Morphologically structured model for antitumoral retamycin production during batch and fed-batch cultivations of Streptomyces olindensis

A morphologically structured model is proposed to describe trends in biomass growth, substrate consumption, and antitumoral retamycin production during batch and fed-batch cultivations of Streptomyces olindensis. Filamentous biomass is structured into three morphological compartments (apical, subapical, and hyphal), and the production of retamycin, a secondary metabolite, is assumed to take place in the subapical cell compartment. Model accounts for the effect of glucose as well as complex nitrogen source on both the biomass growth and retamycin production. Laboratory data from bench-scale batch and fed-batch fermentations were used to estimate some model parameters by nonlinear regression. The predictive capability of the model was then tested for additional fed-batch and continuous experiments not used in the previous fitting procedure. The model predictions show fair agreement to the experimental data. The proposed model can be useful for further studies on process optimization and control.     

Multivariate analysis of noise in genetic regulatory networks

Stochasticity is an intrinsic property of genetic regulatory networks due to the low copy numbers of the major molecular species, such as, DNA, mRNA, and regulatory proteins. Therefore, investigation of the mechanisms that reduce the stochastic noise is essential in understanding the reproducible behaviors of real organisms and is also a key to design synthetic genetic regulatory networks that can reliably work. We use an analytical and systematic method, the linear noise approximation of the chemical master equation along with the decoupling of a stoichiometric matrix. In the analysis of fluctuations of multiple molecular species, the covariance is an important measure of noise. However, usually the representation of a covariance matrix in the natural coordinate system, i.e. the copy numbers of the molecular species, is intractably complicated because reactions change copy numbers of more than one molecular species simultaneously. Decoupling of a stoichiometric matrix, which is a transformation of variables, significantly simplifies the representation of a covariance matrix and elucidates the mechanisms behind the observed fluctuations in the copy numbers. We apply our method to three types of fundamental genetic regulatory networks, that is, a single-gene autoregulatory network, a two-gene autoregulatory network, and a mutually repressive network. We have found that there are multiple noise components differently originating. Each noise component produces fluctuation in the characteristic direction. The resulting fluctuations in the copy numbers of the molecular species are the sum of these fluctuations. In the examples, the limitation of the negative feedback in noise reduction and the trade-off of fluctuations in multiple molecular species are clearly explained. The analytical representations show the full parameter dependence. Additionally, the validity of our method is tested by stochastic simulations.     

Drivers of terrestrial plant production across broad geographical gradients

Terrestrial net primary production (NPP) varies across global climate gradients, but the mechanisms through which climate drives this variation remain subject to debate. Specifically, it is debatable whether NPP is primarily influenced by ‘direct’ effects of climate on the kinetics of plant metabolism or ‘indirect’ effects of climate on plant size, stand biomass, stand age structure and growing season length. We clarify several issues in this debate by presenting multiple lines of evidence that support a primarily indirect influence of climate on global variation in NPP across broad geographical gradients. First, we highlight > 60 years of research that suggests leaf area, growing season length, plant biomass and/or plant age are better predictors of NPP than climate or latitude. Second, we refute recent claims that using biomass and age as predictors of NPP represents circular reasoning. Third, we illustrate why effects of climate on the kinetics of plant production must be evaluated using instantaneous (not annualized) rates of productivity. Fourth, we review recent analyses showing that the effects of biomass and age on NPP are much stronger than the effects of climate. Fifth, we present new analyses of a high‐quality NPP dataset that demonstrate further that biomass, age and growing season length are better predictors of global variation in NPP than climate variables. Our results are consistent with the hypothesis that variation in NPP across global climate gradients primarily reflects the influence of climate on growing season length and stand biomass, as well as stand age, rather than the effects of temperature and precipitation on the kinetics of metabolism. However, this hypothesis should be evaluated further using larger, high‐quality observational and experimental datasets spanning multiple geographical scales.     

Concurrent schedule performance in domestic goats: persistent undermatching

Performance of nine domestic goats responding under concurrent variable-interval variable-interval schedules of food delivery was examined, with results analyzed in terms of the generalized matching equation. Substantial undermatching of response and time allocation ratios to obtained reinforcement ratios was evident. Post-reinforcement pause time ratios approximately matched obtained reinforcement ratios. Subtracting these times from total time allocation values yielded net time allocation ratios, which undermatched obtained reinforcement ratios to a greater degree than whole-session time allocation ratios. Slopes of regression lines relating behavioral outputs to environmental inputs characteristically were below 0.6, which is similar to previous findings in dairy cows tested under comparable conditions.     

