Rule-based spatial modeling with diffusing, geometrically constrained molecules

<p>Abstract</p> <p>Background</p> <p>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.</p> <p>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.</p> <p>Results</p> <p>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.</p> <p>Conclusions</p> <p>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.</p

Reaction-diffusion kinetics on lattice at the microscopic scale

Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME), can simulate for extended spatial and temporal scales but cannot directly account for the microscopic effects in the cell such as volume exclusion and diffusion-influenced reactions. Nonetheless, schemes based on the high-resolution microscopic lattice method (MLM) can directly simulate these effects by representing each finite-sized molecule explicitly as a random walker on fine lattice voxels. The theory and consistency of MLM in simulating diffusion-influenced reactions have not been clarified in detail. Here, we examine MLM in solving diffusion-influenced reactions in 3D space by employing the Spatiocyte simulation scheme. Applying the random walk theory, we construct the general theoretical framework underlying the method and obtain analytical expressions for the total rebinding probability and the effective reaction rate. By matching Collins-Kimball and lattice-based rate constants, we obtained the exact expressions to determine the reaction acceptance probability and voxel size. We found that the size of voxel should be about 2% larger than the molecule. MLM is validated by numerical simulations, showing good agreement with the off-lattice particle-based method, eGFRD. MLM run time is more than an order of magnitude faster than eGFRD when diffusing macromolecules with typical concentrations in the cell. MLM also showed good agreements with eGFRD and mean-field models in case studies of two basic motifs of intracellular signaling, the protein production-degradation process and the dual phosphorylation cycle. Moreover, when a reaction compartment is populated with volume-excluding obstacles, MLM captures the non-classical reaction kinetics caused by anomalous diffusion of reacting molecules

Cell-cell communication enhances the capacity of cell ensembles to sense shallow gradients during morphogenesis

Collective cell responses to exogenous cues depend on cell-cell interactions. In principle, these can result in enhanced sensitivity to weak and noisy stimuli. However, this has not yet been shown experimentally, and, little is known about how multicellular signal processing modulates single cell sensitivity to extracellular signaling inputs, including those guiding complex changes in the tissue form and function. Here we explored if cell-cell communication can enhance the ability of cell ensembles to sense and respond to weak gradients of chemotactic cues. Using a combination of experiments with mammary epithelial cells and mathematical modeling, we find that multicellular sensing enables detection of and response to shallow Epidermal Growth Factor (EGF) gradients that are undetectable by single cells. However, the advantage of this type of gradient sensing is limited by the noisiness of the signaling relay, necessary to integrate spatially distributed ligand concentration information. We calculate the fundamental sensory limits imposed by this communication noise and combine them with the experimental data to estimate the effective size of multicellular sensory groups involved in gradient sensing. Functional experiments strongly implicated intercellular communication through gap junctions and calcium release from intracellular stores as mediators of collective gradient sensing. The resulting integrative analysis provides a framework for understanding the advantages and limitations of sensory information processing by relays of chemically coupled cells.Comment: paper + supporting information, total 35 pages, 15 figure

Simulation tools for particle-based reaction-diffusion dynamics in continuous space

Particle-based reaction-diffusion algorithms facilitate the modeling of the diffusional motion of individual molecules and the reactions between them in cellular environments. A physically realistic model, depending on the system at hand and the questions asked, would require different levels of modeling detail such as particle diffusion, geometrical confinement, particle volume exclusion or particle-particle interaction potentials. Higher levels of detail usually correspond to increased number of parameters and higher computational cost. Certain systems however, require these investments to be modeled adequately. Here we present a review on the current field of particle-based reaction-diffusion software packages operating on continuous space. Four nested levels of modeling detail are identified that capture incrementing amount of detail. Their applicability to different biological questions is discussed, arching from straight diffusion simulations to sophisticated and expensive models that bridge towards coarse grained molecular dynamics

Single-molecule tracking in live cells reveals distinct target-search strategies of transcription factors in the nucleus

Gene regulation relies on transcription factors (TFs) exploring the nucleus searching their targets. So far, most studies have focused on how fast TFs diffuse, underestimating the role of nuclear architecture. We implemented a single-molecule tracking assay to determine TFs dynamics. We found that c-Myc is a global explorer of the nucleus. In contrast, the positive transcription elongation factor P-TEFb is a local explorer that oversamples its environment. Consequently, each c-Myc molecule is equally available for all nuclear sites while P-TEFb reaches its targets in a position-dependent manner. Our observations are consistent with a model in which the exploration geometry of TFs is restrained by their interactions with nuclear structures and not by exclusion. The geometry-controlled kinetics of TFs target-search illustrates the influence of nuclear architecture on gene regulation, and has strong implications on how proteins react in the nucleus and how their function can be regulated in space and time.Nikon France (Research contract)France. Agence nationale de la recherche (PCV DYNAFT 08-PCVI-0013)France. Agence nationale de la recherche (DynamIC ANR-12-BSV5-0018)Fondation pour la recherche médicaleNetherlands Organization for Scientific Research (Rubicon fellowship

Single-molecule tracking in live cells reveals distinct target-search strategies of transcription factors in the nucleus

Gene regulation relies on transcription factors (TFs) exploring the nucleus searching their targets. So far, most studies have focused on how fast TFs diffuse, underestimating the role of nuclear architecture. We implemented a single-molecule tracking assay to determine TFs dynamics. We found that c-Myc is a global explorer of the nucleus. In contrast, the positive transcription elongation factor P-TEFb is a local explorer that oversamples its environment. Consequently, each c-Myc molecule is equally available for all nuclear sites while P-TEFb reaches its targets in a position-dependent manner. Our observations are consistent with a model in which the exploration geometry of TFs is restrained by their interactions with nuclear structures and not by exclusion. The geometry-controlled kinetics of TFs target-search illustrates the influence of nuclear architecture on gene regulation, and has strong implications on how proteins react in the nucleus and how their function can be regulated in space and time