Revised Michaelis-Menten rate law with time-varying molecular concentrations

Despite over a century's use as a dominant paradigm in the description of biochemical rate processes, the Michaelis-Menten (MM) rate law stands on the restrictive assumption that the concentration of the complex of interacting molecules, at each moment, approaches an equilibrium much faster than the molecular concentration changes. The increasingly-appreciated, remedied form of the MM rate law is also based on this quasi-steady state assumption. Although this assumption may be valid for a range of biochemical systems, the exact extent of such systems is not clear. In this study, we relax the quasi-steady state requirement and propose the revised MM rate law for the interactions of molecules with active concentration changes over time. Our revised rate law, characterized by rigorously-derived time delay effects in molecular complex formation, improves the accuracy of models especially for protein-protein and protein-DNA interactions. Our simulation and empirical data analysis show that the improvement is not limited to the quantitatively better characterization of the dynamics, but also allows the prediction for qualitatively new patterns in the systems of interest. The latter include the oscillation condition and period patterns of the mammalian circadian clock and the spontaneous rhythmicity in the degradation rates of circadian proteins, both not properly captured by the previous approaches. Moreover, our revised rate law is capable of more accurate parameter estimation. This work offers an analytical framework for understanding rich dynamics of biomolecular systems, which goes beyond the quasi-steady state assumption.

An Object-Based Method for Tracking Convective Storms in Convection Allowing Models

The steady-state assumption commonly used in object-based tracking algorithms may be insufficient to determine the right track when a convective storm goes through a complicated evolution. Such an issue is exacerbated by the relatively coarse output frequency of current convection allowing model (CAM) forecasts (e.g., hourly), giving rise to many spatially well resolved but temporally not well resolved storms that steady-state assumption could not account for. To reliably track simulated storms in CAM outputs, this study proposed an object-based method with two new features. First, the method explicitly estimated the probability of each probable track based on either its immediate past and future motion or a reliable “first-guess motion” derived from storm climatology or near-storm environmental variables. Second, object size was incorporated into the method to help identify temporally not well resolved storms and minimize false tracks derived for them. Parameters of the new features were independently derived from a storm evolution analysis using 2-min Multi-Radar Multi-Sensor (MRMS) data and hourly CAM forecasts produced by the University of Oklahoma (OU) Multiscale data Assimilation and Predictability Laboratory (MAP) from May 2019. The performance of the new method was demonstrated with hourly MRMS and CAM forecast examples from May 2018. A systematic evaluation of four severe weather events indicated 99% accuracy achieved for over 600 hourly MRMS tracks derived with the proposed tracking method.

Evaluating the Steady-state Performance of the Synthetic Coefficient of Variation Chart

The synthetic coefficient of variation (CV) chart is attractive to practitioners as it allows for a second point to fall outside the control limits before deciding whether the process is out-of-control. The existing synthetic CV chart is designed with a head-start feature, which shows an advantage under the zero-state assumption where shifts happen immediately after process monitoring has started. However, this assumption may not be valid as shifts may happen quite some time after process monitoring has started. This is called the steady-state condition. This paper evaluates the performance of the chart under the steady-state condition. It is shown that the steady-state out-of-control average run length (ARL1) is substantially larger than the zero-state ARL1, hence larger number of samples are needed to detect the out-of-control condition. From the comparison with other CV charts, the steady-state synthetic CV chart does not show better performance, especially for small sample sizes and shift sizes. Hence, the synthetic CV chart is not recommended to be adopted under the steady-state condition, and its good performance is only applicable under the zero-state assumption. The results of this paper enable practitioners to be aware that the performance of the synthetic CV chart may be inferior under actual application (when shifts do not happen at the beginning of process monitoring) compared to its zero-state performance.

