Quantitative Analysis of Nuclear Lamins Imaged by Super-Resolution Light Microscopy

The nuclear lamina consists of a dense fibrous meshwork of nuclear lamins, Type V intermediate filaments, and is similar to 14 nm thick according to recent cryo-electron tomography studies. Recent advances in light microscopy have extended the resolution to a scale allowing for the fine structure of the lamina to be imaged in the context of the whole nucleus. We review quantitative approaches to analyze the imaging data of the nuclear lamina as acquired by structured illumination microscopy (SIM) and single molecule localization microscopy (SMLM), as well as the requisite cell preparation techniques. In particular, we discuss the application of steerable filters and graph-based methods to segment the structure of the four mammalian lamin isoforms (A, C, B1, and B2) and extract quantitative information

Noise Expands the Response Range of the Bacillus subtilis Competence Circuit

Gene regulatory circuits must contend with intrinsic noise that arises due to finite numbers of proteins. While some circuits act to reduce this noise, others appear to exploit it. A striking example is the competence circuit in Bacillus subtilis, which exhibits much larger noise in the duration of its competence events than a synthetically constructed analog that performs the same function. Here, using stochastic modeling and fluorescence microscopy, we show that this larger noise allows cells to exit terminal phenotypic states, which expands the range of stress levels to which cells are responsive and leads to phenotypic heterogeneity at the population level. This is an important example of how noise confers a functional benefit in a genetic decision-making circuit

Effects of bursty protein production on the noisy oscillatory properties of downstream pathways

Experiments show that proteins are translated in sharp bursts; similar bursty phenomena have been observed for protein import into compartments. Here we investigate the effect of burstiness in protein expression and import on the stochastic properties of downstream pathways. We consider two identical pathways with equal mean input rates, except in one pathway proteins are input one at a time and in the other proteins are input in bursts. Deterministically the dynamics of these two pathways are indistinguishable. However the stochastic behavior falls in three categories: (i) both pathways display or do not display noise-induced oscillations; (ii) the non-bursty input pathway displays noise-induced oscillations whereas the bursty one does not; (iii) the reverse of (ii). We derive necessary conditions for these three cases to classify systems involving autocatalysis, trimerization and genetic feedback loops. Our results suggest that single cell rhythms can be controlled by regulation of burstiness in protein production

Computation of Steady-State Probability Distributions in Stochastic Models of Cellular Networks

Cellular processes are “noisy”. In each cell, concentrations of molecules are subject to random fluctuations due to the small numbers of these molecules and to environmental perturbations. While noise varies with time, it is often measured at steady state, for example by flow cytometry. When interrogating aspects of a cellular network by such steady-state measurements of network components, a key need is to develop efficient methods to simulate and compute these distributions. We describe innovations in stochastic modeling coupled with approaches to this computational challenge: first, an approach to modeling intrinsic noise via solution of the chemical master equation, and second, a convolution technique to account for contributions of extrinsic noise. We show how these techniques can be combined in a streamlined procedure for evaluation of different sources of variability in a biochemical network. Evaluation and illustrations are given in analysis of two well-characterized synthetic gene circuits, as well as a signaling network underlying the mammalian cell cycle entry

Network, degeneracy and bow tie. Integrating paradigms and architectures to grasp the complexity of the immune system

Recently, the network paradigm, an application of graph theory to biology, has proven to be a powerful approach to gaining insights into biological complexity, and has catalyzed the advancement of systems biology. In this perspective and focusing on the immune system, we propose here a more comprehensive view to go beyond the concept of network. We start from the concept of degeneracy, one of the most prominent characteristic of biological complexity, defined as the ability of structurally different elements to perform the same function, and we show that degeneracy is highly intertwined with another recently-proposed organizational principle, i.e. 'bow tie architecture'. The simultaneous consideration of concepts such as degeneracy, bow tie architecture and network results in a powerful new interpretative tool that takes into account the constructive role of noise (stochastic fluctuations) and is able to grasp the major characteristics of biological complexity, i.e. the capacity to turn an apparently chaotic and highly dynamic set of signals into functional information

Localized cell death focuses mechanical forces during 3D patterning in a biofilm

From microbial biofilm communities to multicellular organisms, 3D macroscopic structures develop through poorly understood interplay between cellular processes and mechanical forces. Investigating wrinkled biofilms of Bacillus subtilis, we discovered a pattern of localized cell death that spatially focuses mechanical forces, and thereby initiates wrinkle formation. Deletion of genes implicated in biofilm development, together with mathematical modeling, revealed that ECM production underlies the localization of cell death. Simultaneously with cell death, we quantitatively measured mechanical stiffness and movement in WT and mutant biofilms. Results suggest that localized cell death provides an outlet for lateral compressive forces, thereby promoting vertical mechanical buckling, which subsequently leads to wrinkle formation. Guided by these findings, we were able to generate artificial wrinkle patterns within biofilms. Formation of 3D structures facilitated by cell death may underlie self-organization in other developmental systems, and could enable engineering of macroscopic structures from cell populations

Stochastic oscillations persist outside the deterministic oscillatory regime.

