Theory of spatial patterns of intracellular organelles

Trafficking in cancer: from gene deregulation to altered organelles and emerging biophysical properties

Intracellular trafficking supports all cell functions maintaining the exchange of material between membrane-bound organelles and the plasma membrane during endocytosis, cargo sorting, and exocytosis/secretion. Several proteins of the intracellular trafficking machinery are deregulated in diseases, particularly cancer. This complex and deadly disease stays a heavy burden for society, despite years of intense research activity. Here, we give an overview about trafficking proteins and highlight that in addition to their molecular functions, they contribute to the emergence of intracellular organelle landscapes. We review recent evidence of organelle landscape alterations in cancer. We argue that focusing on organelles, which represent the higher-order, cumulative behavior of trafficking regulators, could help to better understand, describe and fight cancer. In particular, we propose adopting a physical framework to describe the organelle landscape, with the goal of identifying the key parameters that are crucial for a stable and non-random organelle organization characteristic of healthy cells. By understanding these parameters, we may gain insights into the mechanisms that lead to a pathological organelle spatial organization, which could help explain the plasticity of cancer cells.

A physical perspective on cytoplasmic streaming

Organisms show a remarkable range of sizes, yet the dimensions of a single cell rarely exceed 100 µm. While the physical and biological origins of this constraint remain poorly understood, exceptions to this rule give valuable insights. A well-known counterexample is the aquatic plant Chara, whose cells can exceed 10 cm in length and 1 mm in diameter. Two spiralling bands of molecular motors at the cell periphery drive the cellular fluid up and down at speeds up to 100 µm s(-1), motion that has been hypothesized to mitigate the slowness of metabolite transport on these scales and to aid in homeostasis. This is the most organized instance of a broad class of continuous motions known as 'cytoplasmic streaming', found in a wide range of eukaryotic organisms-algae, plants, amoebae, nematodes and flies-often in unusually large cells. In this overview of the physics of this phenomenon, we examine the interplay between streaming, transport and cell size and discuss the possible role of self-organization phenomena in establishing the observed patterns of streaming.

Coupling of active motion and advection shapes intracellular cargo transport

Intracellular cargo transport can arise from passive diffusion, active motor-driven transport along cytoskeletal filament networks, and passive advection by fluid flows entrained by such cargo-motor motion. Active and advective transport are thus intrinsically coupled as related, yet different representations of the same underlying network structure. A reaction-advection-diffusion system is used here to show that this coupling affects the transport and localization of a passive tracer in a confined geometry. For sufficiently low diffusion, cargo localization to a target zone is optimized either by low reaction kinetics and decoupling of bound and unbound states, or by a mostly disordered cytoskeletal network with only weak directional bias. These generic results may help to rationalize subtle features of cytoskeletal networks, for example as observed for microtubules in fly oocytes.

From the cell membrane to the nucleus: unearthing transport mechanisms for dynein

Mutations in the motor protein cytoplasmic dynein have been found to cause Charcot-Marie-Tooth disease, spinal muscular atrophy, and severe intellectual disabilities in humans. In mouse models, neurodegeneration is observed. We sought to develop a novel model which could incorporate the effects of mutations on distance travelled and velocity. A mechanical model for the dynein mediated transport of endosomes is derived from first principles and solved numerically. The effects of variations in model parameter values are analysed to find those that have a significant impact on velocity and distance travelled. The model successfully describes the processivity of dynein and matches qualitatively the velocity profiles observed in experiments.

COOPERATIVE TRANSPORT BY SMALL TEAMS OF MOLECULAR MOTORS

Molecular motors power directed transport of cargoes within cells. Even if a single motor is sufficient to transport a cargo, motors often cooperate in small teams. We discuss the cooperative cargo transport by several motors theoretically and explore some of its properties. In particular we emphasize how motor teams can drag cargoes through a viscous environment.

Modeling of intracellular transport and compartmentation

The complexity and internal organization of mammalian cells as well as the regulation of intracellular transport processes has increasingly moved into the focus of investigation during the past two decades. Advanced staining and microscopy techniques help to shed light onto spatial cellular compartmentation and regulation, increasing the demand for improved modeling techniques. In this chapter, we summarize recent developments in the field of quantitative simulation approaches and frameworks for the description of intracellular transport processes. Special focus is therefore laid on compartmented and spatiotemporally resolved simulation approaches. The processes considered include free and facilitated diffusion of molecules, active transport via the microtubule and actin filament network, vesicle distribution, membrane transport, cell cycle-dependent cell growth and morphology variation, and protein production. Commercially and freely available simulation packages are summarized as well as model data exchange and harmonization issues.

Numerical modeling of molecular-motor-assisted transport of adenoviral vectors in a spherical cell

Viral gene delivery in a spherical cell is investigated numerically. The model of intracellular trafficking of adenoviruses is based on molecular-motor-assisted transport equations suggested by Smith and Simmons. These equations are presented in spherical coordinates and extended by accounting for the random component of motion of viral particles bound to filaments. This random component is associated with the stochastic nature of molecular motors responsible for locomotion of viral particles bound to filaments. The equations are solved numerically to simulate viral transport between the cell membrane and cell nucleus during initial stages of viral infection.

The method of separation of variables for solving equations describing molecular-motor-assisted transport of intracellular particles in a dendrite or axon

This paper presents an analytical solution of one-dimensional transient molecular-motor-assisted transport equations that describe transport of different organelles (such as transport vesicles loaded with a cargo of specific proteins) in a neuron's axon or dendrite. Large intracellular organelles are transported in the cytoplasm by a combined action of diffusion and motor-driven transport. In an axon, organelles are transported away from the neuron's body towards the axon's terminal by kinesin-family molecular motors running on tracks composed of microtubules (MTs); old and used components are carried back towards the neuron's body by dynein-family molecular motors. Using the method of separation of variables, a generalized Fourier series solution for this problem is obtained. The solution uses three different orthogonal sets of eigenfunctions to represent the concentration of free organelles transported by diffusion, MT-bound organelles transported away from the neuron's body, and MT-bound organelles transported towards the neuron's body. Binding/detachment kinetic processes between the organelles and the MT are specified by first-order rate constants; these lead to coupling between the three organelle concentrations.

