Constraints on Fluctuations in Sparsely Characterized Biological Systems.

Biochemical processes are inherently stochastic, creating molecular fluctuations in otherwise identical cells. Such "noise" is widespread but has proven difficult to analyze because most systems are sparsely characterized at the single cell level and because nonlinear stochastic models are analytically intractable. Here, we exactly relate average abundances, lifetimes, step sizes, and covariances for any pair of components in complex stochastic reaction systems even when the dynamics of other components are left unspecified. Using basic mathematical inequalities, we then establish bounds for whole classes of systems. These bounds highlight fundamental trade-offs that show how efficient assembly processes must invariably exhibit large fluctuations in subunit levels and how eliminating fluctuations in one cellular component requires creating heterogeneity in another.The work was supported by grant 1137676 from the Division of Mathematical Sciences at the National Science Foundation, and grant GM081563 from the National Institutes of Health.This is the final version of the article. It first appeared from the American Physical Society via http://dx.doi.org/10.1103/PhysRevLett.116.05810

Dynamics of Cilia and Flagella

Cilia and flagella are hair-like appendages of eukaryotic cells. They are actively bending structures that exhibit regular beat patterns and thereby play an important role in many different circumstances where motion on a cellular level is required. Most dramatic is the effect of nodal cilia whose vortical motion leads to a fluid flow that is directly responsible for establishing the left-right axis during embryological development in many vertebrate species, but examples range from the propulsion of single cells, such as the swimming of sperm, to the transport of mucus along epithelial cells, e.g. in the ciliated trachea. Cilia and flagella contain an evolutionary highly conserved structure called the axoneme, whose characteristic architecture is based on a cylindrical arrangement of elastic filaments (microtubules). In the presence of a chemical fuel (ATP), molecular motors (dynein) exert shear forces between neighbouring microtubules, leading to a bending of the axoneme through structural constraints. We address the following two questions: How can these organelles generate regular oscillatory beat patterns in the absence of a biochemical signal regulating the activity of the force generating elements? And how can the beat patterns be so different for apparently very similar structures? We present a theoretical description of the axonemal structure as an actively bending elastic cylinder, and show that in such a system bending waves emerge from a non-oscillatory state via a dynamic instability. The corresponding beat patterns are solutions to a set of coupled partial differential equations presented herein

Kinetic Uncertainty Relations for the Control of Stochastic Reaction Networks.

Nonequilibrium stochastic reaction networks are commonly found in both biological and nonbiological systems, but have remained hard to analyze because small differences in rate functions or topology can change the dynamics drastically. Here, we conjecture exact quantitative inequalities that relate the extent of fluctuations in connected components, for various network topologies. Specifically, we find that regardless of how two components affect each other's production rates, it is impossible to suppress fluctuations below the uncontrolled equivalents for both components: one must increase its fluctuations for the other to be suppressed. For systems in which components control each other in ringlike structures, it appears that fluctuations can only be suppressed in one component if all other components instead increase fluctuations, compared to the case without control. Even the general N-component system-with arbitrary connections and parameters-must have at least one component with increased fluctuations to reduce fluctuations in others. In connected reaction networks it thus appears impossible to reduce the statistical uncertainty in all components, regardless of the control mechanisms or energy dissipation

Thrombostatin Fm19 ‐ A Thrombin Receptor Activation Antagonist

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106110/1/jth01272.pd

Transient fluctuation of the prosperity of firms in a network economy

The transient fluctuation of the prosperity of firms in a network economy is investigated with an abstract stochastic model. The model describes the profit which firms make when they sell materials to a firm which produces a product and the fixed cost expense to the firms to produce those materials and product. The formulae for this model are parallel to those for population dynamics. The swinging changes in the fluctuation in the transient state from the initial growth to the final steady state are the consequence of a topology-dependent time trial competition between the profitable interactions and expense. The firm in a sparse random network economy is more likely to go bankrupt than expected from the value of the limit of the fluctuation in the steady state, and there is a risk of failing to reach by far the less fluctuating steady state

