Endocytosis underlies many cellular functions including signaling and nutrient uptake. The endocytosed cargo gets redistributed across a dynamic network of endosomes undergoing fusion and fission. Here, a theoretical approach is reviewed which can ex
plain how the microscopic properties of endosome interactions cause the emergent macroscopic properties of cargo trafficking in the endosomal network. Predictions by the theory have been tested experimentally and include the inference of dependencies and parameter values of the microscopic processes. This theory could also be used to infer mechanisms of signal-trafficking crosstalk. It is applicable to in vivo systems since fixed samples at few time points suffice as input data.
Cilia and flagella are hair-like extensions of eukaryotic cells which generate oscillatory beat patterns that can propel micro-organisms and create fluid flows near cellular surfaces. The evolutionary highly conserved core of cilia and flagella consi
sts of a cylindrical arrangement of nine microtubule doublets, called the axoneme. The axoneme is an actively bending structure whose motility results from the action of dynein motor proteins cross-linking microtubule doublets and generating stresses that induce bending deformations. The periodic beat patterns are the result of a mechanical feedback that leads to self-organized bending waves along the axoneme. Using a theoretical framework to describe planar beating motion, we derive a nonlinear wave equation that describes the fundamental Fourier mode of the axonemal beat. We study the role of nonlinearities and investigate how the amplitude of oscillations increases in the vicinity of an oscillatory instability. We furthermore present numerical solutions of the nonlinear wave equation for different boundary conditions. We find that the nonlinear waves are well approximated by the linearly unstable modes for amplitudes of beat patterns similar to those observed experimentally.
We show that the synchronization transition of a large number of noisy coupled oscillators is an example for a dynamic critical point far from thermodynamic equilibrium. The universal behaviors of such critical oscillators, arranged on a lattice in a
$d$-dimensional space and coupled by nearest neighbors interactions, can be studied using field theoretical methods. The field theory associated with the critical point of a homogeneous oscillatory instability (or Hopf bifurcation of coupled oscillators) is the complex Ginzburg-Landau equation with additive noise. We perform a perturbative renormalization group (RG) study in a $4-epsilon$ dimensional space. We develop an RG scheme that eliminates the phase and frequency of the oscillations using a scale-dependent oscillating reference frame. Within a Callan-Symanzik RG scheme to two-loop order in perturbation theory, we find that the RG fixed point is formally related to the one of the model $A$ dynamics of the real Ginzburg-Landau theory with an O(2) symmetry of the order parameter. Therefore, the dominant critical exponents for coupled oscillators are the same as for this equilibrium field theory. This formal connection with an equilibrium critical point imposes a relation between the correlation and response functions of coupled oscillators in the critical regime. Since the system operates far from thermodynamic equilibrium, a strong violation of the fluctuation-dissipation relation occurs and is characterized by a universal divergence of an effective temperature. The formal relation between critical oscillators and equilibrium critical points suggests that long-range phase order exists in critical oscillators above two dimensions.
We discuss the motion of colloidal particles relative to a two component fluid consisting of solvent and solute. Particle motion can result from (i) net body forces on the particle due to external fields such as gravity; (ii) slip velocities on the p
article surface due to surface dissipative phenomena. The perturbations of the hydrodynamic flow field exhibits characteristic differences in cases (i) and (ii) which reflect different patterns of momentum flux corresponding to the existence of net forces, force dipoles or force quadrupoles. In the absence of external fields, gradients of concentration or pressure do not generate net forces on a colloidal particle. Such gradients can nevertheless induce relative motion between particle and fluid. We present a generic description of surface dissipative phenomena based on the linear response of surface fluxes driven by conjugate surface forces. In this framework we discuss different transport scenarios including self-propulsion via surface slip that is induced by active processes on the particle surface. We clarify the nature of force balances in such situations.
