Spontaneous polarization in eukaryotic gradient sensing: A mathematical model based on mutual inhibition of frontness and backness pathways

A key problem of eukaryotic cell motility is the signaling mechanism of chemoattractant gradient sensing. Recent experiments have revealed the molecular correlate of gradient sensing: Frontness molecules, such as PI3P and Rac, localize at the front end of the cell, and backness molecules, such as Rho and myosin II, accumulate at the back of the cell. Importantly, this frontness-backness polarization occurs "spontaneously" even if the cells are exposed to uniform chemoattractant profiles. The spontaneous polarization suggests that the gradient sensing machinery undergoes a Turing bifurcation. This has led to several classical activator-inhibitor and activator-substrate models which identify the frontness molecules with the activator. Conspicuously absent from these models is any accounting of the backness molecules. This stands in sharp contrast to experiments which show that the backness pathways inhibit the frontness pathways. Here, we formulate a model based on the mutually inhibitory interaction between the frontness and backness pathways. The model builds upon the mutual inhibition model proposed by Bourne and coworkers (Xu et al, Cell, 114, 201--214, 2003). We show that mutual inhibition alone, without the help of any positive feedback, can trigger spontaneous polarization of the frontness and backness pathways. The spatial distribution of the frontness and backness molecules in response to inhbition and activation of the frontness and backness pathways are consistent with those observed in experiments. Furthermore, depending on the parameter values, the model yields spatial distributions corresponding to chemoattraction (frontness pathways in-phase with the external gradient) and chemorepulsion (frontness pathways out-of-phase with the external gradient).Comment: 20 pages, 11 figure

Mind Your Language: Effects of Spoken Query Formulation on Retrieval Effectiveness

Voice search is becoming a popular mode for interacting with search engines. As a result, research has gone into building better voice transcription engines, interfaces, and search engines that better handle inherent verbosity of queries. However, when one considers its use by non- native speakers of English, another aspect that becomes important is the formulation of the query by users. In this paper, we present the results of a preliminary study that we conducted with non-native English speakers who formulate queries for given retrieval tasks. Our results show that the current search engines are sensitive in their rankings to the query formulation, and thus highlights the need for developing more robust ranking methods

Compact Support Biorthogonal Wavelet Filterbanks for Arbitrary Undirected Graphs

In our recent work, we proposed the design of perfect reconstruction orthogonal wavelet filterbanks, called graph- QMF, for arbitrary undirected weighted graphs. In that formulation we first designed "one-dimensional" two-channel filterbanks on bipartite graphs, and then extended them to "multi-dimensional" separable two-channel filterbanks for arbitrary graphs via a bipartite subgraph decomposition. We specifically designed wavelet filters based on the spectral decomposition of the graph, and stated necessary and sufficient conditions for a two-channel graph filter-bank on bipartite graphs to provide aliasing-cancellation, perfect reconstruction and orthogonal set of basis (orthogonality). While, the exact graph-QMF designs satisfy all the above conditions, they are not exactly k-hop localized on the graph. In this paper, we relax the condition of orthogonality to design a biorthogonal pair of graph-wavelets that can have compact spatial spread and still satisfy the perfect reconstruction conditions. The design is analogous to the standard Cohen-Daubechies-Feauveau's (CDF) construction of factorizing a maximally-flat Daubechies half-band filter. Preliminary results demonstrate that the proposed filterbanks can be useful for both standard signal processing applications as well as for signals defined on arbitrary graphs. Note: Code examples from this paper are available at http://biron.usc.edu/wiki/index.php/Graph FilterbanksComment: Submitted for review in IEEE TS

nn-Colour self-inverse compositions

MacMahon's definition of self-inverse composition is extended to $n$-colour self-inverse composition. This introduces four new sequences which satisfy the same recurrence relation with different initial conditions like the famous Fibonacci and Lucas sequences. For these new sequences explicit formulas, recurrence relations, generating functions and a summation formula are obtained. Two new binomial identities with combinatorial meaning are also given.Comment: 10 page

A comparative study of system size dependence of the effect of non-unitary channels on different classes of quantum states

