Precision of sensing cell length via concentration gradients

Ultrahigh SERS Activity of TiO2@Ag Nanostructure leveraged for Accurately Detecting CTCs in peripheral blood

Circulating tumor cells (CTCs) usually shed from primary and metastatic tumors serve as an important tumor marker, and easily cause fatal distant metastasis in cancer patients. Accurately and effectively detecting...

A Concentration Gradients Tunable Generator with Adjustable Position of the Acoustically Oscillating Bubbles

It is essential to control concentration gradients at specific locations for many biochemical experiments. This paper proposes a tunable concentration gradient generator actuated by acoustically oscillating bubbles trapped in the bubble channels using a controllable position based on the gas permeability of polydimethylsiloxane (PDMS). The gradient generator consists of a glass substrate, a PDMS chip, and a piezoelectric transducer. When the trapped bubbles are activated by acoustic waves, the solution near the gas–liquid interface is mixed. The volume of the bubbles and the position of the gas–liquid interface are regulated through the permeability of the PDMS wall. The tunable concentration gradient can be realized by changing the numbers and positions of the bubbles that enable the mixing of fluids in the main channel, and the amplitude of the applied voltage. This new device is easy to fabricate, responsive, and biocompatible, and therefore has great application prospects. In particular, it is suitable for biological research with high requirements for temporal controllability.

eGFRD in all dimensions

Biochemical reactions often occur at low copy numbers but at once in crowded and diverse environments. Space and stochasticity therefore play an essential role in biochemical networks. Spatial-stochastic simulations have become a prominent tool for understanding how stochasticity at the microscopic level influences the macroscopic behavior of such systems. While particle-based models guarantee the level of detail necessary to accurately describe the microscopic dynamics at very low copy numbers, the algorithms used to simulate them typically imply trade-offs between computational efficiency and biochemical accuracy. eGFRD (enhanced Green's Function Reaction Dynamics) is an exact algorithm that evades such trade-offs by partitioning the N-particle system into M ≤ N analytically tractable one- and two-particle systems; the analytical solutions (Green's functions) then are used to implement an event-driven particle-based scheme that allows particles to make large jumps in time and space while retaining access to their state variables at arbitrary simulation times. Here we present "eGFRD2," a new eGFRD version that implements the principle of eGFRD in all dimensions, thus enabling efficient particle-based simulation of biochemical reaction-diffusion processes in the 3D cytoplasm, on 2D planes representing membranes, and on 1D elongated cylinders representative of, e.g., cytoskeletal tracks or DNA; in 1D, it also incorporates convective motion used to model active transport. We find that, for low particle densities, eGFRD2 is up to 6 orders of magnitude faster than conventional Brownian dynamics. We exemplify the capabilities of eGFRD2 by simulating an idealized model of Pom1 gradient formation, which involves 3D diffusion, active transport on microtubules, and autophosphorylation on the membrane, confirming recent experimental and theoretical results on this system to hold under genuinely stochastic conditions.

Protein gradients in single cells induced by their coupling to "morphogen"-like diffusion

One of the many ways cells transmit information within their volume is through steady spatial gradients of different proteins. However, the mechanism through which proteins without any sources or sinks form such single-cell gradients is not yet fully understood. One of the models for such gradient formation, based on differential diffusion, is limited to proteins with large ratios of their diffusion constants or to specific protein-large molecule interactions. We introduce a novel mechanism for gradient formation via the coupling of the proteins within a single cell with a molecule, that we call a "pronogen," whose action is similar to that of morphogens in multi-cell assemblies; the pronogen is produced with a fixed flux at one side of the cell. This coupling results in an effectively non-linear diffusion degradation model for the pronogen dynamics within the cell, which leads to a steady-state gradient of the protein concentration. We use stability analysis to show that these gradients are linearly stable with respect to perturbations.

Diffusive transport in the presence of stochastically gated absorption

We analyze a population of Brownian particles moving in a spatially uniform environment with stochastically gated absorption. The state of the environment at time t is represented by a discrete stochastic variable k(t)∈{0,1} such that the rate of absorption is γ[1-k(t)], with γ a positive constant. The variable k(t) evolves according to a two-state Markov chain. We focus on how stochastic gating affects the attenuation of particle absorption with distance from a localized source in a one-dimensional domain. In the static case (no gating), the steady-state attenuation is given by an exponential with length constant sqrt[D/γ], where D is the diffusivity. We show that gating leads to slower, nonexponential attenuation. We also explore statistical correlations between particles due to the fact that they all diffuse in the same switching environment. Such correlations can be determined in terms of moments of the solution to a corresponding stochastic Fokker-Planck equation.