Prospects for advancing the understanding of complex biochemical systems

The application of mathematical theories to understanding the behaviour of complex biochemical systems is reviewed. Key aspects of behaviour are identified as the flux through particular pathways in a steady state, the nature and stability of dynamical states, and the thermodynamic properties of systems. The first of these is dealt primarily in theories of metabolic control, and metabolic control analysis (MCA) is an important example. The valid application of this theory is limited to steady-state systems, and the cases where the essential features of control can be derived from calibration experiments which perturb the state of the system by a sufficiently small amount from its operating point. In practice, time-dependent systems exist, it is not always possible to know a priori whether applied perturbations are sufficiently small, and important features of control may lie farther from the operating point than the application of the theory permits. The nature and stability of dynamical and thermodynamical states is beyond the scope of MCA. To understand the significance of these limitations fully, and to address the dynamical and thermodynamical properties, more complete theories are required. Non-linear systems theory offers the possibility of studying important questions regarding control of steady and dynamical states. It can also link to thermodynamic properties of the system including the energetic efficiency of particular pathways. However, its application requires a more detailed characterisation of the system under study. This extra detail may be an essential feature of the study of non-equilibrium states in general, and non-ideal pathways in particular. Progress requires considerably more widespread integration of theoretical and experimental approaches than currently exists.     

On the mathematical modelling of pain

In this review a case is presented for the use of mathematical modelling in the study of pain. The philosophy of mathematical modelling is outlined and a recommendation is made for the use of modern nonlinear techniques and computational neuroscience in the modelling of pain. Classic and more recent examples of modelling in neurobiology in general and pain in particular, at three different levels—molecular, cellular and neural networks—are described and evaluated. Directions for further progress are indicated, particularly in plasticity and in modelling brain mechanisms. Major advantages of mathematical modelling are that it can handle extremely complex theories and it is non-invasive, and so is particularly valuable in the investigation of chronic pain. Special issue dedicated to Dr. Herman Bachelard     

Phase resetting associated with changes of burst shape

Based on our stochastic approach to phase resetting of an ensemble of oscillators, in this article we investigate two stimulation mechanisms which exhibit qualitatively different dynamical behaviour as compared with the stimulation mechanism analysed in a previous study. Both the old as well as one of the new stimulation mechanisms give rise to a characteristic desynchronization behaviour: A stimulus of a given (non-vanishing) intensity administered at a critical initial ensemble phase for a critical duration T _crit annihilates the ensemble's synchronized oscillation. When the stimulation duration exceeds T _crit a transition from type 1 resetting to type 0 resetting occurs. The second new stimulation mechanism does not cause a desynchronization which is connected with a phase singularity. Correspondingly this mechanism only leads to type 1 resetting. In contrast to the stimulation mechanism analysed in a previous study, both new stimulation mechanisms cause burst splitting. According to our results, in this case peak or onset detection algorithms are not able to reveal a correct estimate of the ensemble phase. Thus, whenever stimulation induced burst splitting occurs, phase-resetting curves determined by means of peak or onset detection may be nothing but artifacts. Therefore it is necessary to understand burst splitting in order to develop reliable phase detection algorithms, which are e.g. based on detecting bursts' centers of mass. Our results are important for experimentalists: Burst splitting is, for instance, well-known from tremor resetting experiments. Thus, it often turned out to be at least rather difficult to derive reliable phase-resetting curves from experimental data.     

The IPAT Equation and Its Variants

In the early 1970s Ehrlich and Holdren devised a simple equation in dialogue with Commoner identifying three factors that created environmental impact. Thus, impact (I) was expressed as the product of (1) population, (P); (2) affluence, (A); and (3) technology, (T). This article tracks the various forms the IPAT equation has taken over 30 years as a means of examining an underlying shift among many environmentalists toward a more accepting view of the role technology can play in sustainable development. Although the IPAT equation was once used to determine which single variable was the most damaging to the environment, an industrial ecology view reverses this usage, recognizing that increases in population and affluence can, in many cases, be balanced by improvements to the environment offered by technological systems.