Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Flow-through respirometry systems provide accurate measurement of gas exchange over long periods of time. However, these systems have limitations in tracking rapid changes. When an animal infuses a metabolic gas into the respirometry chamber in a short burst, diffusion and airflow in the chamber gradually alter the original signal before it arrives at the gas analyzer. For single or multiple bursts, the recorded signal is smeared or mixed, which may result in dramatically altered recordings compared to the emitted signal. Recovering the original metabolic signal is a difficult task because of the inherent ill conditioning problem. Here, we present two new methods to recover the fast dynamics of metabolic patterns from recorded data. We first re-derive the equations of the well-known Z-transform method (ZT method) to show the source of imprecision in this method. Then, we develop a new model of analysis for respirometry systems based on the experimentally determined impulse response, which is the response of the system to a very short unit input. As a result, we present a major modification of the ZT method (dubbed the ‘EZT method’) by using a new model for the impulse response, enhancing its precision to recover the true metabolic signals. The second method, the generalized Z-transform (GZT) method, was then developed by generalizing the EZT method; it can be applied to any flow-through respirometry system with any arbitrary impulse response. Experiments verified that the accuracy of recovering the true metabolic signals is significantly improved by the new methods. These new methods can be used more broadly for input estimation in variety of physiological systems.

Insects that are small or exhibit low metabolic rates are considered to not require active ventilation to augment diffusive gas exchange. Some pupae with low metabolic rates exhibit abdominal pumping, a behaviour that is known to drive tracheal ventilation in the adults of many species. However, previous work on pupae suggests that abdominal pumping may serve a non-respiratory role. To study the role of abdominal pumping in pupa of the beetle Zophobas morio, we visualized tracheal dynamics with X-rays while simultaneously measuring haemolymph pressure, abdominal movement, and CO 2 emission. Pupae exhibited frequent tracheal compressions that were coincident with both abdominal pumping and pulsation of pressure in the haemolymph. However, more than 63% of abdominal pumping events occurred without any tracheal collapse and hence ventilation, suggesting that the major function of the abdominal pump is not respiratory. In addition, this study shows that the kinematics of abdominal pumping can be used to infer the status of the spiracles and internal behaviour of the tracheal system.

SUMMARYIn this paper, we present a novel structure of a snake-like robot. This structure enables passive locomotion in snake-like robots. Dynamic equations are obtained for motion in a horizontal plane, using Gibbs–Appell method. Kinematic model of the robot include numerous nonholonomic constraints, which can be omitted at the beginning by choosing proper coordinates to describe the model in Gibbs–Appell framework. In such a case, dynamic equations will be significantly simplified, resulting in considerable reduction of simulation time. Simulation results show that, by proper selection of initial conditions, joint angles operate in a limit cycle and robot can locomote steadily on a passive trajectory. It can be seen that the passive trajectory is approximately a Serpenoid curve.

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In many physiological studies, variables of interest are not directly accessible, requiring that they be estimated indirectly from noisy measured signals. Here, we introduce two empirical methods to estimate the true physiological signals from indirectly measured, noisy data. The first method is an extension of Tikhonov regularization to large-scale problems, using a sequential update approach. In the second method, we improve the conditioning of the problem by assuming that the input is uniform over a known time interval, and then use a least-squares method to estimate the input. These methods were validated computationally and experimentally by applying them to flow-through respirometry data. Specifically, we infused CO2 in a flow-through respirometry chamber in a known pattern, and used the methods to recover the known input from the recorded data. The results from these experiments indicate that these methods are capable of sub-second accuracy. We also applied the methods on respiratory data from a grasshopper to investigate the exact timing of abdominal pumping, spiracular opening, and CO2 emission. The methods can be used more generally for input estimation of any linear system.