Reaction-diffusion systems in intracellular molecular transport and control

Motility efficiency and spatiotemporal synchronization in non-metastatic vs. metastatic breast cancer cells

Metastatic breast cancer cells move not only more rapidly and persistently than their non-metastatic variants but in doing so use the mechanical work of the cytoskeleton more efficiently. The efficiency of the cell motions is defined for entire cells (rather than parts of the cell membrane) and is related to the work expended in forming membrane protrusions and retractions. This work, in turn, is estimated by integrating the protruded and retracted areas along the entire cell perimeter and is standardized with respect to the net translocation of the cell. A combination of cross-correlation, Granger causality, and morphodynamic profiling analyses is then used to relate the efficiency to the cell membrane dynamics. In metastatic cells, the protrusions and retractions are highly "synchronized" both in space and in time and these cells move efficiently. In contrast, protrusions and retractions formed by non-metastatic cells are not "synchronized" corresponding to low motility efficiencies. Our work provides a link between the kinematics of cell motions and their energetics. It also suggests that spatiotemporal synchronization might be one of the hallmarks of invasiveness of cancerous cells.

Engineering spatial gradients of signaling proteins using magnetic nanoparticles

Intracellular biochemical reactions are often localized in space and time, inducing gradients of enzymatic activity that may play decisive roles in determining cell's fate and functions. However, the techniques available to examine such enzymatic gradients of activity remain limited. Here, we propose a new method to engineer a spatial gradient of signaling protein concentration within Xenopus egg extracts using superparamagnetic nanoparticles. We show that, upon the application of a magnetic field, a concentration gradient of nanoparticles with a tunable length extension is established within confined egg extracts. We then conjugate the nanoparticles to RanGTP, a small G-protein controlling microtubule assembly. We found that the generation of an artificial gradient of Ran-nanoparticles modifies the spatial positioning of microtubule assemblies. Furthermore, the spatial control of the level of Ran concentration allows us to correlate the local fold increase in Ran-nanoparticle concentration with the spatial positioning of the microtubule-asters. Our assay provides a bottom-up approach to examine the minimum ingredients generating polarization and symmetry breaking within cells. More generally, these results show how magnetic nanoparticles and magnetogenetic tools can be used to control the spatiotemporal dynamics of signaling pathways.

Relationship between dynamical entropy and energy dissipation far from thermodynamic equilibrium

Connections between microscopic dynamical observables and macroscopic nonequilibrium (NE) properties have been pursued in statistical physics since Boltzmann, Gibbs, and Maxwell. The simulations we describe here establish a relationship between the Kolmogorov-Sinai entropy and the energy dissipated as heat from a NE system to its environment. First, we show that the Kolmogorov-Sinai or dynamical entropy can be separated into system and bath components and that the entropy of the system characterizes the dynamics of energy dissipation. Second, we find that the average change in the system dynamical entropy is linearly related to the average change in the energy dissipated to the bath. The constant energy and time scales of the bath fix the dynamical relationship between these two quantities. These results provide a link between microscopic dynamical variables and the macroscopic energetics of NE processes.

Ultrasensitivity by molecular titration in spatially propagating enzymatic reactions

Delineating design principles of biological systems by reconstitution of purified components offers a platform to gauge the influence of critical physicochemical parameters on minimal biological systems of reduced complexity. Here we unravel the effect of strong reversible inhibitors on the spatiotemporal propagation of enzymatic reactions in a confined environment in vitro. We use micropatterned, enzyme-laden agarose gels which are stamped on polyacrylamide films containing immobilized substrates and reversible inhibitors. Quantitative fluorescence imaging combined with detailed numerical simulations of the reaction-diffusion process reveal that a shallow gradient of enzyme is converted into a steep product gradient by addition of strong inhibitors, consistent with a mathematical model of molecular titration. The results confirm that ultrasensitive and threshold effects at the molecular level can convert a graded input signal to a steep spatial response at macroscopic length scales.

Why Cells are Microscopic: A Transport-Time Perspective

Physical-chemical reasoning is used to demonstrate that the sizes of both prokaryotic and eukaryotic cells are such that they minimize the times needed for the macromolecules to migrate throughout the cells and interact/react with one another. This conclusion does not depend on a particular form of the crowded-medium diffusion model, as thus points toward a potential optimization principle of cellular organisms. In eukaryotes, size optimality renders the diffusive transport as efficient as active transport - in this way, the cells can conserve energetic resources that would otherwise be expended in active transport.

Spatiotemporal control of microtubule nucleation and assembly using magnetic nanoparticles

Decisions on the fate of cells and their functions are dictated by the spatiotemporal dynamics of molecular signalling networks. However, techniques to examine the dynamics of these intracellular processes remain limited. Here, we show that magnetic nanoparticles conjugated with key regulatory proteins can artificially control, in time and space, the Ran/RCC1 signalling pathway that regulates the cell cytoskeleton. In the presence of a magnetic field, RanGTP proteins conjugated to superparamagnetic nanoparticles can induce microtubule fibres to assemble into asymmetric arrays of polarized fibres in Xenopus laevis egg extracts. The orientation of the fibres is dictated by the direction of the magnetic force. When we locally concentrated nanoparticles conjugated with the upstream guanine nucleotide exchange factor RCC1, the assembly of microtubule fibres could be induced over a greater range of distances than RanGTP particles. The method shows how bioactive nanoparticles can be used to engineer signalling networks and spatial self-organization inside a cell environment.

