Robustness of mathematical models for biological systems

The robustness of mathematical models for biological systems is studied by sensitivity analysis and stochastic simulations. Using a neural network model with three genes as the test problem, we study robustness properties of synthesis and degradation processes. For single parameter robustness, sensitivity analysis techniques are applied for studying parameter variations and stochastic simulations are used for investigating the impact of external noise. Results of sensitivity analysis are consistent with those obtained by stochastic simulations. Stochastic models with external noise can be used for studying the robustness not only to external noise but also to parameter variations. For external noise we also use stochastic models to study the robustness of the function of each gene and that of the system.

Biological polarized light reflectors in stomatopod crustaceans

Body parts that can reflect highly polarized light have been found in several species of stomatopod crustaceans (mantis shrimps). These polarized light reflectors can be grossly divided into two major types. The first type, usually red or pink in color to the human visual system, is located within an animal’s cuticle. Reflectors of the second type, showing iridescent blue, are located beneath the exoskeleton and thus are unaffected by the molt cycle. We used reflection spectropolarimetry and transmission electron microscopy (TEM) to study the reflective properties and the structures that reflect highly polarized light in stomatopods. For the first type of reflector, the degree of polarization usually changes dramatically, from less than 20% to over 70%, with a change in viewing angle. TEM examination indicates that the polarization reflection is generated by multilayer thin-film interference. The second type of reflector, the blue colored ones, reflects highly polarized light to all viewing angles. However, these reflectors show a slight chromatic change with different viewing angles. TEM sections have revealed that streams of oval-shaped vesicles might be responsible for the production of the polarized light reflection. In all the reflectors we have examined so far, the reflected light is always maximally polarized at around 500 nm, which is close to the wavelength best transmitted by sea water. This suggests that the polarized light reflectors found in stomatopods are well adapted to the underwater environment. We also found that most reflectors produce polarized light with a horizontal e-vector. How these polarized light reflectors are used in stomatopod signaling remains unknown.