A frequency-dependent decoding mechanism for axonal length sensing

We have recently developed a mathematical model of axonal length sensing in which a system of delay differential equations describe a chemical signaling network. We showed that chemical oscillations emerge due to delayed negative feedback via a Hopf bifurcation, resulting in a frequency that is a monotonically decreasing function of axonal length. In this paper, we explore how frequency-encoding of axonal length can be decoded by a frequency-modulated gene network. If the protein output were thresholded, then this could provide a mechanism for axonal length control. We analyze the robustness of such a mechanism in the presence of intrinsic noise due to finite copy numbers within the gene network.

Aggregation-fragmentation model of robust concentration gradient formation

Concentration gradients of signaling molecules are essential for patterning during development and they have been observed in both unicellular and multicellular systems. In subcellular systems, clustering of the signaling molecule has been observed. We develop a theoretical model of cluster-mediated concentration gradient formation based on the Becker-Döring equations of aggregation-fragmentation processes. We show that such a mechanism produces robust concentration gradients on realistic time and spatial scales so long as the process of clustering does not significantly stabilize the signaling molecule. Finally, we demonstrate that such a model is applicable to the pom1p subcellular gradient in fission yeast.

Cortical regulation of cell size by a sizer cdr2p

Cells can, in principle, control their size by growing to a specified size before commencing cell division. How any cell actually senses its own size remains poorly understood. The fission yeast Schizosaccharomyces pombe are rod-shaped cells that grow to ∼14 µm in length before entering mitosis. In this study, we provide evidence that these cells sense their surface area as part of this size control mechanism. We show that cells enter mitosis at a certain surface area, as opposed to a certain volume or length. A peripheral membrane protein kinase cdr2p has properties of a dose-dependent 'sizer' that controls mitotic entry. As cells grow, the local cdr2p concentration in nodes at the medial cortex accumulates as a measure of cell surface area. Our findings, which challenge a previously proposed pom1p gradient model, lead to a new model in which cells sense their size by using cdr2p to probe the surface area over the whole cell and relay this information to the medial cortex. DOI: http://dx.doi.org/10.7554/eLife.02040.001.

Intracellular chemical gradients: morphing principle in bacteria

Advances in computational biology allow systematic investigations to ascertain whether internal chemical gradients can be maintained in bacteria – an open question at the resolution limit of fluorescence microscopy. While it was previously believed that the small bacterial cell size and fast diffusion in the cytoplasm effectively remove any such gradient, a new computational study published in BMC Biophysics supports the emerging view that gradients can exist. The study arose from the recent observation that phosphorylated CtrA forms a gradient prior to cell division in Caulobacter crescentus, a bacterium known for its complicated cell cycle. Tropini et al. (2012) postulate that such gradients can provide an internal chemical compass, directing protein localization, cell division and cell development. More specifically, they describe biochemical and physical constraints on the formation of such gradients and explore a number of existing bacterial cell morphologies. These chemical gradients may limit in vitro analyses, and may ensure timing control and robustness to fluctuations during critical stages in cell development.

How to build a robust intracellular concentration gradient

Concentration gradients of morphogens are critical regulators of patterning in developmental biology. Increasingly, intracellular concentration gradients have also been found to orchestrate spatial organization, but inside single cells, where they regulate processes such as cell division, polarity and mitotic spindle dynamics. Here, we discuss recent progress in understanding how such intracellular gradients can be built robustly. We focus particularly on the Pom1p gradient in fission yeast, elucidating how various buffering mechanisms operate to ensure precise gradient formation. In this case, a systems-level understanding of the entire mechanism of precise gradient construction is now within reach, with important implications for gradients in both intracellular and developmental contexts.

Noise reduction in the intracellular pom1p gradient by a dynamic clustering mechanism

Chemical gradients can generate pattern formation in biological systems. In the fission yeast Schizosaccharomyces pombe, a cortical gradient of pom1p (a DYRK-type protein kinase) functions to position sites of cytokinesis and cell polarity and to control cell length. Here, using quantitative imaging, fluorescence correlation spectroscopy, and mathematical modeling, we study how its gradient distribution is formed. Pom1p gradients exhibit large cell-to-cell variability, as well as dynamic fluctuations in each individual gradient. Our data lead to a two-state model for gradient formation in which pom1p molecules associate with the plasma membrane at cell tips and then diffuse on the membrane while aggregating into and fragmenting from clusters, before disassociating from the membrane. In contrast to a classical one-component gradient, this two-state gradient buffers against cell-to-cell variations in protein concentration. This buffering mechanism, together with time averaging to reduce intrinsic noise, allows the pom1p gradient to specify positional information in a robust manner.