On a kneading theory for gene-splicing.

Two well-known facets in protein synthesis in eukaryotic cells are transcription of DNA to pre-RNA in the nucleus and the translation of messenger-RNA (mRNA) to proteins in the cytoplasm. A critical intermediate step is the removal of segments (introns) containing ∼97% of the nucleic-acid sites in pre-RNA and sequential alignment of the retained segments (exons) to form mRNA through a process referred to as splicing. Alternative forms of splicing enrich the proteome while abnormal splicing can enhance the likelihood of a cell developing cancer or other diseases. Mechanisms for splicing and origins of splicing errors are only partially deciphered. Our goal is to determine if rules on splicing can be inferred from data analytics on nucleic-acid sequences. Toward that end, we represent a nucleic-acid site as a point in a plane defined in terms of the anterior and posterior sub-sequences of the site. The "point-set" representation expands analytical approaches, including the use of statistical tools, to characterize genome sequences. It is found that point-sets for exons and introns are visually different, and that the differences can be quantified using a family of generalized moments. We design a machine-learning algorithm that can recognize individual exons or introns with 91% accuracy. Point-set distributions and generalized moments are found to differ between organisms.

Image formation from a concave mirror.

Computing locations and extent of images, except in the most trivial configurations or special cases, is a complex task. Even rays emanating from a point source and passing through an optical system generally fail to converge at a single image point, highlighting the care needed to establish image locations. We use three approaches to study image formation in a simple configuration, that of a point source following reflection from a spherical concave mirror. We calculate the caustic surfaces, compute cross sections of flux densities on image surfaces, and compare the results with experimentally generated light intensity fields. One of the two caustic surfaces is one dimensional while the other forms a surface. The latter undergoes a metamorphosis from a distorted cone to an open surface as the source is moved away from the axis. Cross sections of the caustic surfaces with an image plane are found to coincide with peaks in the flux density. Experimental studies validate these conclusions.

Imaging in reflecting spheres.

We study the formation of images in a reflective sphere in three configurations using caustics on the field of light rays. The optical wavefront emerging from a source point reaching a subject following passage through the optical system is, in general, a Gaussian surface with partial focus along the two principal directions of the Gaussian surface; i.e., there are two images of the source point, each with partial focus. As the source point moves, the images move on two surfaces, referred to as viewable surfaces. In our systems, one viewable surface consists of points with radial focus and the other consists of points with azimuthal focus. The problems we study are (1) imaging of a parallel beam of light, (2) imaging of the infinite viewed from a location outside the sphere, and (3) imaging of a planar object viewed through the point of its intersection with the radial line normal to the plane. We verify the existence of two images experimentally and show that the distance between them agrees with the computations.

Cell biology: How to short-circuit the cell cycle.

Although the cell cycle normally progresses from G1toStoG2toM and then back to G1, certain manipulations have been found to 'short circuit' the cycle, causing repetitions of some stages while skipping others. A new study suggests how these changes limit the actions of molecular 'latches' that normally ensure orderly cell cycle progression.

Anomalous scaling of stochastic processes and the Moses effect.

The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t^{1/2}. However, processes in which the probability distribution is not normal and the scaling exponent differs from 1/2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, autocorrelations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect and the Noah effect, respectively. If the increments are nonstationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data are analyzed, revealing that their anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.

Deconvolution of reacting-flow dynamics using proper orthogonal and dynamic mode decompositions.

