Ludvig Lizana

Single-File Diffusion in a Box

We study diffusion of (fluorescently) tagged hard-core interacting particles of finite size in a finite one-dimensional system. We find an exact analytical expression for the tagged particle probability density function using a Bethe ansatz, from which the mean square displacement is calculated. The analysis shows the existence of three regimes of drastically different behavior for short, intermediate, and large times. The results are in excellent agreement with stochastic simulations (Gillespie algorithm).

Controlling the rates of biochemical reactions and signaling networks by shape and volume changes

In biological systems, chemical activity takes place in micrometer- and nanometer-sized compartments that constantly change in shape and volume. These ever-changing cellular compartments embed chemical reactions, and we demonstrate that the rates of such incorporated reactions are directly affected by the ongoing shape reconfigurations. First, we show that the rate of product formation in an enzymatic reaction can be regulated by simple volume contraction–dilation transitions. The results suggest that mitochondria may regulate the dynamics of interior reaction pathways (e.g., the Krebs cycle) by volume changes. We then show the effect of shape changes on reactions occurring in more complex and structured systems by using biomimetic networks composed of micrometer-sized compartments joined together by nanotubes. Chemical activity was measured by implementing an enzymatic reaction–diffusion system. During ongoing reactions, the network connectivity is changed suddenly (similar to the dynamic tube formations found inside Golgi stacks, for example), and the effect on the reaction is registered. We show that spatiotemporal properties of the reaction–diffusion system are extremely sensitive to sudden changes in network topology and that chemical reactions can be initiated, or boosted, in certain nodes as a function of connectivity.

Controlling Chemistry by Geometry in Nanoscale Systems

Scientific literature dealing with the rates, mechanisms, and thermodynamic properties of chemical reactions in condensed media almost exclusively assumes that reactions take place in volumes that do not change over time. The reaction volumes are compact (such as a sphere, a cube, or a cylinder) and do not vary in shape. In this review article, we discuss two important systems at small length scales (approximately 10 nm to 5 microm), in which these basic assumptions are violated. The first system exists in cell biology and is represented by the tiniest functional components (i.e., single cells, organelles, and other physically delineated cellular microenvironments). The second system comprises nanofluidic devices, in particular devices made from soft-matter materials such as lipid nanotube-vesicle networks. In these two systems, transport, mixing, and shape changes can be achieved at or very close to thermal energy levels. In further contrast to macroscopic systems, mixing by diffusion is extremely efficient, and kinetics can be controlled by shape and volume changes.

Structural correlations in bacterial metabolic networks

BackgroundEvolution of metabolism occurs through the acquisition and loss of genes whose products acts as enzymes in metabolic reactions, and from a presumably simple primordial metabolism the organisms living today have evolved complex and highly variable metabolisms. We have studied this phenomenon by comparing the metabolic networks of 134 bacterial species with known phylogenetic relationships, and by studying a neutral model of metabolic network evolution.ResultsWe consider the union-network of 134 bacterial metabolisms, and also the union of two smaller subsets of closely related species. Each reaction-node is tagged with the number of organisms it belongs to, which we denote organism degree (OD), a key concept in our study. Network analysis shows that common reactions are found at the centre of the network and that the average OD decreases as we move to the periphery. Nodes of the same OD are also more likely to be connected to each other compared to a random OD relabelling based on their occurrence in the real data. This trend persists up to a distance of around five reactions. A simple growth model of metabolic networks is used to investigate the biochemical constraints put on metabolic-network evolution. Despite this seemingly drastic simplification, a union-network of a collection of unrelated model networks, free of any selective pressure, still exhibit similar structural features as their bacterial counterpart.ConclusionsThe OD distribution quantifies topological properties of the evolutionary history of bacterial metabolic networks, and lends additional support to the importance of horizontal gene transfer during bacterial metabolic evolution where new reactions are attached at the periphery of the network. The neutral model of metabolic network growth can reproduce the main features of real networks, but we observe that the real networks contain a smaller common core, while they are more similar at the periphery of the network. This suggests that natural selection and biochemical correlations can act both to diversify and to narrow down metabolic evolution.

Diffusive transport in networks built of containers and tubes.

We have developed analytical and numerical methods to study the transport of noninteracting particles in large networks consisting of M d -dimensional containers C1,...,C(M) with radii R(i) linked together by tubes of length l(ij) and radii a(ij) where i,j = 1,2,...,M. Tubes may join directly with each other, forming junctions. It is possible that some links are absent. Instead of solving the diffusion equation for the full problem we formulated an approach that is computationally more efficient. We derived a set of rate equations that govern the time dependence of the number of particles in each container, N1(t), N2(t),...,N(M)(t). In such a way the complicated transport problem is reduced to a set of M first-order integro-differential equations in time, which can be solved efficiently by the algorithm presented here. The workings of the method have been demonstrated on a couple of examples: networks involving three, four, and seven containers and one network with a three-point junction. Already simple networks with relatively few containers exhibit interesting transport behavior. For example, we showed that it is possible to adjust the geometry of the networks so that the particle concentration varies in time in a wave-like manner. Such behavior deviates from simple exponential growth and decay occurring in the two-container system.

Thermoactuated diffusion control in soft matter nanofluidic devices.

The diffusive transport rate in a soft matter nanofluidic device is controlled with a thermoactuated hydrogel valve. The device consists of three giant unilamellar vesicles linearly conjugated by lipid nanotubes, with a solution of the stimuli-responsive polymer poly(N-isopropyl acrylamide) (PNIPAAm) in the central vesicle. The valve states high (transport) rate and low (transport) rate are obtained by heat-activated switching between PNIPAAms dissolved and compact aggregated states. We show that three parameters influence the diffusion rate within the device: the increase of the transport rate caused by a decrease in PNIPAAm concentration upon compaction, the temperature dependence of the buffer viscosity, and the volume excluded by the PNIPAAm hydrogel compartment.