Organic switches for surfaces and devices

The pursuit to achieve miniaturization has tantalized researchers across the fields of chemistry, physics, biology, materials science and engineering for over half a century because of its many alluring potential applications. As alternatives to traditional "top-down" manufacturing, "bottom-up" approaches, originating from the (supra)molecular level, have enabled researchers to develop switches which can be manipulated on surfaces at nanoscale dimensions with deft precision using simple external triggers. Once on surfaces, these organic switches have been shown to modulate both the physical and chemical surface properties. In this Progress Report, we shed light on recent advances made in our laboratories towards integrated systems using all-organic switches on a variety of substrates. Design concepts are revealed, as well as the overall impact of all-organic switches on the properties of their substrates, while emphasizing the considerable promise and formidable challenges these advanced composite materials pose when it comes to conferring function on them.

Microtubule guidance tested through controlled cell geometry

In moving cells dynamic microtubules (MTs) target and disassemble substrate adhesion sites (focal adhesions; FAs) in a process that enables the cell to detach from the substrate and propel itself forward. The short-range interactions between FAs and MT plus ends have been observed in several experimental systems, but the spatial overlap of these structures within the cell has precluded analysis of the putative long-range mechanisms by which MTs growing through the cell body reach FAs in the periphery of the cell. In the work described here cell geometry was controlled to remove the spatial overlap of cellular structures thus allowing for unambiguous observation of MT guidance. Specifically, micropatterning of living cells was combined with high-resolution in-cell imaging and gene product depletion by means of RNA interference to study the long-range MT guidance in quantitative detail. Cells were confined on adhesive triangular microislands that determined cell shape and ensured that FAs localized exclusively at the vertices of the triangular cells. It is shown that initial MT nucleation at the centrosome is random in direction, while the alignment of MT trajectories with the targets (i.e. FAs at vertices) increases with an increasing distance from the centrosome, indicating that MT growth is a non-random, guided process. The guided MT growth is dependent on the presence of FAs at the vertices. The depletion of either myosin IIA or myosin IIB results in depletion of F-actin bundles and spatially unguided MT growth. Taken together our findings provide quantitative evidence of a role for long-range MT guidance in MT targeting of FAs.

Tomography and static-mechanical properties of adherent cells

A tomography approach is used to reconstruct 3D cell shapes and, simultaneously, the shapes/positions of the nuclei within these cells. Subjecting the cells to well-defined microconfinements of various diameters allow for relating the steady-state shapes of cells to their static-mechanical properties. The observed shapes show striking regularities between different cell types and all fit to a model that takes into account the cell membrane, cortical actin, and the nucleus.

Theoretical insights into bacterial chemotaxis

Research into understanding bacterial chemotactic systems has become a paradigm for Systems Biology. Experimental and theoretical researchers have worked hand-in-hand for over 40 years to understand the intricate behavior driving bacterial species, in particular how such small creatures, usually not more than 5 µm in length, detect and respond to small changes in their extracellular environment. In this review we highlight the importance that theoretical modeling has played in providing new insight and understanding into bacterial chemotaxis. We begin with an overview of the bacterial chemotaxis sensory response, before reviewing the role of theoretical modeling in understanding elements of the system on the single cell scale and features underpinning multiscale extensions to population models.

Real-time ion-flux imaging in the growth of micrometer-scale structures and membranes

Real-time ion flux imaging: an ion-sensitive field-effect transistor (ISFET) array is coupled with optical microscopy to image the growth of, and ion flux through, micrometer-scale tubes and membranes built from polyoxometalate clusters. The correlation between the optical and ionic imaging data is excellent, showcasing the use of ISFET arrays for high-resolution spatial and temporal mapping of ionic movements.

Nanobiology and physiology of growth hormone secretion

Growth hormone (GH) secretion is controlled by hypothalamic releasing hormones from the median eminence together with hormones and neuropeptides produced by peripheral organs. Secretion of GH involves movement of secretory vesicles along microtubules, transient ‘docking’ with the porosome in the cell membrane and subsequent release of GH. Release of GH is stimulated by GH releasing hormone (GHRH) and inhibited by somatostatin (SRIF). Ghrelin may be functioning to stimulate GH release from somatotropes acting via the GH secretagogue (GHS) receptor (GHSR). However, recent physiological studies militate against this. In addition, ghrelin does influence GH release acting within the hypothalamus. Release of GH from the somatotropes involves the GH-containing secretory granules moving close to the cell surface followed by transitory fusion of the secretory granules with the porosomes located in multiple secretory pits in the cell membrane. Other peptides/proteins can influence GH secretion, particularly in species of non-mammalian vertebrates.

Great expectations: can artificial molecular machines deliver on their promise?

