Physics

Polymerization of dendritic actin networks underlies important mechanical processes in cell biology such as the protrusion of lamellipodia, propulsion of growth cones in dendrites of neurons, intracellular transport of organelles and pathogens, among others. The forces required for these mechanical functions have been deduced from mechano-chemical models of actin polymerization; most models are focused on single growing filaments, and only a few address polymerization of filament networks through simulations. Here we propose a continuum model of surface growth and filament nucleation to describe polymerization of dendritic actin networks. The model describes growth and elasticity in terms of macroscopic stresses, strains and filament density rather than focusing on individual filaments. The microscopic processes underlying polymerization are subsumed into kinetic laws characterizing the change of filament density and the propagation of growing surfaces. This continuum model can predict the evolution of actin networks in disparate experiments. A key conclusion of the analysis is that existing laws relating force to polymerization speed of single filaments cannot predict the response of growing networks. Therefore a new kinetic law, consistent with the dissipation inequality, is proposed to capture the evolution of dendritic actin networks under different loading conditions. This model may be extended to other settings involving a more complex interplay between mechanical stresses and polymerization kinetics, such as the growth of networks of microtubules, collagen filaments, intermediate filaments and carbon nanotubes.

The high fidelity of DNA polymerase is critical for the faithful replication of genomic DNA. Several approaches were proposed to quantify the fidelity of DNA polymerase. Direct measurements of the error frequency of the replication products definitely give the true fidelity but turn out very hard to implement. Two biochemical kinetic approaches, the steady-state assay and the transient-state assay, were then suggested and widely adopted. In these assays, the error frequency is indirectly estimated by using the steady-state or the transient-state kinetic theory combined with the measured kinetic rates. However, whether these indirectly estimated fidelities are equivalent to the true fidelity has never been clarified theoretically, and in particular there are different strategies to quantify the proofreading efficiency of DNAP but often lead to inconsistent results. The reason for all these confusions is that it's mathematically challenging to formulate a rigorous and general theory of the true fidelity. Recently we have succeeded to establish such a theoretical framework. In this paper, we develop this theory to make a comprehensive examination on the theoretical foundation of the kinetic assays and the relation between fidelities obtained by different methods. We conclude that while the steady-state assay and the transient-state assay can always measure the true fidelity of exonuclease-deficient DNA polymerases, they only do so for exonuclease-efficient DNA polymerases conditionally (the proper way to use these assays to quantify the proofreading efficiency is also suggested). We thus propose a new kinetic approach, the single-molecule assay, which indirectly but precisely characterizes the true fidelity of either exonuclease-deficient or exonuclease-efficient DNA polymerases.

Synaptic transmission between neurons is governed by a cascade of stochastic reaction-diffusion events that lead to calcium-induced vesicle release of neurotransmitter. Since experimental measurements of such systems are challenging due their nanometer and sub-millisecond scale, numerical simulations remain the principal tool for studying calcium dependent synaptic vesicle fusion, despite limitations of time-consuming calculations. In this paper we develop an analytical solution to rapidly explore dynamical stochastic reaction-diffusion problems, based on first-passage times. This is the first analytical model that accounts simultaneously for relevant statistical features of calcium ion diffusion, buffering, and its binding/unbinding reaction with a vesicular sensor. In particular, unbinding kinetics are shown to have a major impact on the calcium sensor's occupancy probability on a millisecond scale and therefore cannot be neglected. Using Monte Carlo simulations we validated our analytical solution for instantaneous calcium influx and that through voltage-gated calcium channels. Overall we present a fast and rigorous analytical tool to study simplified reaction-diffusion systems that allow a systematic exploration of the biophysical parameters at a molecular scale, while correctly accounting for the statistical nature of molecular interactions within cells, that can also serve as a building block for more general cell signaling simulators.

We built a flexible platform to study the mechanical operation of the organ of Corti (OoC) in the transduction of basilar membrane (BM) vibrations to oscillations of an inner hair cell bundle (IHB). The anatomical components that we consider are the outer hair cells (OHCs), the outer hair cell bundles, Deiters cells, Hensen cells, the IHB and various sections of the reticular lamina. In each of the components we apply Newton's equations of motion. The components are coupled to each other and are further coupled to the endolymph fluid motion in the subtectorial gap. This allows us to obtain the forces acting on the IHB, and thus study its motion as a function of the parameters of the different components. Some of the components include a nonlinear mechanical response. We found that slight bending of the apical ends of the OHCs can have a significant impact on the passage of motion from the BM to the IHB, including critical oscillator behaviour. In particular, our model implies that the components of the OoC could cooperate to enhance frequency selectivity, amplitude compression and signal to noise ratio in the passage from the BM to the IHB. Since the model is modular, it is easy to modify the assumptions and parameters for each component.

The equilibration of a trivalent polygonal network in two dimensions (2D) is a universal phenomenon in nature, but the underlying mathematical mechanism remains unclear. In this study, a relaxation algorithm based on a simple geometrical rule was developed to simulate the equilibration. The proposed algorithm was implemented in Python language. The simulated relaxation changed the polygonal cell of the Voronoi network from an ellipse's inscribed polygon toward the ellipse's maximal inscribed polygon. Meanwhile, the Aboav-Weaire's law, which describes the neighboring relationship between cells, still holds statistically. The succeed of simulation strongly supports the ellipse packing hypothesis that was proposed to explain the dynamic behaviors of a trivalent 2D structure. The simulation results also showed that the edge of large cells tends to be shorter than edges of small cells, and vice versa. In addition, the relaxation increases the area and edge length of large cells, and it decreases the area and edge length of small cells. The pattern of changes in the area of different-edged cells due to relaxation is almost the same as the growth pattern described by the von-Neumann-Mullins law. The results presented in this work can help to understand the mathematical mechanisms of the dynamic behaviors of trivalent 2D structures.