The fidelity of dynamic signaling by noisy biomolecular networks

This is the final version of the article. Available from Public Library of Science via the DOI in this record.Cells live in changing, dynamic environments. To understand cellular decision-making, we must therefore understand how fluctuating inputs are processed by noisy biomolecular networks. Here we present a general methodology for analyzing the fidelity with which different statistics of a fluctuating input are represented, or encoded, in the output of a signaling system over time. We identify two orthogonal sources of error that corrupt perfect representation of the signal: dynamical error, which occurs when the network responds on average to other features of the input trajectory as well as to the signal of interest, and mechanistic error, which occurs because biochemical reactions comprising the signaling mechanism are stochastic. Trade-offs between these two errors can determine the system's fidelity. By developing mathematical approaches to derive dynamics conditional on input trajectories we can show, for example, that increased biochemical noise (mechanistic error) can improve fidelity and that both negative and positive feedback degrade fidelity, for standard models of genetic autoregulation. For a group of cells, the fidelity of the collective output exceeds that of an individual cell and negative feedback then typically becomes beneficial. We can also predict the dynamic signal for which a given system has highest fidelity and, conversely, how to modify the network design to maximize fidelity for a given dynamic signal. Our approach is general, has applications to both systems and synthetic biology, and will help underpin studies of cellular behavior in natural, dynamic environments.We acknowledge support from a Medical Research Council and Engineering and Physical Sciences Council funded Fellowship in Biomedical Informatics (CGB) and a Scottish Universities Life Sciences Alliance chair in Systems Biology (PSS). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

The interplay of intrinsic and extrinsic bounded noises in genetic networks

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a genetic network. The influence of intrinsic and extrinsic noises on genetic networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: $(i)$ the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, $(ii)$ a model of enzymatic futile cycle and $(iii)$ a genetic toggle switch. In $(ii)$ and $(iii)$ we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possibile functional role of bounded noises

Acculturation, Body Mass Index, Waist Circumference, and Physical Activity in Mexican Origin Women

Purpose: Longer time in the United States (US) is associated with increased risk of obesity in Hispanic immigrants, particularly for women. Although previous research has established an association between nutrition and acculturation, little attention has focused on physical activity. In this study, we examine the associations between acculturation on Mexican origin women’s body mass index (BMI), waist circumference (WC), and report of moderate to vigorous physical activity (MVPA). Method: Mexican origin women ≥18 years (n=120) from South Carolina (n=60) and Texas Lower Rio Grande Valley (n=60) completed a survey and anthropometric measures. Participants reported MVPA in hours per week, country of birth, age at migration (\u3c16\u3eyears, 16-25 years, and ≥26 years), and language use. Using these latter two as indicators of acculturation, we evaluated associations between acculturation and BMI, WC, and MVPA. Results: Age standardized means for BMI indicated lowest BMI and waist circumference measures among women either with middle-range English language proficiency or who had immigrated to the US between the ages of 16-25; however, the relationship with BMI was more robust. Age standardized means for MVPA show that women who migrated at younger ages (\u3c16\u3eyears) had the lowest MVPA levels, followed by those migrating as younger adults (16-25 years), then adults (≥26 years). Similarly, women with lowest English proficiency levels had the lowest reported MVPA and those with highest English proficiency had highest reported MVPA. Conclusions: The relationship between acculturation and obesity and MVPA is multifaceted. While the relationship between MVPA and the two indicators of acculturation appear to be linear, the direction of association varied by acculturation indicator. Moreover, the association with acculturation indicators and measures of obesity was not linear. The findings from this study have implications in how researchers interpret the relationship between acculturation, obesity and obesity risk factors

Bicoid signal extraction with a selection of parametric and nonparametric signal processing techniques.

The maternal segmentation coordinate gene bicoid plays a significant role during Drosophila embryogenesis. The gradient of Bicoid, the protein encoded by this gene, determines most aspects of head and thorax development. This paper seeks to explore the applicability of a variety of signal processing techniques at extracting bicoid expression signal, and whether these methods can outperform the current model. We evaluate the use of six different powerful and widely-used models representing both parametric and nonparametric signal processing techniques to determine the most efficient method for signal extraction in bicoid. The results are evaluated using both real and simulated data. Our findings show that the Singular Spectrum Analysis technique proposed in this paper outperforms the synthesis diffusion degradation model for filtering the noisy protein profile of bicoid whilst the exponential smoothing technique was found to be the next best alternative followed by the autoregressive integrated moving average