The Natural Rate of Interest and the Optimal Rate of Interest in the Steady State

The “natural rate of interest” is the hypothetical, risk-free real rate of interest that would obtain in a closed economy, if net public debt were zero. It is considerably less than the optimal steady-state rate of interest, which is equal to the system’s growth rate. This holds for a very general “meta-model.” The fundamental equation of capital theory holds on the optimal steady-state path: T = Z − D, where T is the overall economic period of production, Z is the representative private “waiting period” of consumers and D is the public debt ratio. Prosperity is at least 30% lower at the natural rate of interest than at the optimal rate.

Amplification characteristics in active tapered segmented cladding fiber with large mode area

A kind of tapered segmented cladding fiber (T-SCF) with large mode area (LMA) is proposed, and the mode and amplification characteristics of T-SCFs with concave, linear, and convex tapered structures are investigated based on finite-element method (FEM) and few-mode steady-state rate equation. Simulation results indicate that the concave tapered structure can introduce high loss for high-order modes (HOMs) that is advantageous to achieve single-mode operation, whereas the convex tapered structure provides large effective mode area that can help to mitigate nonlinear effects. Meanwhile, the small-to-large amplification scheme shows further advantages on stripping off HOMs, and the large-to-small amplification scheme decreases the heat load density induced by the high-power pump. Moreover, single-mode propagation performance, effective mode area, and heat load density of the T-SCF are superior to those of tapered step index fiber (T-SIF). These theoretical model and numerical results can provide instructive suggestions for designing high-power fiber lasers and amplifiers.

Comment on “Crystallization of Supercooled Liquids: Self-Consistency Correction of the Steady-State Nucleation Rate” by Abyzov et al., Entropy 2020, 22, 558

It is shown that in the growth region (above the critical nucleation size) the transient distributions obtained numerically from the Becker-Döring equation (BDE) by Abyzov et al., Entropy 2020, 22, 558, are in accurate correspondence with the matched asymptotic (singular perturbation) solution by Shneidman, Sov. Phys. Tech. Phys. 1988, 33, 1338. The solution is unmodified by “self-consistency” corrections which affect only the steady state rate. Sensitivity of the results to selection of a specific form of the BDE (the “nucleation model”) also is briefly discussed.

Biophysical comparison of ATP synthesis mechanisms shows a kinetic advantage for the rotary process

The ATP synthase (F-ATPase) is a highly complex rotary machine that synthesizes ATP, powered by a proton electrochemical gradient. Why did evolution select such an elaborate mechanism over arguably simpler alternating-access processes that can be reversed to perform ATP synthesis? We studied a systematic enumeration of alternative mechanisms, using numerical and theoretical means. When the alternative models are optimized subject to fundamental thermodynamic constraints, they fail to match the kinetic ability of the rotary mechanism over a wide range of conditions, particularly under low-energy conditions. We used a physically interpretable, closed-form solution for the steady-state rate for an arbitrary chemical cycle, which clarifies kinetic effects of complex free-energy landscapes. Our analysis also yields insights into the debated “kinetic equivalence” of ATP synthesis driven by transmembrane pH and potential difference. Overall, our study suggests that the complexity of the F-ATPase may have resulted from positive selection for its kinetic advantage.

A steady-state physiological model for intracellular dimethylsulfoxide in marine phytoplankton

Environmental context Dimethylsulfoxide (DMSO) is important in the biogeochemical cycle of sulfur. Using a mathematical flux model of DMSO production and loss rates, we find that the high intracellular DMSO concentrations measured in phytoplankton cannot be produced without invoking unrealistically high intracellular concentrations of the precursor dimethylsulfoniopropionate, or much lower phytoplankton cellular efflux rates than currently reported. Our study emphasises the need for further investigations of DMSO fluxes across intracellular and outer cell membranes. Abstract Despite 20+ years of research, the mechanisms whereby marine phytoplankton accumulate high dimethylsulfoxide (DMSO) concentrations (up to 1–70mmol per litre of cell volume) are still puzzling. In order to evaluate reported intracellular DMSO concentrations, we constructed a kinetic steady-state rate model of intracellular DMSO concentrations in microalgae based on reported DMSO production from the oxidation of dimethylsulfoniopropionate (DMSP) and loss by diffusion out of the cell. Based on measured rates of DMSO diffusion across the outer cell membrane of model algal species, the steady-state model indicates that sustaining intracellular DMSO concentrations in the millimolar range by the oxidation of intracellular DMSP would require steady-state intracellular DMSP concentrations that are 40 to 10000 times higher than values measured in prymnesiophytes and diatoms, high- and low-DMSP algal groups. However, if DMSO is mainly produced within the chloroplast by the oxidation of DMSP by photosynthetically produced reactive oxygen species, it would have to diffuse through multiple chloroplast membranes before being lost from the cell across the outer membrane. Consequently, its loss rate might be considerably slower than our model predicts, allowing the build-up of higher intracellular DMSO concentrations. Possible biases in sample handling and DMSO analyses could also explain the discrepancy between modelled and measured intracellular DMSO.

Programming and regulation of metabolic homeostasis

Evidence is presented that the rate and equilibrium constants in mitochondrial oxidative phosphorylation set and maintain metabolic homeostasis in eukaryotic cells. These internal constants determine the energy state ([ATP]/[ADP][Pi]), and the energy state maintains homeostasis through a bidirectional sensory/signaling control network that reaches every aspect of cellular metabolism. The energy state is maintained with high precision (to ∼1 part in 1010), and the control system can respond to transient changes in energy demand (ATP utilization) of more than 100 times the resting rate. Epigenetic and environmental factors are able to “fine-tune” the programmed set point over a narrow range to meet the special needs associated with cell differentiation and chronic changes in metabolic requirements. The result is robust across-platform control of metabolism, which is essential to cellular differentiation and the evolution of complex organisms. A model of oxidative phosphorylation is presented, for which the steady-state rate expression has been derived and computer programmed. The behavior of oxidative phosphorylation predicted by the model is shown to fit the experimental data available for isolated mitochondria as well as for cells and tissues. This includes measurements from several different mammalian tissues as well as from insect flight muscle and plants. The respiratory chain and oxidative phosphorylation is remarkably similar for all higher plants and animals. This is consistent with the efficient synthesis of ATP and precise control of metabolic homeostasis provided by oxidative phosphorylation being a key to cellular differentiation and the evolution of structures with specialized function.