The development and fabrication of mechanical devices powered by artificial molecular machines is one of the contemporary goals of nanoscience. Before this goal can be realized, however, we must learn how to control the coupling/uncoupling to the environment of individual switchable molecules, and also how to integrate these bistable molecules into organized, hierarchical assemblies that can perform significant work on their immediate environment at nano-, micro- and macroscopic levels. In this tutorial review, we seek to draw an all-important distinction between artificial molecular switches which are now ten a penny-or a dime a dozen-in the chemical literature and artificial molecular machines which are few and far between despite the ubiquitous presence of their naturally occurring counterparts in living systems. At the single molecule level, a prevailing perspective as to how machine-like characteristics may be achieved focuses on harnessing, rather than competing with, the ineluctable effects of thermal noise. At the macroscopic level, one of the major challenges inherent to the construction of machine-like assemblies lies in our ability to control the spatial ordering of switchable molecules-e.g., into linear chains and then into muscle-like bundles-and to influence the cross-talk between their switching kinetics. In this regard, situations where all the bistable molecules switch synchronously appear desirable for maximizing mechanical power generated. On the other hand, when the bistable molecules switch "out of phase," the assemblies could develop intricate spatial or spatiotemporal patterns. Assembling and controlling synergistically artificial molecular machines housed in highly interactive and robust architectural domains heralds a game-changer for chemical synthesis and a defining moment for nanofabrication.

Spatial distribution and dose-response relationship for different operation modes in a reaction-diffusion model of the MAPK cascade

The mitogen-activated protein kinase (MAPK) cascade plays a critical role in the control of cell growth. Deregulation of this pathway contributes to the development of many cancers. To better understand its signal transduction, we constructed a reaction-diffusion model for the MAPK pathway. We modeled the three layers of phosphorylation-dephosphorylation reactions and diffusion processes from the cell membrane to the nucleus. Based on different types of feedback in the MAPK cascade, four operation modes are introduced. For each of the four modes, spatial distributions and dose-response curves of active kinases (i.e. ppMAPK) are explored by numerical simulation. The effects of propagation length, diffusion coefficient and feedback strength on the pathway dynamics are investigated. We found that intrinsic bistability in the MAPK cascade can generate a traveling wave of ppMAPK with constant amplitude when the propagation length is short. ppMAPK in this mode of intrinsic bistability decays more slowly than it does in all other modes as the propagation length increases. Moreover, we examined the global and local responses to Ras-GTP of these four modes, and demonstrated how the shapes of these dose-response curves change as the propagation length increases. Also, we found that larger diffusion constant gives a higher response level on the zero-order regime and makes the ppMAPK profiles flatter under strong Ras-GTP stimulus. Furthermore, we observed that spatial responses of ppMAPK are more sensitive to negative feedback than to positive feedback in the broader signal range. Finally, we showed how oscillatory signals pass through the kinase cascade, and found that high frequency signals are damped faster than low frequency ones.

Convective mixing induced by acid-base reactions

When two miscible solutions, each containing a reactive species, are put in contact in the gravity field, local variations in the density due to the reaction can induce convective motion and mixing. We characterize here both experimentally and theoretically such buoyancy-driven instabilities induced by the neutralization of a strong acid by a strong base in aqueous solutions. The diverse patterns obtained are shown to depend on the type of reactants used and on their relative concentrations. They have their origin in a combination of classical hydrodynamic instabilities including differential diffusion of the solutes involved while temperature effects only play a marginal role.

The role of RanGTP gradient in vertebrate oocyte maturation

The maturation of vertebrate oocyte into haploid gamete, the egg, consists of two specialized asymmetric cell divisions with no intervening S-phase. Ran GTPase has an essential role in relaying the active role of chromosomes in their own segregation by the meiotic process. In addition to its conserved role as a key regulator of macromolecular transport between nucleus and cytoplasm, Ran has important functions during cell division, including in mitotic spindle assembly and in the assembly of nuclear envelope at the exit from mitosis. The cellular functions of Ran are mediated by RanGTP interactions with nuclear transport receptors (NTRs) related to importin β and depend on the existence of chromosome-centered RanGTP gradient. Live imaging with FRET biosensors indeed revealed the existence of RanGTP gradient throughout mouse oocyte maturation. NTR-dependent transport of cell cycle regulators including cyclin B1, Wee2, and Cdc25B between the oocyte cytoplasm and germinal vesicle (GV) is required for normal resumption of meiosis. After GVBD in mouse oocytes, RanGTP gradient is required for timely meiosis I (MI) spindle assembly and provides long-range signal directing egg cortex differentiation. However, RanGTP gradient is not required for MI spindle migration and may be dispensable for MI spindle function in chromosome segregation. In contrast, MII spindle assembly and function in maturing mouse and Xenopus laevis eggs depend on RanGTP gradient, similar to X. laevis MII-derived egg extracts.

"Nanoarmoured" droplets of different shapes formed by interfacial self-assembly and crosslinking of metal nanoparticles

Films comprising metal nanoparticles are assembled on the surfaces of liquid droplets of different shapes and macroscopic dimensions. These films are reinforced by dithiol crosslinks and are mechanically rugged yet permeable to the diffusion of small molecules.