Funded Grants

Biological Transport in Complex and Dynamic Environments

Life is motion. One of the unique and defining characteristics of living creatures is the ability to transport material and information in a directed, regulated and timely fashion. Consider the basic unit of almost all forms of life - the cell. If the cell were a completely closed system with an impenetrable membrane, it would eventually reach equilibrium and die. The very existence of a functioning cell constitutes a never-ending fight against entropy. The cell therefore, has to exchange material and information with the exterior world. In addition, it has to keep all its various organelles with different functions intact and separate and facilitate the transmission of information and materials between these organelles in a well-regulated and timely fashion. In many ways, the interior of a eukaryotic cell is like a teeming metropolis. The nucleus, which is the repository of genetic information, mirrors the city hall, being a seat of legislative power while also doubling as the public library. The mitochondrion, which generates most of the cell’s supply of fuel (ATP) is the power-station of the city, while the Golgi apparatus that is responsible for packaging and processing proteins and lipids functions as the post-office. The endoplasmic reticulum functions as a factory manufacturing proteins upon demand, while the lysosome, which is involved with the digestion of waste, performs the same function as a recycling center. Just as in a city, there needs to be a constant flow of information and material between these vital units. In a city, we have well developed networks of highways and roads with trucking and postal units that take care of transportation along these networks. In the cell, the highways and roads are provided by an interconnected network of filamentous proteins such as actin, microtubules and intermediate filaments that make up the cell’s cytoskeleton. Molecular size motors such as myosin and kinesin are able to walk along these filaments powered by fuel in the form of ATP. These motors have the ability to drag cargo vesicles, which are filled with different kinds of macromolecules and carry molecules encoding destination addresses on their surfaces. The motors then perform the function of delivery trucks: transporting the cargo vesicles to different destinations, which either choose to accept them or not, depending on the attached address. Specific examples of vesicle trafficking include transport from the endoplasmic reticulum to the Golgi apparatus, transport between the Golgi stacks and the trans-Golgi network and the export of newly synthesized proteins from the trans-Golgi network to the lysosomes and cell membrane.

In a city, the failure of the trafficking system and the disruption of lines of communication can lead to paralysis and chaos. Similarly, at the cellular level, the disruption of any of the steps involved in transport can lead to scores of diseases ranging from cystic fibrosis to Alzheimer's disease. Understanding the nature of intracellular transport processes is thus of crucial importance. A great deal has been learnt, by studying individual motors moving along single tracks in carefully controlled conditions. It is enticing to combine this molecular level knowledge with the general analogy of transport in a city and conclude that we have a reasonably good understanding of intracellular transport. However, nothing could be further from the truth.

The reason is that our analogy simply cannot be scaled down to the cellular level. At the length scales of the motors in the cell, a staggering coincidence occurs, with forces of thermal, chemical, mechanical and electrostatic origin all having roughly the same order of magnitude. The motors therefore operate in a chaotic and hostile environment where the forces they can exert are comparable to the stickiness with the tracks and the forces exerted by other molecules colliding with them. In addition, as we shall show, the cytoskeletal network is not an ordered array of tracks, but actually has a fractal geometry. Furthermore, the filaments that make up the network can be in a continual state of turn-over- shrinking, growing and getting chopped up- all of these processes being controlled by dozens of regulatory proteins. Scaled back up to human dimensions, this would mean that the cargo trucks travel on an ever-changing fractal network of muddy roads while being bombarded by a rain of boulders. Given these conditions it is almost a miracle that the cargo can actually get to its destination and hence keep us alive.

Thus, our deterministic notions of transport based on trucks on highways simply fails at the cellular level. What is needed is then a completely different view- a statistical description of transport along fractal and dynamic networks. Fortunately, there have been decades of research on diffusion and transport in fractal networks in the Physics community. This kind of approach has been essential in describing the transport of fluids through porous media, the transport of macromolecules through polymer gels and the transport of electrons in disordered media among various other applications. Our goal is to bring this statistical mechanical understanding of transport in disordered and fractal media from the Physics community and apply it to the problem of intracellular transport. There are several aspects of this problem that pose exciting challenges. Firstly, there has been no characterization of the actual geometry of the underlying cytoskeletal network from a transport perspective, even treating it as static. We will characterize the geometry using a variety of fractal exponents such as the fractal dimension, topological dimension and random walk dimension among others. Knowing these exponents will allow us to make very concrete statements about the transport behavior in these systems. In particular, I am interested in the range of these exponents in vivo and whether there exists transitions between regimes with different exponents that could be triggered by changing regulatory protein concentrations. Diffusion is known to be anomalous on fractal substrates and it would be exciting to see the character of diffusion on these cytoskeletal networks. Secondly, as mentioned above, the network is not static but highly dynamic. We will look explicitly at the time required to move between specific points in the network, how it is influenced by the dynamics of the network, the range of behaviors we can expect in vivo and again whether there exist dynamical transitions between qualitatively different transport regimes that can be triggered by regulatory proteins.

From a fundamental complex systems perspective, these systems exhibit an interplay between stochastic motion, structural complexity of the environment and its dynamics, not typically present in traditional physical systems, leading to novel transport phenomena. Insights into these systems can be applied to the general problem of transport on complex time-dependent networks that could have implications for such systems as information transfer and routing on dynamic computer networks and the spreading of populations and diseases on large-scale time-evolving ecological and human networks.