Thomas Hinze

Rule-based spatial modeling with diffusing, geometrically constrained molecules

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.

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.

REGISTER MACHINE COMPUTATIONS ON BINARY NUMBERS BY OSCILLATING AND CATALYTIC CHEMICAL REACTIONS MODELLED USING MASS-ACTION KINETICS

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.

Hill kinetics meets P systems: a case study on gene regulatory networks as computing agents in silico and in vivo

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.

Towards evolutionary network reconstruction tools for systems biology

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.

A protein substructure based p system for description and analysis of cell signalling networks

The way how cell signals are generated, encoded, transferred, modified, and utilized is essential for understanding information processing inside living organisms. The tremendously growing biological knowledge about proteins and their interactions draws a more and more detailed image of a complex functional network. Considering signalling networks as computing devices, the detection of structural principles, especially modularization into subunits and interfaces between them, can help to seize ideas for their description and analysis. Algebraic models like P systems prove to be appropriate to this. We utilize string-objects to carry information about protein binding domains and their ligands. Embedding these string-objects into a deterministic graph structured P system with dynamical behavior, we introduce a model that can describe cell signalling pathways on a submolecular level. Beyond questions of formal languages, the model facilitates tracing the evolutionary development from single protein components towards functional interacting networks. We exemplify the model by means of the yeast pheromone pathway.

Modelling signalling networks with incomplete information about protein activation states: a p system framework of the KaiABC oscillator

Reconstruction of signal transduction network models based on incomplete information about network structure and dynamical behaviour is a major challenge in current systems biology. In particular, interactions within signalling networks are frequently characterised by partially unknown protein phosphorylation and dephosphorylation cascades at a submolecular description level. For prediction of promising network candidates, reverse engineering techniques typically enumerate the reaction search space. Considering an underlying amount of phosphorylation sites, this implies a potentially exponential number of individual reactions in conjunction with corresponding protein activation states. To manage the computational complexity, we extend P systems with string-objects by a subclass for protein representation able to process wild-carded together with specific information about protein binding domains and their ligands. This variety of reactants works together with assigned term-rewriting mechanisms derived from discretised reaction kinetics. We exemplify the descriptional capability and flexibility of the framework by discussing model candidates for the circadian clock formed by the KaiABC oscillator found in the cyanobacterium Synechococcus elongatus. A simulation study of its dynamical behaviour demonstrates effects of superpositioned protein abundance courses based on regular expressions corresponding to dedicated protein activation states.

Enhancing parameter estimation of biochemical networks by exponentially scaled search steps

A first method of revealing a fingerprint involves the charging of the surface bearing the fingerprint to a high electric potential and applying finely divided carbon to the charged surface to form a pattern thereon corresponding to the fingerprint. The finely divided carbon may be dusted or sprayed on or may be in suspension in a dielectric liquid into which the charged surface is introduced. In another method the surface is charged while submerged in the dielectric liquid, under the action of an electric field in the dielectric. In another method an electrically charged sheet is brought into contact with a surface bearing a fingerprint and after being removed, the charged sheet has applied to its surface finely divided carbon which adheres thereto depending on the charge pattern remaining thereon after contact with the fingerprint. The pattern of finely divided carbon can be fixed in position by applying thereover a transparent protective layer.

Membrane Systems and Tools Combining Dynamical Structures with Reaction Kinetics for Applications in Chronobiology

This chapter addresses three coordinated chronobiological studies demonstrating the convergence of experimental observations, fine-grained spatio-temporal modelling, and predictive simulation. Due to the discrete manner of molecular assembly in cell signalling and gene regulation, we define a framework of membrane systems equipped with discretised forms of reaction kinetics in concert with variable intramolecular structures. Our first study is dedicated to circadian clocks inducing daily biological rhythms. As an inspiring example, the KaiABC core oscillator reaches its functionality by cyclically varying protein structures. Within our second study, we present a meta-model of an entire circadian clockwork able to adapt its oscillation to an external stimulus in terms of a frequency control system acting in a phase-locked loop. Substrate concentration courses resulting from gene expression reflect its oscillatory behaviour utilised in a periodical trigger for subsequent processes. In this context, our third study cytometrically quantifies the dynamical behaviour of a bistable toggle switch resulting from mutual gene regulation.

Chemical analog computers for clock frequency control based on p modules

Living organisms comprise astonishing capabilities of information processing for efficient adaptation to environmental changes. Resulting chemical control loops and regulator circuits are expected to exhibit a high functional similarity to technical counterparts subsumed by analog computers. A fascinating example is given by circadian clocks providing an endogenous biological rhythm adapted to the daily variation of sunlight and darkness. Its underlying biochemical principle of operation suggests a general functional scheme corresponding to frequency control using phase-locked loops (PLL). From a systems biology point of view, clock systems can be decomposed into specific modules like low-pass filters, arithmetic signal comparators, and controllable core oscillators. Each of them processes analog chemical signals on the fly. We introduce P modules in order to capture structure, behaviour, and interface of pure chemical analog computer models in terms of building blocks along with two simulation case studies. The first one is focused on chemical analog computer components including a controllable Goodwin-type core oscillator while the second one evolves an entire PLL-based frequency control by means of a pure chemical circadian clock model.