A statistical method for revealing form-function relations in biological networks

Over the past decade, a number of researchers in systems biology have sought to relate the function of biological systems to their network-level descriptions -- lists of the most important players and the pairwise interactions between them. Both for large networks (in which statistical analysis is often framed in terms of the abundance of repeated small subgraphs) and for small networks which can be analyzed in greater detail (or even synthesized in vivo and subjected to experiment), revealing the relationship between the topology of small subgraphs and their biological function has been a central goal. We here seek to pose this revelation as a statistical task, illustrated using a particular setup which has been constructed experimentally and for which parameterized models of transcriptional regulation have been studied extensively. The question "how does function follow form" is here mathematized by identifying which topological attributes correlate with the diverse possible information-processing tasks which a transcriptional regulatory network can realize. The resulting method reveals one form-function relationship which had earlier been predicted based on analytic results, and reveals a second for which we can provide an analytic interpretation. Resulting source code is distributed via http://formfunction.sourceforge.net.Comment: To appear in Proc. Natl. Acad. Sci. USA. 17 pages, 9 figures, 2 table

Telling time with an intrinsically noisy clock

Intracellular transmission of information via chemical and transcriptional networks is thwarted by a physical limitation: the finite copy number of the constituent chemical species introduces unavoidable intrinsic noise. Here we provide a method for solving for the complete probabilistic description of intrinsically noisy oscillatory driving. We derive and numerically verify a number of simple scaling laws. Unlike in the case of measuring a static quantity, response to an oscillatory driving can exhibit a resonant frequency which maximizes information transmission. Further, we show that the optimal regulatory design is dependent on the biophysical constraints (i.e., the allowed copy number and response time). The resulting phase diagram illustrates under what conditions threshold regulation outperforms linear regulation.Comment: 10 pages, 5 figure

Temporal precision of molecular events with regulation and feedback

Cellular behaviors such as migration, division, and differentiation rely on precise timing, and yet the molecular events that govern these behaviors are highly stochastic. We investigate regulatory strategies that decrease the timing noise of molecular events. Autoregulatory feedback increases noise. Yet, we find that in the presence of regulation by a second species, autoregulatory feedback decreases noise. To explain this finding, we develop a method to calculate the optimal regulation function that minimizes the timing noise. The method reveals that the combination of feedback and regulation minimizes noise by maximizing the number of molecular events that must happen in sequence before a threshold is crossed. We compute the optimal timing precision for all two-node networks with regulation and feedback, derive a generic lower bound on timing noise, and discuss our results in the context of neuroblast migration during Caenorhabditis elegans development.Comment: 8 pages, 4 figure

A stochastic spectral analysis of transcriptional regulatory cascades

The past decade has seen great advances in our understanding of the role of noise in gene regulation and the physical limits to signaling in biological networks. Here we introduce the spectral method for computation of the joint probability distribution over all species in a biological network. The spectral method exploits the natural eigenfunctions of the master equation of birth-death processes to solve for the joint distribution of modules within the network, which then inform each other and facilitate calculation of the entire joint distribution. We illustrate the method on a ubiquitous case in nature: linear regulatory cascades. The efficiency of the method makes possible numerical optimization of the input and regulatory parameters, revealing design properties of, e.g., the most informative cascades. We find, for threshold regulation, that a cascade of strong regulations converts a unimodal input to a bimodal output, that multimodal inputs are no more informative than bimodal inputs, and that a chain of up-regulations outperforms a chain of down-regulations. We anticipate that this numerical approach may be useful for modeling noise in a variety of small network topologies in biology

Efeito do pré-condicionamento ácido nas forças de adesão em esmalte in vitro de dois sistemas adesivos: universal vs. self-etch

