Automated methods are described for the determination of survival curves in C. elegans, enabling rapid and statistically rigorous studies of lifespan in this organism. The measurement of lifespan pervades aging research. Because lifespan results from complex interactions between genetic, environmental and stochastic factors, it varies widely even among isogenic individuals. The actions of molecular mechanisms on lifespan are therefore visible only through their statistical effects on populations. Indeed, survival assays in Caenorhabditis elegans have provided critical insights into evolutionarily conserved determinants of aging. To enable the rapid acquisition of survival curves at an arbitrary statistical resolution, we developed a scalable imaging and analysis platform to observe nematodes over multiple weeks across square meters of agar surface at 8-μm resolution. The automated method generates a permanent visual record of individual deaths from which survival curves are constructed and validated, producing data consistent with results from the manual method of survival curve acquisition for several mutants in both standard and stressful environments. Our approach permits rapid, detailed reverse-genetic and chemical screens for effects on survival and enables quantitative investigations into the statistical structure of aging.

Metabolic rate, heart rate, lifespan, and many other physiological properties vary with body mass in systematic and interrelated ways. Present empirical data suggest that these scaling relationships take the form of power laws with exponents that are simple multiples of one quarter. A compelling explanation of this observation was put forward a decade ago by West, Brown, and Enquist (WBE). Their framework elucidates the link between metabolic rate and body mass by focusing on the dynamics and structure of resource distribution networks—the cardiovascular system in the case of mammals. Within this framework the WBE model is based on eight assumptions from which it derives the well-known observed scaling exponent of 3/4. In this paper we clarify that this result only holds in the limit of infinite network size (body mass) and that the actual exponent predicted by the model depends on the sizes of the organisms being studied. Failure to clarify and to explore the nature of this approximation has led to debates about the WBE model that were at cross purposes. We compute analytical expressions for the finite-size corrections to the 3/4 exponent, resulting in a spectrum of scaling exponents as a function of absolute network size. When accounting for these corrections over a size range spanning the eight orders of magnitude observed in mammals, the WBE model predicts a scaling exponent of 0.81, seemingly at odds with data. We then proceed to study the sensitivity of the scaling exponent with respect to variations in several assumptions that underlie the WBE model, always in the context of finite-size corrections. Here too, the trends we derive from the model seem at odds with trends detectable in empirical data. Our work illustrates the utility of the WBE framework in reasoning about allometric scaling, while at the same time suggesting that the current canonical model may need amendments to bring its predictions fully in line with available datasets. The rate at which an organism produces energy to live increases with body mass to the 3/4 power. Ten years ago West, Brown, and Enquist posited that this empirical relationship arises from the structure and dynamics of resource distribution networks such as the cardiovascular system. Using assumptions that capture physical and biological constraints, they defined a vascular network model that predicts a 3/4 scaling exponent. In our paper we clarify that this model generates the 3/4 exponent only in the limit of infinitely large organisms. Our calculations indicate that in the finite-size version of the model metabolic rate and body mass are not related by a pure power law, which we show is consistent with available data. We also show that this causes the model to produce scaling exponents significantly larger than the observed 3/4. We investigate how changes in certain assumptions about network structure affect the scaling exponent, leading us to identify discrepancies between available data and the predictions of the finite-size model. This suggests that the model, the data, or both, need reassessment. The challenge lies in pinpointing the physiological and evolutionary factors that constrain the shape of networks driving metabolic scaling.

Modelers of molecular signaling networks must cope with the combinatorial explosion of protein states generated by posttranslational modifications and complex formation. Rule-based models provide a powerful alternative to approaches that require explicit enumeration of all possible molecular species of a system. Such models consist of formal rules stipulating the (partial) contexts wherein specific protein–protein interactions occur. These contexts specify molecular patterns that are usually less detailed than molecular species. Yet, the execution of rule-based dynamics requires stochastic simulation, which can be very costly. It thus appears desirable to convert a rule-based model into a reduced system of differential equations by exploiting the granularity at which rules specify interactions. We present a formal (and automated) method for constructing a coarse-grained and self-consistent dynamical system aimed at molecular patterns that are distinguishable by the dynamics of the original system as posited by the rules. The method is formally sound and never requires the execution of the rule-based model. The coarse-grained variables do not depend on the values of the rate constants appearing in the rules, and typically form a system of greatly reduced dimension that can be amenable to numerical integration and further model reduction techniques.

This paper describes the fabrication of a microfluidic device for rapid immobilization of large numbers of live C. elegans for performing morphological analysis, microsurgery, and fluorescence imaging in a high-throughput manner. The device consists of two principal elements: (i) an array of 128 wedge-shaped microchannels, or clamps, which physically immobilize worms, and (ii) a branching network of distribution channels, which deliver worms to the array. The flow of liquid through the device (driven by a constant pressure difference between the inlet and the outlet) automatically distributes individual worms into each clamp. It was possible to immobilize more than 100 worms in less than 15 min. The immobilization process was not damaging to the worms: following removal from the array of clamps, worms lived typical lifespans and reproduced normally. The ability to monitor large numbers of immobilized worms easily and in parallel will enable researchers to investigate physiology and behavior in large populations of C. elegans.