Liquid-liquid phase separation occurs not only in bulk liquid, but also on surfaces. In physiology, the nature and function of condensates on cellular structures remain unexplored. Here, we study how the condensed protein TPX2 behaves on microtubules to initiate branching microtubule nucleation, which is critical for spindle assembly in eukaryotic cells. Using fluorescence, electron, and atomic force microscopies and hydrodynamic theory, we show that TPX2 on a microtubule reorganizes according to the Rayleigh-Plateau instability, like dew droplets patterning a spider web. After uniformly coating microtubules, TPX2 forms regularly spaced droplets from which branches nucleate. Droplet spacing increases with greater TPX2 concentration. A stochastic model shows that droplets make branching nucleation more efficient by confining the space along the microtubule where multiple necessary factors colocalize to nucleate a branch.

In the emerging field of 3D bioprinting, cell damage due to large deformations is considered a main cause for cell death and loss of functionality inside the printed construct. Those deformations, in turn, strongly depend on the mechano-elastic response of the cell to the hydrodynamic stresses experienced during printing. In this work, we present a numerical model to simulate the deformation of biological cells in arbitrary three-dimensional flows. We consider cells as an elastic continuum according to the hyperelastic Mooney-Rivlin model. We then employ force calculations on a tetrahedralized volume mesh. To calibrate our model, we perform a series of FluidFM(R) compression experiments with REF52 cells demonstrating that all three parameters of the Mooney-Rivlin model are required for a good description of the experimental data at very large deformations up to 80%. In addition, we validate the model by comparing to previous AFM experiments on bovine endothelial cells and artificial hydrogel particles. To investigate cell deformation in flow, we incorporate our model into Lattice Boltzmann simulations via an Immersed-Boundary algorithm. In linear shear flows, our model shows excellent agreement with analytical calculations and previous simulation data.

The motion of cells in tissues is an ubiquitous phenomenon. In particular, in monolayered cell colonies in vitro, pronounced collective behavior with swirl-like motion has been observed deep within a cell colony, while at the same time, the colony remains cohesive, with not a single cell escaping at the edge. Thus, the colony displays liquid-like properties inside, in coexistence with a cell-free "vacuum" outside. How can adhesion be strong enough to keep cells together, while at the same time not jam the system in a glassy state? What kind of minimal model can describe such a behavior? Which other signatures of activity arise from the internal fluidity? We propose a novel active Brownian particle model with attraction, in which the interaction potential has a broad minimum to give particles enough wiggling space to be collectively in the fluid state. We demonstrate that for moderate propulsion, this model can generate the fluid-vacuum coexistence described above. In addition, the combination of the fluid nature of the colony with cohesion leads to preferred orientation of the cell polarity, pointing outward, at the edge, which in turn gives rise to a tensile stress in the colony -- as observed experimentally for epithelial sheets. For stronger propulsion, collective detachment of cell clusters is predicted. Further addition of an alignment preference of cell polarity and velocity direction results in enhanced coordinated, swirl-like motion, increased tensile stress and cell-cluster detachment.

Birds are known for their extremely acute sense of vision. The very peculiar structural distribution of five different types of cones in the retina underlies this exquisite ability to sample light. It was recently found that each cone population as well as their total population display a disordered pattern in which long wave-length density fluctuations vanish. This property, known as hyperuniformity is also present in perfect crystals. In situations like the avian retina in which both the global structure and that of each component display hyperuniformity, the system is said to be multi-hyperuniform. In this work, we aim at devising a minimal statistical-mechanical model that can reproduce the main features of the spatial distribution of photoreceptors in avian retina, namely the presence of disorder, multi-hyperuniformity and local hetero-coordination. This last feature is key to avoid local clustering of the same type of photoreceptors, an undesirable feature for the efficient sampling of light. For this purpose we formulate a simple model that definitively exhibits the required structural properties, namely an equimolar three-component mixture (one component to sample each primary color, red, green, and blue) of non-additive hard disks to which a long-range logarithmic repulsion is added between like particles. A Voronoi analysis of our idealized system of photoreceptors shows that the space-filling Voronoi polygons interestingly display a rather uniform area distribution, symmetrically centered around that of a regular lattice, a structural property also found in human retina. Disordered multi-hyperuniformity offers an alternative to generate photoreceptor patterns with minimal long-range concentration and density fluctuations. This is the key to overcome the difficulties in devising an efficient visual system in which crystal-like order is absent.

Nanodiamond hosting temperature-sensing centers constitutes a closed thermodynamic system, with the only window of energy exchange with the environment without direct contacts of a sensor with intracellular substrates, which is in fact the property of an ideal nanosized thermometer. Here, a new design of a nanodiamond thermometer, based on a 500-nm luminescent nanodiamond embedded into the inner channel of a glass submicron pipette is reported. All-optical detection of temperature, based on spectral changes of the emission of "silicon-vacancy" centers with temperature, is used. We demonstrate the applicability of the thermometric tool to the study of temperature distribution near a local heater, placed in an aqueous medium. The calculated and experimental values of temperatures are shown to coincide within the measurement error at gradients up to 20 °C/{\mu}m. Until now, temperature measurements on the submicron scale at such high gradients have not been performed. The new thermometric tool opens up unique opportunities to answer the urgent paradigm-shifting questions of cell physiology thermodynamics.