A unified mathematical description that expresses the characteristics of whole systems is necessary for an understanding of signal transduction cascades. In this study we explore an algebraic method, named extreme signaling flow, enhanced from the concept of extreme pathway, to analyze signal transduction systems. This method enables us to represent the long-term potentiation (LTP) and the long-term depression (LTD) of hippocampal neuronal plasticity in an integrated simulation model. The model is validated by comparing the results of redundancy, reaction participation, and in silico knockout analysis with biological knowledge available from the literature. The following properties are assumed in these computational analyses: (1) LTP is fault-tolerant under network modification, (2) protein kinase C and MAPK have numerous routes to LTP induction, (3) calcium-calmodulin kinase II has a few routes to LTP induction, and (4) calcineurin has many routes to LTD induction. These results demonstrate that our approach produces an integrated framework for analyzing properties of large-scale systems with complicated signal transduction.

The circadian clock of Drosophila is a model pathway for research in biological clock mechanisms, both with traditional experimental approaches and with emerging systems biology approaches utilizing mathematical modeling and in silico computer simulation. Dynamic diurnal oscillations are achieved by the complex interaction of components as a system, and mathematical reconstruction has proven to be an invaluable means of understanding such systematic behavior. In this study, we implemented eight published models of the Drosophila circadian clock in Systems Biology Markup Language (SBML) for comparative systems biology studies using E-Cell Simulation Environment version 3, to examine the system-level requirements for the clock mechanism to be robust, by calculating the period and amplitude sensitivity coefficients with simulation experiments. While all models were generally robust as determined by the network topology of the oscillatory feedback loop structure, existing models place relatively strong emphasis on transcription regulation, although this is a limitation on robustness. We suggest that more comprehensive modeling including protein phosphorylation, polymerization, and nuclear transport with regard to amplitude sensitivity will be necessary for understanding the light entrainment and temperature compensation of circadian clocks.

An enormous body of information has been obtained by molecular and cellular biology in the last half century. However, even these powerful approaches are not adequate when it comes to higher-level biological structures, such as tissues, organs, and individual organisms, because of the complexities involved. Thus, accumulation of data at the higher levels supports and broadens the context for that obtained on the molecular and cellular levels. Under such auspices, an attempt to elucidate mesoscopic and macroscopic subjects based on plentiful nanoscopic and microscopic data is of great potential value. On the other hand, fully realistic simulation is impracticable because of the extensive cost entailed and enormous amount of data required. Abstraction and modeling that balance the dual requirements of prediction accuracy and manageable calculation cost are of great importance for systems biology. We have constructed an ammonia metabolism model of the hepatic lobule, a histological component of the liver, based on a single-hepatocyte model that consists of the biochemical kinetics of enzymes and transporters. To bring the calculation cost within reason, the porto-central axis, which is an elemental structure of the lobule, is defined as the systems biological unit of the liver, and is accordingly modeled. A model including both histological structure and position-specific gene expression of major enzymes largely represents the physiological dynamics of the hepatic lobule in nature. In addition, heterogeneous gene expression is suggested to have evolved to optimize the energy efficiency of ammonia detoxification at the macroscopic level, implying that approaches like this may elucidate how properties at the molecular and cellular levels, such as regulated gene expression, modify higher-level phenomena of multicellular tissue, organs, and organisms.