Analytical and computational studies of reacting flows are extremely challenging due in part to nonlinearities of the underlying system of equations and long-range coupling mediated by heat and pressure fluctuations. However, many dynamical features of the flow can be inferred through low-order models if the flow constituents (e.g., eddies or vortices) and their symmetries, as well as the interactions among constituents, are established. Modal decompositions of high-frequency, high-resolution imaging, such as measurements of species-concentration fields through planar laser-induced florescence and of velocity fields through particle-image velocimetry, are the first step in the process. A methodology is introduced for deducing the flow constituents and their dynamics following modal decomposition. Proper orthogonal (POD) and dynamic mode (DMD) decompositions of two classes of problems are performed and their strengths compared. The first problem involves a cellular state generated in a flat circular flame front through symmetry breaking. The state contains two rings of cells that rotate clockwise at different rates. Both POD and DMD can be used to deconvolve the state into the two rings. In POD the contribution of each mode to the flow is quantified using the energy. Each DMD mode can be associated with an energy as well as a unique complex growth rate. Dynamic modes with the same spatial symmetry but different growth rates are found to be combined into a single POD mode. Thus, a flow can be approximated by a smaller number of POD modes. On the other hand, DMD provides a more detailed resolution of the dynamics. Two classes of reacting flows behind symmetric bluff bodies are also analyzed. In the first, symmetric pairs of vortices are released periodically from the two ends of the bluff body. The second flow contains von Karman vortices also, with a vortex being shed from one end of the bluff body followed by a second shedding from the opposite end. The way in which DMD can be used to deconvolve the second flow into symmetric and von Karman vortices is demonstrated. The analyses performed illustrate two distinct advantages of DMD: (1) Unlike proper orthogonal modes, each dynamic mode is associated with a unique complex growth rate. By comparing DMD spectra from multiple nominally identical experiments, it is possible to identify "reproducible" modes in a flow. We also find that although most high-energy modes are reproducible, some are not common between experimental realizations; in the examples considered, energy fails to differentiate between reproducible and nonreproducible modes. Consequently, it may not be possible to differentiate reproducible and nonreproducible modes in POD. (2) Time-dependent coefficients of dynamic modes are complex. Even in noisy experimental data, the dynamics of the phase of these coefficients (but not their magnitude) are highly regular. The phase represents the angular position of a rotating ring of cells and quantifies the downstream displacement of vortices in reacting flows. Thus, it is suggested that the dynamical characterizations of complex flows are best made through the phase dynamics of reproducible DMD modes.

Controlling networks of nonlinearly-coupled nodes using response surfaces.

Control of complex processes is a major goal of network analyses. Most approaches to control nonlinearly coupled systems require the network topology and/or network dynamics. Unfortunately, neither the full set of participating nodes nor the network topology is known for many important systems. On the other hand, system responses to perturbations are often easily measured. We show how the collection of such responses -a response surface- can be used for network control. Analyses of model systems show that response surfaces are smooth and hence can be approximated using low order polynomials. Importantly, these approximations are largely insensitive to stochastic fluctuations in data or measurement errors. They can be used to compute how a small set of nodes need to be altered in order to direct the network close to a pre-specified target state. These ideas, illustrated on a nonlinear electrical circuit, can prove useful in many contexts including in reprogramming cellular states.

Dynamical-systems analysis and unstable periodic orbits in reacting flows behind symmetric bluff bodies.

Dynamical systems analysis is performed for reacting flows stabilized behind four symmetric bluff bodies to determine the effects of shape on the nature of flame stability, acoustic coupling, and vortex shedding. The task requires separation of regular, repeatable aspects of the flow from experimental noise and highly irregular, nonrepeatable small-scale structures caused primarily by viscous-mediated energy cascading. The experimental systems are invariant under a reflection, and symmetric vortex shedding is observed throughout the parameter range. As the equivalence ratio-and, hence, acoustic coupling-is reduced, a symmetry-breaking transition to von Karman vortices is initiated. Combining principal-components analysis with a symmetry-based filtering, we construct bifurcation diagrams for the onset and growth of von Karman vortices. We also compute Lyapunov exponents for each flame holder to help quantify the transitions. Furthermore, we outline changes in the phase-space orbits that accompany the onset of von Karman vortex shedding and compute unstable periodic orbits (UPOs) embedded in the complex flows prior to and following the bifurcation. For each flame holder, we find a single UPO in flows without von Karman vortices and a pair of UPOs in flows with von Karman vortices. These periodic orbits organize the dynamics of the flow and can be used to reduce or control flow irregularities. By subtracting them from the overall flow, we are able to deduce the nature of irregular facets of the flows.

A dynamical systems approach to the control of chaotic dynamics in a spatiotemporal jet flow.

We present a strategy for control of chaos in open flows and provide its experimental validation in the near field of a transitional jet flow system. The low-dimensional chaotic dynamics studied here results from vortex ring formation and their pairings over a spatially extended region of the flow that was excited by low level periodic forcing of the primary instability. The control method utilizes unstable periodic orbits (UPO) embedded within the chaotic attractor. Since hydrodynamic instabilities in the open flow system are convective, both monitoring and control can be implemented at a few locations, resulting in a simple and effective control algorithm. Experiments were performed in an incompressible, initially laminar, 4 cm diameter circular air jet, at a Reynolds number of 23,000, housed in a low-noise, large anechoic chamber. Distinct trajectory bundles surrounding the dominant UPOs were found from experimentally derived, time-delayed embedding of the chaotic attractor. Velocity traces from a pair of probes placed at the jet flow exit and farther downstream were used to empirically model the UPOs and compute control perturbations to be applied at the jet nozzle lip. Open loop control was used to sustain several nearly periodic states.