Cell-assisted assembly of colloidal crystallites

Many cells ingest foreign particles through a process known as phagocytosis. It now turns out that some cell types organize phagocytosed microparticles into crystalline arrays. Much like the classic crystallization of colloidal particles in a thermal bath, crystallization within the cell is driven by the spatial confinement of mutually repelling particles, in this case by the cell membrane. Cytoskeleton-driven motions exert a randomizing force, similar to but stronger than thermal forces; these motions anneal defects and purify the colloidal crystals within the cells. Bidisperse mixtures of microspheres phase separate within the cell, with the larger particles crystallizing around the nucleus and the smaller particles crystallizing around the perimeter of the large particle array. Mitochondria also participate in this kind of size segregation, which appears to be driven by membrane tension and curvature minimization. Beyond the curiosity of the phenomenon itself, cell-assisted colloidal assembly may prove useful as a new tool to study a variety of biophysical processes including cytoskeletal rearrangements, organelle-membrane interactions, the in vivo mechanics of microtubules, the cooperativity of molecular motors and intracellular traffic jams on cytoskeletal filaments.

Modeling of pattern regulation in melanophores

Melanosomes, pigment granules in melanophores, play a principal role in physiological color adaptation of fish and frog. Melanophores regulate melanosome trafficking on cytoskeletal filaments to generate a range of spatiotemporal patterns. Here, we present the first comprehensive model of spatiotemporal evolution of melanosome patterns. The model encompasses both physical and biochemical aspects of melanosome dynamics. It consists of (i) a kinetic description of biochemical reactions involved in intracellular signaling, (ii) a system of macroscopic reaction-diffusion-convection equations for melanosome concentration, and (iii) a set of constitutive relationships for coupling transport with the biochemical network. The model relates molecular-level regulatory actions to cell-level melanosome distribution, allowing unification of existing experimental observations and qualitative hypotheses into an integrated, consistent framework. The model reproduces salient features of melanosome patterns, both during transient and steady state. It gives useful insights into how cells coordinate motor-assisted transport to maintain and adapt spatial organization of intracellular organelles. In particular, we calculate the optimal transition paths from aggregation to dispersion in fish melanophores. The calculations suggest that fish melanophores optimally control intracellular signaling to maximize the efficiency of motor-assisted transport during dispersion.

Systems biology of virus entry in mammalian cells

In this article, we define systems biology of virus entry in mammalian cells as the discipline that combines several approaches to comprehensively understand the collective physical behaviour of virus entry routes, and to understand the coordinated operation of the functional modules and molecular machineries that lead to this physical behaviour. Clearly, these are extremely ambitious aims, but recent developments in different life science disciplines slowly allow us to set them as realistic, although very distant, goals. Besides classical approaches to obtain high‐resolution information of the molecules, particles and machines involved, we require approaches that can monitor collective behaviour of many molecules, particles and machines simultaneously, in order to reveal design principles of the systems as a whole. Here we will discuss approaches that fall in the latter category, namely time‐lapse imaging and single‐particle tracking (SPT) combined with computational analysis and modelling, and genome‐wide RNA interference approaches to reveal the host components required for virus entry. These techniques should in the future allow us to assign host genes to the systems’ functions and characteristics, and allow emergence‐driven, in silico assembly of networks that include interactions with increasing hierarchy (molecules–multiprotein complexes–vesicles and organelles), and kinetics and subcellular spatiality, in order to allow realistic simulations of virus entry in real time.

Effects of tetracaine on voltage-activated calcium sparks in frog intact skeletal muscle fibers

The properties of Ca²⁺ sparks in frog intact skeletal muscle fibers depolarized with 13 mM [K⁺] Ringer's are well described by a computational model with a Ca²⁺ source flux of amplitude 2.5 pA (units of current) and duration 4.6 ms (18 °C; Model 2 of Baylor et al., 2002). This result, in combination with the values of single-channel Ca²⁺ current reported for ryanodine receptors (RyRs) in bilayers under physiological ion conditions, 0.5 pA (Kettlun et al., 2003) to 2 pA (Tinker et al., 1993), suggests that 1–5 RyR Ca²⁺ release channels open during a voltage-activated Ca²⁺ spark in an intact fiber. To distinguish between one and greater than one channel per spark, sparks were measured in 8 mM [K⁺] Ringer's in the absence and presence of tetracaine, an inhibitor of RyR channel openings in bilayers. The most prominent effect of 75–100 μM tetracaine was an approximately sixfold reduction in spark frequency. The remaining sparks showed significant reductions in the mean values of peak amplitude, decay time constant, full duration at half maximum (FDHM), full width at half maximum (FWHM), and mass, but not in the mean value of rise time. Spark properties in tetracaine were simulated with an updated spark model that differed in minor ways from our previous model. The simulations show that (a) the properties of sparks in tetracaine are those expected if tetracaine reduces the number of active RyR Ca²⁺ channels per spark, and (b) the single-channel Ca²⁺ current of an RyR channel is ≤1.2 pA under physiological conditions. The results support the conclusion that some normal voltage-activated sparks (i.e., in the absence of tetracaine) are produced by two or more active RyR Ca²⁺ channels. The question of how the activation of multiple RyRs is coordinated is discussed.