Modeling temperature entrainment of circadian clocks using the Arrhenius equation and a reconstructed model from Chlamydomonas reinhardtii.

Endogenous circadian rhythms allow living organisms to anticipate daily variations in their natural environment. Temperature regulation and entrainment mechanisms of circadian clocks are still poorly understood. To better understand the molecular basis of these processes, we built a mathematical model based on experimental data examining temperature regulation of the circadian RNA-binding protein CHLAMY1 from the unicellular green alga Chlamydomonas reinhardtii, simulating the effect of temperature on the rates by applying the Arrhenius equation. Using numerical simulations, we demonstrate that our model is temperature-compensated and can be entrained to temperature cycles of various length and amplitude. The range of periods that allow entrainment of the model depends on the shape of the temperature cycles and is larger for sinusoidal compared to rectangular temperature curves. We show that the response to temperature of protein (de)phosphorylation rates play a key role in facilitating temperature entrainment of the oscillator in Chlamydomonas reinhardtii. We systematically investigated the response of our model to single temperature pulses to explain experimentally observed phase response curves.

Biochemical frequency control by synchronisation of coupled repressilators: an in silico study of modules for circadian clock systems.

Exploration of chronobiological systems emerges as a growing research field within bioinformatics focusing on various applications in medicine, agriculture, and material sciences. From a systems biological perspective, the question arises whether biological control systems for regulation of oscillatory signals and their technical counterparts utilise similar mechanisms. If so, modelling approaches and parameterisation adopted from building blocks can help to identify general components for frequency control in circadian clocks along with gaining insight into mechanisms of clock synchronisation to external stimuli like the daily rhythm of sunlight and darkness. Phase-locked loops could be an interesting candidate in this context. Both, biology and engineering, can benefit from a unified view resulting from systems modularisation. In a first experimental study, we analyse a model of coupled repressilators. We demonstrate its ability to synchronise clock signals in a monofrequential manner. Several oscillators initially deviate in phase difference and frequency with respect to explicit reaction and diffusion rates. Accordingly, the duration of the synchronisation process depends on dedicated reaction and diffusion parameters whose settings still lack to be sufficiently captured analytically.

Rule-based spatial modeling with diffusing, geometrically constrained molecules.

BACKGROUND: We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined. For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided. RESULTS: Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa. CONCLUSIONS: We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly.

Toward integration of in vivo molecular computing devices: successes and challenges.

The computing power unleashed by biomolecule based massively parallel computational units has been the focus of many interdisciplinary studies that couple state of the art ideas from mathematical logic, theoretical computer science, bioengineering, and nanotechnology to fulfill some computational task. The output can influence, for instance, release of a drug at a specific target, gene expression, cell population, or be a purely mathematical entity. Analysis of the results of several studies has led to the emergence of a general set of rules concerning the implementation and optimization of in vivo computational units. Taking two recent studies on in vivo computing as examples, we discuss the impact of mathematical modeling and simulation in the field of synthetic biology and on in vivo computing. The impact of the emergence of gene regulatory networks and the potential of proteins acting as "circuit wires" on the problem of interconnecting molecular computing device subunits is also highlighted.