Modeling novelty habituation during exploratory activity in Drosophila.

Habituation is a common form of non-associative learning in which the organism gradually decreases its response to repeated stimuli. The decrease in exploratory activity of many animal species during exposure to a novel open field arena is a widely studied habituation paradigm. However, a theoretical framework to quantify how the novelty of the arena is learned during habituation is currently missing. Drosophila melanogaster display a high mean absolute activity and a high probability for directional persistence when first introduced to a novel arena. Both measures decrease during habituation to the arena. Here, we propose a phenomenological model of habituation for Drosophila exploration based on two principles: Drosophila form a spatial representation of the arena edge as a set of connected local patches, and repeated exposure to these patches is essential for the habituation of the novelty. The level of exposure depends on the number of visitations and is quantified by a variable referred to as "coverage". This model was tested by comparing predictions against the experimentally measured behavior of wild type Drosophila. The novelty habituation of wild type Canton-S depends on coverage and is specifically independent of the arena radius. Our model describes the time dependent locomotor activity, ΔD, of Canton-S using an experimentally established stochastic process Pn(ΔD), which depends on the coverage. The quantitative measures of exploration and habituation were further applied to three mutant genotypes. Consistent with a requirement for vision in novelty habituation, blind no receptor potential A(7) mutants display a failure in the decay of probability for directional persistence and mean absolute activity. The rutabaga(2080) habituation mutant also shows defects in these measures. The kurtz(1) non-visual arrestin mutant demonstrates a rapid decay in these measures, implying reduced motivation. The model and the habituation measures offer a powerful framework for understanding mechanisms associated with open field habituation.

Modeling Drosophila positional preferences in open field arenas with directional persistence and wall attraction.

In open field arenas, Drosophila adults exhibit a preference for arena boundaries over internal walls and open regions. Herein, we investigate the nature of this preference using phenomenological modeling of locomotion to determine whether local arena features and constraints on movement alone are sufficient to drive positional preferences within open field arenas of different shapes and with different internal features. Our model has two components: directional persistence and local wall force. In regions far away from walls, the trajectory is entirely characterized by a directional persistence probability, P(r,θ), for each movement defined by the step size, r, and the turn angle, θ. In close proximity to walls, motion is computed from P(r,θ), and a local attractive force which depends on the distance between the fly and points on the walls. The directional persistence probability was obtained experimentally from trajectories of wild type Drosophila in a circular open field arena and the wall force was computed to minimize the difference between the radial distributions from the model and Drosophila in the same circular arena. The two-component model for fly movement was challenged by comparing the positional preferences from the two-component model to wild type Drosophila in a variety of open field arenas. In most arenas there was a strong concordance between the two-component model and Drosophila. In more complex arenas, the model exhibits similar trends, but some significant differences were found. These differences suggest that there are emergent features within these complex arenas that have significance for the fly, such as potential shelter. Hence, the two-component model is an important step in defining how Drosophila interact with their environment.

Open-field arena boundary is a primary object of exploration for Drosophila.

Drosophila adults, when placed into a novel open-field arena, initially exhibit an elevated level of activity followed by a reduced stable level of spontaneous activity and spend a majority of time near the arena edge, executing motions along the walls. In order to determine the environmental features that are responsible for the initial high activity and wall-following behavior exhibited during exploration, we examined wild-type and visually impaired mutants in arenas with different vertical surfaces. These experiments support the conclusion that the wall-following behavior of Drosophila is best characterized by a preference for the arena boundary, and not thigmotaxis or centrophobicity. In circular arenas, Drosophila mostly move in trajectories with low turn angles. Since the boundary preference could derive from highly linear trajectories, we further developed a simulation program to model the effects of turn angle on the boundary preference. In an hourglass-shaped arena with convex-angled walls that forced a straight versus wall-following choice, the simulation with constrained turn angles predicted general movement across a central gap, whereas Drosophila tend to follow the wall. Hence, low turn angled movement does not drive the boundary preference. Lastly, visually impaired Drosophila demonstrate a defect in attenuation of the elevated initial activity. Interestingly, the visually impaired w(1118) activity decay defect can be rescued by increasing the contrast of the arena's edge, suggesting that the activity decay relies on visual detection of the boundary. The arena boundary is, therefore, a primary object of exploration for Drosophila.

