Limits and tradeoffs in the control of autocatalytic systems

Despite the complexity of biological networks, we find that certain common architectures govern network structures. These architectures impose fundamental constraints on system performance and create tradeoffs that the system must balance in the face of uncertainty in the environment. This means that while a system may be optimized for a specific function through evolution, the optimal achievable state must follow these constraints. One such constraining architecture is autocatalysis, as seen in many biological networks including glycolysis and ribosomal protein synthesis. Using a minimal model, we show that ATP autocatalysis in glycolysis imposes stability and performance constraints and that the experimentally well-studied glycolytic oscillations are in fact a consequence of a tradeoff between error minimization and stability. We also show that additional complexity in the network results in increased robustness. Ribosome synthesis is also autocatalytic where ribosomes must be used to make more ribosomal proteins. When ribosomes have higher protein content, the autocatalysis is increased. We show that this autocatalysis destabilizes the system, slows down response, and also constrains the system’s performance. On a larger scale, transcriptional regulation of whole organisms also follows architectural constraints and this can be seen in the differences between bacterial and yeast transcription networks. We show that the degree distributions of bacterial transcription network follow a power law distribution while the yeast network follows an exponential distribution. We then explored the evolutionary models that have previously been proposed and show that neither the preferential linking model nor the duplication-divergence model of network evolution generates the power-law, hierarchical structure found in bacteria. However, in real biological systems, the generation of new nodes occurs through both duplication and horizontal gene transfers, and we show that a biologically reasonable combination of the two mechanisms generates the desired network.

Complexity of rupture propagation in large earthquakes in relation to tectonic environment

Complexity in the earthquake rupture process can result from many factors. This study investigates the origin of such complexity by examining several recent, large earthquakes in detail. In each case the local tectonic environment plays an important role in understanding the source of the complexity.

Several large shallow earthquakes (M_s > 7.0) along the Middle American Trench have similarities and differences between them that may lead to a better understanding of fracture and subduction processes. They are predominantly thrust events consistent with the known subduction of the Cocos plate beneath N. America. Two events occurring along this subduction zone close to triple junctions show considerable complexity. This may be attributable to a more heterogeneous stress environment in these regions and as such has implications for other subduction zone boundaries.

An event which looks complex but is actually rather simple is the 1978 Bermuda earthquake (M_s ~ 6). It is located predominantly in the mantle. Its mechanism is one of pure thrust faulting with a strike N 20°W and dip 42°NE. Its apparent complexity is caused by local crustal structure. This is an important event in terms of understanding and estimating seismic hazard on the eastern seaboard of N. America.

A study of several large strike-slip continental earthquakes identifies characteristics which are common to them and may be useful in determining what to expect from the next great earthquake on the San Andreas fault. The events are the 1976 Guatemala earthquake on the Motagua fault and two events on the Anatolian fault in Turkey (the 1967, Mudurnu Valley and 1976, E. Turkey events). An attempt to model the complex P-waveforms of these events results in good synthetic fits for the Guatemala and Mudurnu Valley events. However, the E. Turkey event proves to be too complex as it may have associated thrust or normal faulting. Several individual sources occurring at intervals of between 5 and 20 seconds characterize the Guatemala and Mudurnu Valley events. The maximum size of an individual source appears to be bounded at about 5 x 10²⁶ dyne-cm. A detailed source study including directivity is performed on the Guatemala event. The source time history of the Mudurnu Valley event illustrates its significance in modeling strong ground motion in the near field. The complex source time series of the 1967 event produces amplitudes greater by a factor of 2.5 than a uniform model scaled to the same size for a station 20 km from the fault.

Three large and important earthquakes demonstrate an important type of complexity --- multiple-fault complexity. The first, the 1976 Philippine earthquake, an oblique thrust event, represents the first seismological evidence for a northeast dipping subduction zone beneath the island of Mindanao. A large event, following the mainshock by 12 hours, occurred outside the aftershock area and apparently resulted from motion on a subsidiary fault since the event had a strike-slip mechanism.

An aftershock of the great 1960 Chilean earthquake on June 6, 1960, proved to be an interesting discovery. It appears to be a large strike-slip event at the main rupture's southern boundary. It most likely occurred on the landward extension of the Chile Rise transform fault, in the subducting plate. The results for this event suggest that a small event triggered a series of slow events; the duration of the whole sequence being longer than 1 hour. This is indeed a "slow earthquake".

Perhaps one of the most complex of events is the recent Tangshan, China event. It began as a large strike-slip event. Within several seconds of the mainshock it may have triggered thrust faulting to the south of the epicenter. There is no doubt, however, that it triggered a large oblique normal event to the northeast, 15 hours after the mainshock. This event certainly contributed to the great loss of life-sustained as a result of the Tangshan earthquake sequence.

What has been learned from these studies has been applied to predict what one might expect from the next great earthquake on the San Andreas. The expectation from this study is that such an event would be a large complex event, not unlike, but perhaps larger than, the Guatemala or Mudurnu Valley events. That is to say, it will most likely consist of a series of individual events in sequence. It is also quite possible that the event could trigger associated faulting on neighboring fault systems such as those occurring in the Transverse Ranges. This has important bearing on the earthquake hazard estimation for the region.

Evolution of developmental gene regulatory networks in echinoids

Developmental gene regulatory networks (dGRNs) are assemblages of regulatory genes that direct embryonic development of animal body plans and their morpho-logical structures. dGRNs exhibit recursively-wired circuitry that is encoded in the genome and executed during development. Alteration to the regulatory architecture of dGRNs causes variation in developmental programs both during the development of an individual organism and during the evolution of an individual lineage. The ex-planatory power of these networks is best exemplified by the global dGRN directing early development of the euechinoid sea urchin Strongylocentrotus purpuratus. This network consists of numerous regulatory genes engaging in hundreds of genomic regulatory transactions that collectively direct the delineation of early embryonic domains and the specification of cell lineages. Research on closely-related euechi-noid sea urchins, e.g. Lytechinus variegatus and Paracentrotus lividus, has revealed marked conservation of dGRN architecture in echinoid development, suggesting little appreciable alteration has occurred since their divergence in evolution at least 90 million years ago (mya).

We sought to test whether this observation extends to all sea urchins (echinoids) and undertook a systematic analysis of over 50 regulatory genes in the cidaroid sea urchin Eucidaris tribuloides, surveing their regulatory activity and function in a sea urchin that diverged from euechinoid sea urchins at least 268 mya. Our results revealed extensive alterations have occurred to all levels of echinoid dGRN archi-tecture since the cidaroid-euechinoid divergence. Alterations to mesodermal sub-circuits were particularly striking, including functional di˙erences in specification of non-skeletogenic mesenchyme (NSM), skeletogenic mesenchyme (SM), and en-domesodermal segregation. Specification of endomesodermal embryonic domains revealed that, while their underlying network circuitry had clearly diverged, regu-latory states established in pregastrular embryos of these two groups are strikingly similar. Analyses of E. tribuloides specification leading to the estab-lishment of dorsal-ventral (aboral-oral) larval polarity indicated that regulation of regulatory genes expressed in mesodermal embryonic domains had incurred significantly more alterations than those expressed in endodermal and ectodermal domains. Taken together, this study highlights the ability of dGRN architecture to buffer extensive alterations in the evolution and early development of echinoids and adds further support to the notion that alterations can occur at all levels of dGRN architecture and all stages of embryonic development.