Data-driven flow-map models for data-efficient discovery of dynamics and fast uncertainty quantification of biological and biochemical systems

Computational models are increasingly used to investigate and predict the complex dynamics of biological and biochemical systems. Nevertheless, governing equations of a biochemical system may not be (fully) known, which would necessitate learning the system dynamics directly from, often limited and noisy, observed data. On the other hand, when expensive models are available, systematic and efficient quantification of the effects of model uncertainties on quantities of interest can be an arduous task. This paper leverages the notion of flow-map (de)compositions to present a framework that can address both of these challenges via learning data-driven models useful for capturing the dynamical behavior of biochemical systems. Data-driven flow-map models seek to directly learn the integration operators of the governing differential equations in a black-box manner, irrespective of structure of the underlying equations. As such, they can serve as a flexible approach for deriving fast-to-evaluate surrogates for expensive computational models of system dynamics, or, alternatively, for reconstructing the long-term system dynamics via experimental observations. We present a data-efficient approach to data-driven flow-map modeling based on polynomial chaos Kriging. The approach is demonstrated for discovery of the dynamics of various benchmark systems and a coculture bioreactor subject to external forcing, as well as for uncertainty quantification of a microbial electrosynthesis reactor. Such data-driven models and analyses of dynamical systems can be paramount in the design and optimization of bioprocesses and integrated biomanufacturing systems.     

Moving calls: a vocal mechanism underlying quorum decisions in cohesive groups

Members of social groups need to coordinate their behaviour when choosing between alternative activities. Consensus decisions enable group members to maintain group cohesion and one way to reach consensus is to rely on quorums. A quorum response is where the probability of an activity change sharply increases with the number of individuals supporting the new activity. Here, we investigated how meerkats (Suricata suricatta) use vocalizations in the context of movement decisions. Moving calls emitted by meerkats increased the speed of the group, with a sharp increase in the probability of changing foraging patch when the number of group members joining the chorus increased from two up to three. These calls had no apparent effect on the group's movement direction. When dominant individuals were involved in the chorus, the group's reaction was not stronger than when only subordinates called. Groups only increased speed in response to playbacks of moving calls from one individual when other group members emitted moving calls as well. The voting mechanism linked to a quorum probably allows meerkat groups to change foraging patches cohesively with increased speed. Such vocal coordination may reflect an aggregation rule linking individual assessment of foraging patch quality to group travel route.     

Molecular Mechanism of Polypeptide Translocation Catalyzed by the Escherichia coli ClpA Protein Translocase

The removal of damaged or unneeded proteins by ATP-dependent proteases is crucial for cell survival in all organisms. Integral components of ATP-dependent proteases are motor proteins that unfold stably folded proteins that have been targeted for removal. These protein unfoldases/polypeptide translocases use ATP to unfold the target proteins and translocate them into a proteolytic component. Despite the central role of these motor proteins in cell homeostasis, a number of important questions regarding the molecular mechanisms of enzyme catalyzed protein unfolding and translocation remain unanswered. Here, we demonstrate that Escherichia coli ClpA, in the absence of the proteolytic component ClpP, processively and directionally steps along the polypeptide backbone with a kinetic step size of ∼ 14 amino acids, independent of the concentration of ATP with a rate of ∼ 19 amino acids s⁻¹ at saturating concentrations of ATP. In contrast to earlier studies by others, we have developed single-turnover fluorescence stopped-flow methods that allow us to quantitatively examine the molecular mechanism of the motor component ClpA decoupled from the proteolytic component ClpP. For the first time, we reveal that in the absence of ClpP ClpA translocates polypeptides directionally, processively and in discrete steps similar to other motor proteins that translocate vectorially on a linear lattice, such as nucleic acid helicases and kinesin. We believe that the methods employed here will be generally applicable to the examination of other AAA?+ protein translocases involved in a variety of important biological functions where the substrate is not covalently modified; for example, membrane fusion, membrane transport, protein disaggregation, and protein refolding.     

Light‐based Regeneration Niches: Evidence from 21 Dipterocarp Species using Size‐specific RGRs

A continuing challenge in tropical ecology is to explain the coexistence of large numbers of rain forest tree species. One possible coexistence mechanism is partitioning of the highly variable and dynamic forest light environment, in which species that grow better in one light treatment grow worse in another. To test whether species respond differently to the light environment, we estimated growth rates of 21 Dipterocarpaceae species from Malaysian Borneo grown in shade houses for 2 yr in three light treatments (0.3%, 3%, and 18% full sunlight). We made regular measurements of height, diameter, and aboveground biomass, enabling us to calculate growth rates for each response. We estimated size‐specific growth rates using nonlinear mixed‐effects models, as average relative growth rate was strongly size dependent. For all species, the greatest diameter growth rate was achieved in 18 percent full sunlight, whereas for five of the twenty‐one species, the greatest height growth rate was achieved in three percent full sunlight. We investigated correlations among growth rates in different light treatments, but no negative correlations were found, indicating that species growing well in one light treatment did not grow poorly in the others. There were substantial crossovers, however, in species ranks among the three light treatments, indicating that there was no single growth rate hierarchy common to all light treatments. The lack of a single consistent growth hierarchy across light treatments indicates that heterogeneity in the forest light environment could contribute to the maintenance of the diversity of Dipterocarpaceae found in lowland Bornean rain forests via light‐based regeneration niches.     