A robust topology-based algorithm for gene expression profiling.

Early and accurate diagnoses of cancer can significantly improve the design of personalized therapy and enhance the success of therapeutic interventions. Histopathological approaches, which rely on microscopic examinations of malignant tissue, are not conducive to timely diagnoses. High throughput genomics offers a possible new classification of cancer subtypes. Unfortunately, most clustering algorithms have not been proven sufficiently robust. We propose a novel approach that relies on the use of statistical invariants and persistent homology, one of the most exciting recent developments in topology. It identifies a sufficient but compact set of genes for the analysis as well as a core group of tightly correlated patient samples for each subtype. Partitioning occurs hierarchically and allows for the identification of genetically similar subtypes. We analyzed the gene expression profiles of 202 tumors of the brain cancer glioblastoma multiforme (GBM) given at the Cancer Genome Atlas (TCGA) site. We identify core patient groups associated with the classical, mesenchymal, and proneural subtypes of GBM. In our analysis, the neural subtype consists of several small groups rather than a single component. A subtype prediction model is introduced which partitions tumors in a manner consistent with clustering algorithms but requires the genetic signature of only 59 genes.

Effective models of periodically driven networks.

Circadian rhythms are governed by a highly coupled, complex network of genes. Due to feedback within the network, any modification of the system's state requires coherent changes in several nodes. A model of the underlying network is necessary to compute these modifications. We use an effective modeling approach for this task. Rather than inferred biochemical interactions, our method utilizes microarray data from a group of mutants for its construction. With simulated data, we develop an effective model for a circadian network in a peripheral tissue, subject to driving by the suprachiasmatic nucleus, the mammalian pacemaker. The effective network can predict time-dependent gene expression levels in other mutants.

Using effective subnetworks to predict selected properties of gene networks.

BACKGROUND: Difficulties associated with implementing gene therapy are caused by the complexity of the underlying regulatory networks. The forms of interactions between the hundreds of genes, proteins, and metabolites in these networks are not known very accurately. An alternative approach is to limit consideration to genes on the network. Steady state measurements of these influence networks can be obtained from DNA microarray experiments. However, since they contain a large number of nodes, the computation of influence networks requires a prohibitively large set of microarray experiments. Furthermore, error estimates of the network make verifiable predictions impossible. METHODOLOGY/PRINCIPAL FINDINGS: Here, we propose an alternative approach. Rather than attempting to derive an accurate model of the network, we ask what questions can be addressed using lower dimensional, highly simplified models. More importantly, is it possible to use such robust features in applications? We first identify a small group of genes that can be used to affect changes in other nodes of the network. The reduced effective empirical subnetwork (EES) can be computed using steady state measurements on a small number of genetically perturbed systems. We show that the EES can be used to make predictions on expression profiles of other mutants, and to compute how to implement pre-specified changes in the steady state of the underlying biological process. These assertions are verified in a synthetic influence network. We also use previously published experimental data to compute the EES associated with an oxygen deprivation network of E.coli, and use it to predict gene expression levels on a double mutant. The predictions are significantly different from the experimental results for less than of genes. CONCLUSIONS/SIGNIFICANCE: The constraints imposed by gene expression levels of mutants can be used to address a selected set of questions about a gene network.

A theory for the arrangement of sensory organs in Drosophila.

We study the arrangements of recurved bristles on the anterior wing margin of wild-type and mutant Drosophila. The epidermal or neural fate of a proneural cell depends on the concentrations of proteins of the achaete-scute complex. At puparium formation, concentrations of proteins are nearly identical in all cells of the anterior wing and each cell has the potential for neural fate. In wild-type flies, the action of regulatory networks drives the initial state to one where a bristle grows out of every fifth cell. Recent experiments have shown that the frequency of recurved bristles can be made to change by adjusting the mean concentrations of the zinc-finger transcription factor Senseless and the micro-RNA miR-9a. Specifically, mutant flies with reduced levels of miR-9a exhibit ectopic bristles, and those with lower levels of both miR-9a and Senseless show regular organization of recurved bristles, but with a lower periodicity of 4. We argue that these characteristics can be explained assuming an underlying Turing-type bifurcation whereby a periodic pattern spontaneously emerges from a uniform background. However, bristle patterns occur in a discrete array of cells, and are not mediated by diffusion. We argue that intracellular actions of transmembrane proteins such as Delta and Notch can play a role of diffusion in destabilizing the homogeneous state. In contrast to diffusion, intercellular actions can be activating or inhibiting; further, there can be lateral cross-species interactions. We introduce a phenomenological model to study bristle arrangements and make several model-independent predictions that can be tested in experiments. In our theory, miRNA-9a is one of the components of the underlying network and has no special regulatory role. The loss of periodicity in its absence is due to the transfer of the system to a bistable state.