<p>The deterministic oscillatory regime is defined by for the induction rate <i>α</i>_<i>k</i>. (A) At low induction rate , where the deterministic model predicts excitable dynamics, the stochastic dynamics are oscillatory. The oscillations arise from repeated noise-induced excitations. (B) At high induction rate , where the deterministic model predicts mono-stable dynamics, the stochastic dynamics are also oscillatory. The oscillations here arise because noise prevents damping to the mono-stable state (see the deterministic curves in the right panels). The effect is much stronger for the native circuit (notice that the left panel is 15 times outside the deterministically oscillatory regime) because, unlike in the SynEx circuit, one of the species, ComS, is at low copy number and therefore subject to significant intrinsic noise. The deterministic model is given in Eqs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004793#pcbi.1004793.e021" target="_blank">6</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004793#pcbi.1004793.e022" target="_blank">7</a>, while the stochastic model is given in Eqs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004793#pcbi.1004793.e016" target="_blank">1</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004793#pcbi.1004793.e020" target="_blank">5</a>. In A, the deterministic initial conditions are ComK molecules and ComS molecules (native), and ComK molecules and MecA molecules (SynEx). In B, the deterministic initial conditions are ComK molecules and ComS molecules (native), and ComK molecules and MecA molecules (SynEx). In the excitable regime (A), the initial conditions are chosen to demonstrate the single, transient excitation.</p

Stochastic modeling of <i>B. subtilis</i> competence.

<p>(A) The deterministic model of each circuit (see Eqs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004793#pcbi.1004793.e021" target="_blank">6</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004793#pcbi.1004793.e022" target="_blank">7</a>) exhibits three dynamic regimes (excitable, oscillatory, and mono-stable), depending on the ComK induction rate <i>α</i>_<i>k</i>, which models stress level. (B) The stochastic model (see Eqs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004793#pcbi.1004793.e016" target="_blank">1</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004793#pcbi.1004793.e020" target="_blank">5</a>) reveals the ensuing distribution of ComK levels in each of the three dynamic regimes (excitable, oscillatory, and mono-stable). The fraction of the distribution in the responsive state <i>f</i> (determined by the inflection points, see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004793#sec007" target="_blank">Materials and Methods</a>) is shaded. (C) Whereas the deterministic model exhibits sharp transitions between the dynamic regimes (dashed lines), the stochastic model exhibits a continuous dependence of <i>f</i> on induction rate. We see that for both circuits, stochasticity extends the viable response range (0 < <i>f</i> < 1) beyond the transitions predicted by the deterministic model, in both directions, by the factors given above the arrows (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004793#sec007" target="_blank">Materials and Methods</a>). Parameters are as in [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004793#pcbi.1004793.ref016" target="_blank">16</a>] and are given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004793#pcbi.1004793.s001" target="_blank">S1 Text</a>. In A and B, from left to right, the values of the control parameter are <i>α</i>_<i>k</i> = {0.072, 1.15, 36}/hour (native) and <i>α</i>_<i>k</i> = {0.036, 1.8, 36}/hour (SynEx). In A, from left to right, the initial conditions are ComK molecules and ComS molecules (native), and ComK molecules and MecA molecules (SynEx); in the excitable regime (left), the initial conditions are chosen to demonstrate the single, transient excitation.</p

Architectures and model parameters of the native and SynEx circuits.

<p>The top row summarizes the regulatory interactions, while the bottom row depicts the model details. (A) In the native circuit, ComK is produced with the induction rate <i>α</i>_<i>k</i> and activates its own expression with Hill function parameters <i>β</i>_<i>k</i>, <i>k</i>_<i>k</i>, and <i>h</i>. ComS is expressed at the basal rate <i>α</i>_<i>s</i> and is repressed by ComK with Hill function parameters <i>β</i>_<i>s</i>, <i>k</i>_<i>s</i>, and <i>p</i>. ComK and ComS are degraded at rates <i>λ</i>_<i>k</i> and <i>λ</i>_<i>s</i>, respectively, and, additionally, both compete for binding to the degradation enzyme MecA. MecA degrades ComK and ComS with maximal rates <i>δ</i>_<i>k</i> and <i>δ</i>_<i>s</i>, respectively, and with Michaelis-Menten constants Γ_<i>k</i> and Γ_<i>s</i>, respectively. (B) In the SynEx circuit, ComK is produced with the induction rate <i>α</i>_<i>k</i> and activates its own expression with Hill function parameters <i>β</i>_<i>k</i>, <i>k</i>_<i>k</i>, and <i>h</i>. MecA is expressed at the basal rate <i>α</i>_<i>m</i> and is activated by ComK with Hill function parameters <i>β</i>_<i>m</i>, <i>k</i>_<i>m</i>, and <i>p</i>. ComK and MecA are degraded at rates <i>λ</i>_<i>k</i> and <i>λ</i>_<i>m</i>, respectively, and MecA enzymatically degrades ComK with rate <i>δ</i>.</p