Chaos Podcasts, Videos and Multimedia
Competitive autocatalytic reactions in chaotic flows with diffusion
Conor P. Schlick, Paul B. Umbanhowar, Julio M. Ottino and Richard M. Lueptow
Northwestern University, Evanston, Illinois 60208, USA
Watch the videos:
The three videos show simulations of a competitive autocatalytic reaction undergoing chaotic advection and diffusion. Species A (white) reacts autocatalytically with B (blue) and C (red), i.e. A+B->2B and A+C->2C.
In videos 1 and 2, the velocity field is time-periodic sine flow, with different starting locations of B and C (see figure 5, simulations S1 and S2 in the paper).
In video 3 is journal bearing flow (see figure 13, simulation S1 in the paper).
We investigate chaotic advection and diffusion in autocatalytic reactions for time-periodic sine flow computationally using a mapping method with operator splitting. We specifically consider three different autocatalytic reaction schemes: a single autocatalytic reaction, competitive autocatalytic reactions, which can provide insight into problems of chiral symmetry breaking and homochirality, and competitive autocatalytic reactions with recycling. In competitive autocatalytic reactions, species B and C both undergo an autocatalytic reaction with species A such that and A+B→2BA+C→2C. Small amounts of initially spatially localized B and C and a large amount of spatially homogeneous A are advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that local finite-time Lyapunov exponents (FTLEs) can accurately predict the final average concentrations of B and C after the reaction completes. The species that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If B and C start in regions with similar FTLEs, their average concentrations at the end of the reaction will also be similar. When a recycling reaction is added, the system evolves towards a single species state, with the FTLE often being useful in predicting which species fills the entire domain and which is depleted. The FTLE approach is also demonstrated for competitive autocatalytic reactions in journal bearing flow, an experimentally realizable flow that generates chaotic dynamics.
Chaos 24, 013109 (2014)
Chaos Podcasts, Videos and Multimedia
Interviews with the Guest Editors on the Focus Issue: Quantitative Approaches to Genetic Networks
Read the articles in the Focus Issue
James J. Collins
Biomedical Engineering, Boston University, Boston, MA
In this interview, Professor Collins discusses the Focus Issue on Quantitative Approaches to Genetic Networks and answers the following questions:
Q1. Your 2000 Nature paper on the genetic toggle switch is considered one of the founding papers of the emerging field of synthetic biology.
Could you describe the factors that led you to choose the toggle switch for your first synthetic biology project?
Q2. What were the main technical difficulties you faced in getting the constructs to function as a toggle switch?
Q3. Skipping forward to the current time, can you share with us some of your ideas concerning the potential future uses of synthetic biology in technology and medicine?
Q4. What role do you envisage for theory in the future developments of synthetic biology?
Department of Physics, Pennsylvania State University, University Park, PA
Q1. Your early papers with Barabasi on scaling in complex networks have had a major influence on research in a large range of disciplines. When you carried out analyses of the structure of networks, what did you find were the most exciting or surprising findings?
A: The most surprising to me was how powerful a simple two-mechanism model can be. Albert-Laszlo Barabasi and I developed a simple model of network evolution aiming to give a possible explanation for the observed power law scaling of the distribution of node degrees. The original model, based on growth and linear preferential attachment, gives networks with a power law degree distribution. If one replaces linear preferential attachment with random attachment, the degree distribution is instead described by an exponential function. If one takes away the growth in the number of nodes, the functional form of the degree distribution depends on the number of edges. This combined simplicity and discerning power made it easy for the community to add additional, customizable features to the model.
Q2. You have now largely switched to the analysis of genetic networks. What led you to focus on genetic networks rather than some of the other complex networks found in natural and engineered systems?
A: Toward the end of my doctoral research I was drawn to trying to understand propagation and flow processes that take place on networks. Realizing that these processes tend to be different in technological, social and biological systems, I needed to choose which system to learn more about and ultimately specialize in. I had been interested in living systems since high school, but my stronger interest in applied mathematics, and the necessity to choose majors before applying to college in my birth country, made it impossible to pursue these interests earlier. My success with network structure modeling emboldened me to turn to biological systems. The specific biological systems I had focused on since depended on many factors, including on the availability of collaborators. These networks include genetic networks, but also networks of cells and networks of plants and their pollinators.
Q3. Many, including your group, have considered simplified models based on logical structures to be involved in genetic control systems. How good is the current evidence that this will provide a strong computational framework for analysis of genetic networks?
A: There are dozens of individual studies showing that simplified logic-based models are a good choice as a first model. At the present level of knowledge about genetic networks, where it is possible to piece together the existing fragmentary knowledge but the resulting network may be missing components and interactions, constructing a continuous model is almost hopeless. The continuous model would need to make too many assumptions on how to represent and parameterize the interactions among components, and it would be very hard to validate all those assumptions. The logic-based models are compatible with several mechanisms and have no or very few parameters to estimate. They can predict which components and interactions are key to the normal functioning of the system, and what would happen in case of big perturbations, like the disruption of a key component. Experimental testing of these predictions leads to new biological knowledge, which then can be used to construct more detailed, more quantitative models. I see these simple models as the first step in establishing the coveted feedback loop between modeling and experiment.
Q4. What are emerging areas in the theoretical analysis of genetic control networks?
A: The introduction to the Focus Issue summarizes these areas much better than I could do in a couple of sentences. I invite the readers to check it out.
Introduction to Focus Issue: Quantitative Approaches to Genetic Networks
Réka Albert, James J. Collins and Leon Glass
Chaos 23, 025001 (2013)