Creating perfectly ordered quantum dot arrays via self-assembly.

Several applications involving quantum dots require perfect long-range ordered arrays. Unfortunately, self-assembly (the choice method to fabricate quantum dots) leads to patterns that, although short range ordered, exhibit defects equivalent to grain boundaries and dislocations on a large scale. We note that rotational invariance of film growth is one reason for formation of defects, and hence study an anisotropic model of quantum dot formation. However, nonlinear stability analysis shows that even in the extreme limit of anisotropy, square arrays whose orientations are in a finite range are linearly stable; consequently structures created in the film continue to have defects. Building on insights developed by the authors earlier on a simpler monolayer self-assembly model, we propose controlling the deposition through a mask to generate ordered quantum dots arrays. General principles to estimate geometrical characteristics of the mask are given. Numerical integration of the model shows that perfectly ordered square arrays of quantum dots can indeed be created using masked deposition.

Nanostructures with long-range order in monolayer self-assembly.

A key ingredient for continued expansion of nanotechnologies is the ability to create perfectly ordered arrays on a small scale with both site and size control. Self-assembly-i.e., the spontaneous formation of nanostructures-is a highly promising alternative to traditional fabrication methods. However, efforts to obtain perfect long-range order via self-assembly have been frustrated in practice as ensuing patterns contain defects. We use an idea based on the fundamental physics of pattern formation to introduce a strategy to consistently obtain perfect patterns.

Mouse let-7 miRNA populations exhibit RNA editing that is constrained in the 5'-seed/ cleavage/anchor regions and stabilize predicted mmu-let-7a:mRNA duplexes.

Massively parallel sequencing of millions of < 30-nt RNAs expressed in mouse ovary, embryonic pancreas (E14.5), and insulin-secreting beta-cells (betaTC-3) reveals that approximately 50% of the mature miRNAs representing mostly the mmu-let-7 family display internal insertion/deletions and substitutions when compared to precursor miRNA and the mouse genome reference sequences. Approximately, 12%-20% of species associated with mmu-let-7 populations exhibit sequence discrepancies that are dramatically reduced in nucleotides 3-7 (5'-seed) and 10-15 (cleavage and anchor sites). This observation is inconsistent with sequencing error and leads us to propose that the changes arise predominantly from post-transcriptional RNA-editing activity operating on miRNA:target mRNA complexes. Internal nucleotide modifications are most enriched at the ninth nucleotide position. A common ninth base edit of U-to-G results in a significant increase in stability of down-regulated let-7a targets in inhibin-deficient mice (Inha-/-). An excess of U-insertions (14.8%) over U-deletions (1.5%) and the presence of cleaved intermediates suggest that a mammalian TUTase (terminal uridylyl transferase) mediated dUTP-dependent U-insertion/U-deletion cycle may be a possible mechanism. We speculate that mRNA target site-directed editing of mmu-let-7a duplex-bulges stabilizes "loose" miRNA:mRNA target associations and functions to expand the target repertoire and/or enhance mRNA decay over translational repression. Our results also demonstrate that the systematic study of sequence variation within specific RNA classes in a given cell type from millions of sequences generated by next-generation sequencing (NGS) technologies ("intranomics") can be used broadly to infer functional constraints on specific parts of completely uncharacterized RNAs.

Nonstationary increments, scaling distributions, and variable diffusion processes in financial markets.

Fat-tailed distributions have been reported in fluctuations of financial markets for more than a decade. Sliding interval techniques used in these studies implicitly assume that the underlying stochastic process has stationary increments. Through an analysis of intraday increments, we explicitly show that this assumption is invalid for the Euro-Dollar exchange rate. We find several time intervals during the day where the standard deviation of increments exhibits power law behavior in time. Stochastic dynamics during these intervals is shown to be given by diffusion processes with a diffusion coefficient that depends on time and the exchange rate. We introduce methods to evaluate the dynamical scaling index and the scaling function empirically. In general, the scaling index is significantly smaller than previously reported values close to 0.5. We show how the latter as well as apparent fat-tailed distributions can occur only as artifacts of the sliding interval analysis.