cell types, interacting through 8,224 small-molecule transport and macromolecule degradation events. Moreover, we compiled 912 negative associations between organisms and metabolic compounds that are not transportable or degradable by those organisms. Our network may facilitate experimental and computational endeavors for the mechanistic investigations of host-associated microbial communities.

A modified von Bertalanffy growth model dependent on temperature and body size.

Fish growth models are widely used in fisheries as well in aquacultures and ecology. Water temperature is one of the most important factors determining the growth of fish. In the present study, we propose a growth model that includes the effect of water temperature on the growth in the von Bertalanffy growth model. Our model was applied to fit the growth data of bullhead (Cottus gobio), brown trout (Salmo trutta L.), juvenile salmon (Salmo salar), and Araucanian herring (Strangomera bentincki). The model reproduces the growth patterns of each species and fits a set of appropriate parameter values for each species. Moreover, the model reflects the seasonal growth rates quite well.