Three-Factor Kinetic Equation of Catalyst Deactivation

The three-factor kinetic equation of catalyst deactivation was obtained in terms of apparent kinetic parameters. The three factors correspond to the main cycle with a linear, detailed mechanism regarding the catalytic intermediates, a cycle of reversible deactivation, and a stage of irreversible deactivation (aging), respectively. The rate of the main cycle is obtained for the fresh catalyst under a quasi-steady-state assumption. The phenomena of reversible and irreversible deactivation are presented as special separate factors (hierarchical separation). In this case, the reversible deactivation factor is a function of the kinetic apparent parameters of the reversible deactivation and of those of the main cycle. The irreversible deactivation factor is a function of the apparent kinetic parameters of the main cycle, of the reversible deactivation, and of the irreversible deactivation. The conditions of such separability are found. The obtained equation is applied successfully to describe the literature data on the reversible catalyst deactivation processes in the dehydration of acetaldehyde over TiO2 anatase and in crotonaldehyde hydrogenation on supported metal catalysts.

On the Distributed Construction of Stable Networks in Polylogarithmic Parallel Time

We study the class of networks, which can be created in polylogarithmic parallel time by network constructors: groups of anonymous agents that interact randomly under a uniform random scheduler with the ability to form connections between each other. Starting from an empty network, the goal is to construct a stable network that belongs to a given family. We prove that the class of trees where each node has any k≥2 children can be constructed in O(logn) parallel time with high probability. We show that constructing networks that are k-regular is Ω(n) time, but a minimal relaxation to (l,k)-regular networks, where l=k−1, can be constructed in polylogarithmic parallel time for any fixed k, where k>2. We further demonstrate that when the finite-state assumption is relaxed and k is allowed to grow with n, then k=loglogn acts as a threshold above which network construction is, again, polynomial time. We use this to provide a partial characterisation of the class of polylogarithmic time network constructors.

Reply to “Comments on ‘Global and Regional Entropy Production by Radiation Estimated from Satellite Observations’”

This reply addresses a comment on the study by Kato and Rose (herein referred to as KR2020). The comment raises four points of criticism. These are 1) on notations used, 2) on a steady-state assumption made, 3) on the result of entropy production change with Earth’s albedo, and 4) disputing the statement that a simple energy balance model cannot produce absorption temperature change with Earth’s albedo. We concur on points 2 and 3 raised by the comment and recognize the significance of entropy storage due to ocean heating in the analysis of how entropy production changes with the shortwave absorptivity of Earth. Once entropy storage is considered, the results of KR2020 indicate that the increase of entropy production rate by irreversible processes, including by radiative processes, is smaller than the increase of entropy storage when absorptivity is increased. This is a manifestation of the primary contribution of positive top-of-atmosphere net irradiances (i.e., energy input to Earth) to heating the ocean and is consistent with an energy budget perspective. Once entropy storage is separated, the entropy production by irreversible processes increases with the shortwave absorptivity.

Toward transient subgrid-scale gravity wave representation in atmospheric models. Part I: Propagation model including non-dissipative direct wave-mean-flow interactions

Current gravity-wave (GW) parameterization (GWP) schemes are using the steady-state assumption, where an instantaneous balance between GWs and mean flow is postulated, thereby neglecting transient, non-dissipative direct interactions between the GW field and the resolved flow. These schemes rely exclusively on wave dissipation, by GW breaking or near critical layers, as a mechanism leading to forcing of the mean flow. In a transient GWP, without steady-state assumption, non-dissipative direct wave-mean-flow interactions are enabled as an additional mechanism. Idealized studies have shown that this is potentially important, so that the transient GWP Multi-Scale Gravity-Wave Model (MS-GWaM) has been implemented into a state-of-the-art weather and climate model. In this implementation, MS-GWaM leads to a zonal-mean circulation well in agreement with observations, and increases GW momentum-flux intermittency as compared to steady-state GWPs, bringing it into better agreement with super-pressure balloon observations. Transient effects taken into account by MS-GWaM are shown to make a difference even on monthly time-scales: in comparison with steady-state GWPs momentum fluxes in the lower stratosphere are increased and the amount of the missing drag at Southern Hemispheric high latitudes is decreased to a modest but non-negligible extent. An analysis of the contribution of different wavelengths to the GW signal in MS-GWaM suggests that small scale GWs play an important role down to horizontal and vertical wavelengths of 50km (or even smaller) and 200m respectively.