Computational tools for inversion and uncertainty estimation in respirometry.

In many physiological systems, real-time endogeneous and exogenous signals in living organisms provide critical information and interpretations of physiological functions; however, these signals or variables of interest are not directly accessible and must be estimated from noisy, measured signals. In this paper, we study an inverse problem of recovering gas exchange signals of animals placed in a flow-through respirometry chamber from measured gas concentrations. For large-scale experiments (e.g., long scans with high sampling rate) that have many uncertainties (e.g., noise in the observations or an unknown impulse response function), this is a computationally challenging inverse problem. We first describe various computational tools that can be used for respirometry reconstruction and uncertainty quantification when the impulse response function is known. Then, we address the more challenging problem where the impulse response function is not known or only partially known. We describe nonlinear optimization methods for reconstruction, where both the unknown model parameters and the unknown signal are reconstructed simultaneously. Numerical experiments show the benefits and potential impacts of these methods in respirometry.

Physiological responses to gravity in an insect.

Gravity is one of the most ubiquitous environmental effects on living systems: Cellular and organismal responses to gravity are of central importance to understanding the physiological function of organisms, especially eukaryotes. Gravity has been demonstrated to have strong effects on the closed cardiovascular systems of terrestrial vertebrates, with rapidly responding neural reflexes ensuring proper blood flow despite changes in posture. Invertebrates possess open circulatory systems, which could provide fewer mechanisms to restrict gravity effects on blood flow, suggesting that these species also experience effects of gravity on blood pressure and distribution. However, whether gravity affects the open circulatory systems of invertebrates is unknown, partly due to technical measurement issues associated with small body size. Here we used X-ray imaging, radio-tracing of hemolymph, and micropressure measurements in the American grasshopper, Schistocerca americana, to assess responses to body orientation. Our results show that during changes in body orientation, gravity causes large changes in blood and air distribution, and that body position affects ventilation rate. Remarkably, we also found that insects show similar heart rate responses to body position as vertebrates, and contrasting with the classic understanding of open circulatory systems, have flexible valving systems between thorax and abdomen that can separate pressures. Gravitational effects on invertebrate cardiovascular and respiratory systems are likely to be widely distributed among invertebrates and to have broad influence on morphological and physiological evolution.

Effects of fish caudal fin sweep angle and kinematics on thrust production during low-speed thunniform swimming.

Scombrid fish lunate caudal fins are characterized by a wide range of sweep angles. Scombrid that have small sweep-angle caudal fins move at higher swimming speeds, suggesting that smaller angles produce more thrust. Furthermore, scombrids occasionally use high angles of attack (AoA) suggesting this also has some thrust benefit. This work examined the hypothesis that a smaller sweep angle and higher AoA improved thrust in swimmers by experimentally analyzing a robophysical model. The robophysical model was tested in a water tunnel at speeds between 0.35 and 0.7 body lengths per second. Three swept caudal fins were analyzed at three different AoA, three different freestream velocities, and four different Strouhal numbers, for a total of 108 cases. Results demonstrated that the fin with the largest sweep angle of 50° resulted in lower thrust production than the 40° and 30° fins, especially at higher Strouhal numbers. Larger AoA up to 25° increased thrust production at the higher Strouhal numbers, but at lower Strouhal numbers, produced less thrust. Differences in thrust production due to fin sweep angle and AoA were attributed to the variation in spanwise flow and leading edge vortex dynamics.

Functional compartmentalization in the hemocoel of insects.

The insect circulatory system contains an open hemocoel, in which the mechanism of hemolymph flow control is ambiguous. As a continuous fluidic structure, this cavity should exhibit pressure changes that propagate quickly. Narrow-waisted insects create sustained pressure differences across segments, but their constricted waist provides an evident mechanism for compartmentalization. Insects with no obvious constrictions between segments may be capable of functionally compartmentalizing the body, which could explain complex hemolymph flows. Here, we test the hypothesis of functional compartmentalization by measuring pressures in a beetle and recording abdominal movements. We found that the pressure is indeed uniform within the abdomen and thorax, congruent with the predicted behavior of an open system. However, during some abdominal movements, pressures were on average 62% higher in the abdomen than in the thorax, suggesting that functional compartmentalization creates a gradient within the hemocoel. Synchrotron tomography and dissection show that the arthrodial membrane and thoracic muscles may contribute to this dynamic pressurization. Analysis of volume change suggests that the gut may play an important role in regulating pressure by translating between body segments. Overall, this study suggests that functional compartmentalization may provide an explanation for how fluid flows are managed in an open circulatory system.

Recovering signals in physiological systems with large datasets.

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.

Estimation of Instantaneous Gas Exchange in Flow-Through Respirometry Systems: A Modern Revision of Bartholomew's Z-Transform Method.

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.

Tracheal compression in pupae of the beetle Zophobas morio.

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 CO2 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.

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes.

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.