Leaf growth characteristics of Vitis vinifera and prediction of final lamina length for studies of powdery mildew

Total functional leaf area is a key factor in determining crop yield. A nonlinear mixed‐effects model was employed to estimate growth responses for individual leaves using repeated measures of lamina length ≥30 mm, in the absence of disease. Resulting growth curves make allowances for, and allow assessment of, leaf to leaf variability. The major source of variability in leaf growth was identified as differences in thermal time required to reach half final lamina length. Juvenile leaves of Vitis vinifera are susceptible to infection by the powdery mildew fungus (Erysiphe necator) which impairs leaf function. The model was used to predict unobserved final lamina length for a subset of leaves inoculated with E. necator immediately after observations ceased. The severity of infection by E. necator varies among infected leaves. A previous study identified which of the inoculated leaves developed symptoms of severe powdery mildew. Maximum severity of infection was found to occur when individual leaves were at 85.3–97.9% of predicted final lamina length.     

Impacts of statistical feedback on the flexibility-accuracy trade-offin biological systems

Biological systems possess the ability to adapt quickly andadequately to both environmental and internal changes. This vital ability cannot be explained in terms ofconventional stochastic processes because such processes arecharacterized by atrade-off between flexibility and accuracy, that is, they either show shorttransition times (large Kramers escape rates) to broad steady-statedistributions or long transition times to sharply peaked distributions. To develop a stochastic theory for systemsexhibiting both flexibility and accuracy, we study systems under the impact of white noise multiplied with anaccordant statistical measure, here the probability density. Thisresults in negative feedback and circular causality: the more probable a stable state the lessit will be affected by noise and, conversely, the less a stable state is affected by noisethe more probable it is. Using nonlinear Fokker-Planckequations, steady states are computed via transformations ofsolutions of the corresponding linear Fokker-Planck equations. Transients reveal rapidly evolving and sharply peaked probability densities and thus mimic systems characterized by both flexibility and accuracy.     

The Sinus Node as a Nonlinear Dynamic System

The Sinus Node (SN) of the heart is the natural pacemaker driving electrical impulses into the atria, an ordinary excitable medium. In order to avoid wave interference, the SN operation must be of such a nature that no reflections from the atria should occur. It is shown that such a behavior is achieved when the SN operates in a nonlinear dynamical regime situated away from relaxation.     

On measurements of the higher harmonics of transmembrane current

The higher harmonics of the current caused by an alternating voltage applied to bilayer lipid membranes made of diphytanoyl phosphatidylcholine (DPhPC) in decane and tetradecane were measured. A universal relation between the amplitudes of harmonics was proposed and experimentally verified. This allowed the coefficients of expansion of the capacitance in even powers of voltage to be calculated for the DPhPC membrane in tetradecane; it also permitted comparison of the inhomogeneity in the thickness of the DPhPC membranes in decane and tetradecane.     

Metrics from nonlinear dynamics adapted for characterizing the behavior of nonequilibrium enzymatic rate functions

Several metrics from nonlinear dynamics and statistical mechanics have been characterized on computer-generated number series with various signal-to-noise ratios, demonstrating their individual reliability as a function of sample size and their relationships to each other. The root mean square (RMS) evaluates amplitude, and the power spectral density (PSD) provides a visual display of the frequency spectrum; both measures have very high reliability even for an N as low as 50. The Fractal Dimension (D) is shown to converge rapidly and also to be reliable when N is as low as 50. These three measures (RMS, PSD, and D) have been applied to the complex kinetics of tyrosine hydroxylase time courses (50-point curves) at various BH4 concentrations (near physiological, but far from equilibrium levels). Recently developed measures of spectral entropy and the Liapunov Exponent, -lambda are also characterized.     

Evidence for species differences in the pattern of androgen receptor distribution in relation to species differences in an androgen‐dependent behavior

Chickens (Gallus gallus domesticus) and Japanese quail (Coturnix japonica), two closely related gallinaceous bird species, exhibit a form of vocalization—crowing—which differs between the species in two components: its temporal acoustic pattern and its accompanying postural motor pattern. Previous work utilizing the quail‐chick chimera technique demonstrated that the species‐specific characteristics of the two crow components are determined by distinct brain structures: the midbrain confers the acoustic pattern, and the caudal hindbrain confers the postural pattern. Crowing is induced by androgens, acting directly on androgen receptors. As a strategy for identifying candidate neurons in the midbrain and caudal hindbrain that could be involved in crow production, we performed immunocytochemistry for androgen receptors in these brain regions in both species. We also investigated midbrain‐to‐hindbrain vocal‐motor projections. In the midbrain, both species showed prominent androgen receptor immunoreactivity in the nucleus intercollicularis, as had been reported in previous studies. In the caudal hindbrain, we discovered characteristic species differences in the pattern of androgen receptor distribution. Chickens, but not quail, showed strong immunoreactivity in the tracheosyringeal division of the hypoglossal nucleus, whereas quail, but not chickens, possessed strong immunoreactivity in a region of the ventrolateral medulla. Some of these differences in hindbrain androgen receptor distribution may be related to the species differences in the postural component of crowing behavior. The results of the present study imply that the spatial distribution of receptor proteins can vary even between closely related species. Such variation in receptor distribution could underlie the evolution of species differences in behavior. © 2002 Wiley Periodicals, Inc. J Neurobiol 52: 203–220, 2002