BackgroundWe 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.ResultsOur 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.ConclusionsWe 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.

Systems biology is the ever-growing field of integrating molecular knowledge about biological organisms into an understanding at the systems level. For this endeavour, automatic network reconstruction tools are urgently needed. In the present contribution, we show how the applicability of evolutionary algorithms to systems biology can be improved by a domain-specific representation and algorithmic extensions, especially a separation of network structure evolution from evolution of kinetic parameters. In a case study, our presented tool is applied to a model of the mitotic spindle checkpoint in the human cell cycle.

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.

Abstract. Modeling and simulation of biological reaction networks is an essential task in systems biology aiming at formalization, understanding, and prediction of processes in living organisms. Currently, a variety of modeling approaches for specific purposes coexists. P systems form such an approach which owing to its algebraic nature opens growing fields of application. Here, emulating the dynamical system behavior based on reaction kinetics is of particular interest to explore network functions. We demonstrate a transformation of Hill kinetics for gene regulatory networks (GRNs) into the P systems framework. Examples address the switching dynamics of GRNs acting as NAND gate and RS flip-flop. An adapted study in vivo experimentally verifies both practicability for computational units and validity of the system model.

Biocomputing emerged as a promising paradigm capable of coping efficiently with challenges of programming decentralized but concerted reaction systems. The chemical programming metaphor subsumes different encoding techniques into molecular or spatial structures in conjunction with artificial reaction networks. Here, a variety of supplementary assumptions like predefined polymeric sequences or availability of inhibiting reactions is frequently used. Inspired by the idea to build chemical computers based on minimal requirements in chemistry from a theoretical perspective, we introduce a pure chemical register machine model operating on binary numbers. The register machine architecture is composed of reaction network motifs acting as fast switching logic gates, oscillators, and self-reproducible bit storage units. The dynamical machine behavior consistently employs mass-action kinetics. Two case studies, calculating the maximum of three natural numbers as well as numerical addition, illustrate the practicability of the design along with dynamical simulations.

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.

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