Tese de Mestrado, Medicina Dentária, Universidade de Lisboa, Faculdade de Medicina Dentária, 2014Objectives: The purpose of this study was to evaluate the effect of pre-etching on in vitro enamel bond strength of two adhesive systems: one universal adhesive and one two-step self-etch. Methods: In this study were used 8 caries-free human molars. The specimens were partially split in two halves and were assigned to two groups (n=8). On the enamel surfaces were applied two different adhesive systems: Scotchbond Universal (3M ESPE Seefeld, Germany) following manufacturer's instructions as a total-etch; Clearfil SE Bond (Kuraray, Okayama, Japan) applied as a total-etch. Build-ups were constructed with ENAMEL plus HRi (Micerium S.p.A. Avegno (GE) Italy) and cured in three increments of 2mm each. Specimens were kept in 37ºC destilated water for 24 hours and then sectioned with a slow-speed Diamond saw under water in X and Y directions to obtain bonded beams that were tested to failure in tension at a crosshead speed of 1 mm/minute. Statistical analyses were computed using T-student. The failures interfaces were observed under an optical microscope and registered. Results: There were not statistically significant differences among the two groups. Conclusions: A new universal adhesive system has similar bond strength than a two-step self-etch adhesive when pre-etching is performed.Objetivos: O presente trabalho tem como objetivo avaliar o efeito do pré-condicionamento ácido nas forças de adesão em esmalte in vitro de dois sistemas adesivos: um adesivo universal e um self-etch de dois passos. Materiais e Métodos: Neste estudo utilizaram-se 8 dentes molares humanos livres de cárie. Foram realizados cortes de maneira a hemissecionar as coroas dos dentes mesiodistalmente e estas foram aleatoriamente divididas em 2 grupos (n=8). Às superfícies em esmalte foram aplicados 2 sistemas adesivos distintos: Scotchbond Universal (3M ESPE Seefeld, Germany) segundo instruções do fabricante pela técnica total-etch; Clearfil SE Bond (Kuraray, Okayama, Japan) pela ténica total-etch, tendo sido restauradas com o compósito ENAMEL plus HRi (Micerium S.p.A. Avegno (GE) Italy) fotopolimerizados em três incrementos, cada um com 2mm. Os espécimenes foram armazenados em água destilada a 37ºC durante 24h e depois seccionados em palitos de aproximadamente 1mm2 com um disco de diamante sob refrigeração com água, nas direções X e Y de maneira a obter palitos. Todas as amostras foram testadas até à fratura em testes de microtração, a uma velocidade de 1mm/minuto. A análise estatística foi feita utilizando o T-student. As fraturas foram observadas num estereomicroscópio e registadas. Resultados: Os dois grupos estudados não apresentam diferenças estatisticamente significativas (p<0,05). Conclusão: Um adesivo universal parece proporcionar forças de adesão em esmalte similares a adesivos self-etch de dois passos quando efectuado pré-condicionamento ácido

Pulse Sequence Resilient Fast Brain Segmentation

Accurate automatic segmentation of brain anatomy from $T_1$-weighted~($T_1$-w) magnetic resonance images~(MRI) has been a computationally intensive bottleneck in neuroimaging pipelines, with state-of-the-art results obtained by unsupervised intensity modeling-based methods and multi-atlas registration and label fusion. With the advent of powerful supervised convolutional neural networks~(CNN)-based learning algorithms, it is now possible to produce a high quality brain segmentation within seconds. However, the very supervised nature of these methods makes it difficult to generalize them on data different from what they have been trained on. Modern neuroimaging studies are necessarily multi-center initiatives with a wide variety of acquisition protocols. Despite stringent protocol harmonization practices, it is not possible to standardize the whole gamut of MRI imaging parameters across scanners, field strengths, receive coils etc., that affect image contrast. In this paper we propose a CNN-based segmentation algorithm that, in addition to being highly accurate and fast, is also resilient to variation in the input $T_1$-w acquisition. Our approach relies on building approximate forward models of $T_1$-w pulse sequences that produce a typical test image. We use the forward models to augment the training data with test data specific training examples. These augmented data can be used to update and/or build a more robust segmentation model that is more attuned to the test data imaging properties. Our method generates highly accurate, state-of-the-art segmentation results~(overall Dice overlap=0.94), within seconds and is consistent across a wide-range of protocols.Comment: Accepted at MICCAI 201

Stochastic pump effect and geometric phases in dissipative and stochastic systems

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).Comment: Review. 35 pages. J. Phys. A: Math, Theor. (in press

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Information transmission in genetic regulatory networks: a review

Genetic regulatory networks enable cells to respond to the changes in internal and external conditions by dynamically coordinating their gene expression profiles. Our ability to make quantitative measurements in these biochemical circuits has deepened our understanding of what kinds of computations genetic regulatory networks can perform and with what reliability. These advances have motivated researchers to look for connections between the architecture and function of genetic regulatory networks. Transmitting information between network's inputs and its outputs has been proposed as one such possible measure of function, relevant in certain biological contexts. Here we summarize recent developments in the application of information theory to gene regulatory networks. We first review basic concepts in information theory necessary to understand recent work. We then discuss the functional complexity of gene regulation which arrises from the molecular nature of the regulatory interactions. We end by reviewing some experiments supporting the view that genetic networks responsible for early development of multicellular organisms might be maximizing transmitted 'positional' information.Comment: Submitted to J Phys: Condens Matter, 31 page