Olgierd Cybulski

Bacterial Growth and Adaptation in Microdroplet Chemostats

We describe herein microfluidic technology for manipulating and monitoring continuous growth of populations of bacteria. A system consisting of approximately ten input and output channels controls more than 100 microdroplet chemostats and enables the manipulation of chemical factors in each microchemostat independently over time. Herein, we characterize the dynamics of bacterial populations in microdroplet chemostats and cellular responses to a range of stable or changing antibiotic concentrations. This method allows for parallel, long-term studies of microbial ecology, physiology, evolution, and adaptation to chemical environments. The introduction of the chemostat by Leo Szilard was a milestone in the field of microbiology. Chemostats facilitate the continuous culture of bacteria, yeast, and algae by continuously replenishing a constant volume of fluid to maintain specific concentrations of cells and growth factors. Chemostats have facilitated a wide-range of studies, including microbial ecology, predator–prey dynamics, and the evolution of drug resistance. The consumption of large quantities of reagents and the significant operational challenges of traditional chemostats limit their use. Single-phase, microfluidic versions of chemostats minimize incubation volumes, and yet are limited by their complexity: the proportionality between the number of input/ output controls and the number of chemostats hamper large scale parallelization. Single-phase microfluidic systems are prone to biofilm formation, which makes them either singleuse devices or requiring additional steps to minimize cell adhesion. Droplet microfluidics offer a unique solution to creating many parallel chemostats. The earliest example of this technology in microbiology was first demonstrated by Joshua Lederberg nearly 60 years ago. In the interim, the field of microfluidics solved many of the technical challenges associated with using this approach to study microbes. Compartmentalizing cells and nutrients in microdroplets of liquid can reduce the complexity and cost of operating many parallel chemostats. Recently, bacteria have been incubated in droplets in channels over short time intervals, however sustained cell growth over hundreds of generations in a series of fully addressable microdroplets has not been possible. Herein, we describe an automated microdroplet system that transcends existing challenges and enables users to manipulate the chemical composition of droplets for longterm bacterial studies. The microfluidic system (Figure 1) performs three functions: 1) formation of microdroplets containing cells, reagents, and soluble growth factors; 2) cycling microdroplets for cell incubation and monitoring; and 3) splitting and fusing microdroplets to control the concentration of chemical factors over time. After loading the reservoirs with liquid samples, we used a source of pressure and external valves to regulate the flow of

Pattern formation in nonextensive thermodynamics: Selection criterion based on the Renyi entropy production

We analyze a system of two different types of Brownian particles confined in a cubic box with periodic boundary conditions. Particles of different types annihilate when they come into close contact. The annihilation rate is matched by the birth rate, thus the total number of each kind of particles is conserved. When in a stationary state, the system is divided by an interface into two subregions, each occupied by one type of particles. All possible stationary states correspond to the Laplacian eigenfunctions. We show that the system evolves towards those stationary distributions of particles which minimize the Renyi entropy production. In all cases, the Renyi entropy production decreases monotonically during the evolution despite the fact that the topology and geometry of the interface exhibit abrupt and violent changes.

Accurate Genetic Switch in Escherichia coli: Novel Mechanism of Regulation by Co-repressor

Understanding a biological module involves recognition of its structure and the dynamics of its principal components. In this report we present an analysis of the dynamics of the repression module within the regulation of the trp operon in Escherichia coli. We combine biochemical data for reaction rate constants for the trp repressor binding to trp operator and in vivo data of a number of tryptophan repressors (TrpRs) that bind to the operator. The model of repression presented in this report greatly differs from previous mathematical models. One, two or three TrpRs can bind to the operator and repress the transcription. Moreover, reaction rates for detachment of TrpRs from the operator strongly depend on tryptophan (Trp) concentration, since Trp can also bind to the repressor-operator complex and stabilize it. From the mathematical modeling and analysis of reaction rates and equilibrium constants emerges a high-quality, accurate and effective module of trp repression. This genetic switch responds accurately to fast consumption of Trp from the interior of a cell. It switches with minimal dispersion when the concentration of Trp drops below a thousand molecules per cell.

Between giant oscillations and uniform distribution of droplets: The role of varying lumen of channels in microfluidic networks.

The simplest microfluidic network (a loop) comprises two parallel channels with a common inlet and a common outlet. Recent studies that assumed a constant cross section of the channels along their length have shown that the sequence of droplets entering the left (L) or right (R) arm of the loop can present either a uniform distribution of choices (e.g., RLRLRL...) or long sequences of repeated choices (RRR...LLL), with all the intermediate permutations being dynamically equivalent and virtually equally probable to be observed. We use experiments and computer simulations to show that even small variation of the cross section along channels completely shifts the dynamics either into the strong preference for highly grouped patterns (RRR...LLL) that generate system-size oscillations in flow or just the opposite-to patterns that distribute the droplets homogeneously between the arms of the loop. We also show the importance of noise in the process of self-organization of the spatiotemporal patterns of droplets. Our results provide guidelines for rational design of systems that reproducibly produce either grouped or homogeneous sequences of droplets flowing in microfluidic networks.

Dynamic charge separation in a liquid crystalline meniscus

Oscillating electric fields can sustain a macroscopic and steady separation of electrostatic charges. The control over the dynamic charge separation (dyCHASE) is presented for the example of circular menisci of thin, free standing smectic films. These films are subject to an in-plane, alternating radial electric field. The boundaries of the menisci become charged and unstable in the electric field and deform into pulsating, flower-like shapes. This instability ensues only at frequencies of the electric field that are lower than a critical one. The critical frequency is a linear function of the strength of the electric field. Since the speed of electrophoretic drift of ions is also linearly related to the strength of the field, the linear relation between critical frequency and the amplitude of the field sets a characteristic length scale in the system. We postulate that dyCHASE is due to (i) electrophoretic motion of ions in the liquid crystalline (LC) film, (ii) microscopic separation of charges over distances similar in magnitude to the Debye screening length, and (iii) further, macroscopic separation of charges through an electro-hydrodynamic instability. Interestingly, the electrophoretic motion of ions couples with the macroscopic motion of the LC material that can be observed with the use of simple optical microscopy.