We investigate the effect of different types of non-unitary quantum channels on multi-qubit quantum systems. For an $n$-qubit system and a particular channel, in order to draw unbiased conclusions about the system as a whole as opposed to specific states, we evolve a large number of randomly generated states under the given channel. We increase the number of qubits and study the effect of system size on the decoherence processes. The entire scheme is repeated for various types of environments which include dephasing channel, depolarising channel, collective dephasing channel and zero temperature bath. Non-unitary channels representing the environments are modeled via their Karus operator decomposition or master equation approach. Further, for a given $n$ we restrict ourselves to the study of particular subclasses of entangled states, namely the GHZ-type and W-type states. We generate random states within these classes and study the class behaviors under different quantum channels for various values of $n$.Comment: 10 pages revtex 10 pdf figure

Pure competition of multiple species during mixed-substrate microbial growth: Extending the resource-based theory

The simultaneous growth of multiple microbial species is a problem of fundamental ecological interest. In media containing more than one growth-limiting substrate, multiple species can coexist. The question then arises: Can single-species data predict the existence and stability of mixed-culture steady states in mixed-substrate environments? This question has been extensively studied with the help of resource-based models. These studies have shown that the single-species data required to predict mixed-culture behavior consists of the growth isoclines and consumption vectors, which in turn are determined from single-substrate data by making specific assumptions about the kinetics of mixed-substrate growth. Here, we show that these assumptions are not valid for microbial growth on mixtures of substitutable substrates. However, the theory can be developed by determining the growth isoclines and consumption vectors directly from the mixed-substrate data, thus obviating the need for specific assumptions about the kinetics of mixed-substrate growth. We show furthermore that in addition to the growth isoclines and consumption vectors, the single-species, mixed-substrate data yields a new family of curves, which we call the consumption curves. Consideration of the growth isoclines and the consumption curves yields deeper insights into the behavior of the mixed cultures. It yields a priori bounds on the substrate concentrations achieved during coexistence, permits the extension of the theory to systems in which the growth isoclines are non-monotonic, and clarifies earlier results obtained by considering only the growth isoclines.Comment: 21 page

Bistability of the lac operon during growth of Escherichia coli on lactose and lactose + glucose

The lac operon of Escherichia coli exhibits bistability. Early studies showed that bistability occurs during growth on TMG/succinate and lactose + glucose, but not during growth on lactose. More recent studies with lacGFP-transfected cells show bistability with TMG/succinate, but not with lactose and lactose + glucose. In the literature, these results are attributed to variations of the positive feedback generated by induction. Specifically, during growth on TMG/succinate, induction generates positive feedback because the permease stimulates the accumulation of TMG, which, in turn, promotes the synthesis of more permease. This positive feedback is attenuated during growth on lactose because hydrolysis of lactose by galactosidase suppresses the stimulatory effect of the permease. But the stabilizing effect of dilution also changes dramatically as a function of the medium composition. For instance, during growth on TMG/succinate, the dilution rate of the permease is proportional to its activity, $e$, because the specific growth rate is independent of $e$. However, during growth on lactose, the permease dilution rate is proportional to $e^2$ because the specific growth rate is proportional to the specific lactose uptake rate, which in turn, proportional to $e$. Here, we show that: (a) This dependence on $e^2$ creates such a strong stabilizing effect that bistability is virtually impossible during growth on lactose, even in the face of positive feedback. (b) This stabilizing effect is weakened during growth on lactose + glucose because the specific growth rate on glucose is independent of $e$, so that the dilution rate once again contains a term that is proportional to $e$. We discuss the experimental data in the light of these results.Comment: 34 pages, Bull Math Bio

Bacterial gene regulation in diauxic and nondiauxic growth

When bacteria are grown on a mixture of two growth-limiting substrates, they exhibit a rich spectrum of substrate consumption patterns including diauxic growth, simultaneous consumption, and bistable growth. In previous work, we showed that a minimal model accounting only for enzyme induction and dilution captures all the substrate consumption patterns. Here, we construct the bifurcation diagram of the minimal model. The bifurcation diagram explains several general properties of mixed-substrate growth. (1) In almost all cases of diauxic growth, the "preferred" substrate is the one that, by itself, supports a higher specific growth rate. In the literature, this property is often attributed to optimality of regulatory mechanisms. Here, we show that the minimal model, which contains only induction, displays the property under fairly general conditions. This suggests that the higher growth rate of the preferred substrate is an intrinsic property of the induction and dilution kinetics.(2) The model explains the phenotypes of various mutants containing lesions in the regions encoding for the operator, repressor, and peripheral enzymes. A particularly striking phenotype is the "reversal of the diauxie" in which the wild-type and mutant strains consume the very same two substrates in opposite order. This phenotype is difficult to explain in terms of molecular mechanisms, but it turns out to be a natural consequence of the model. We show furthermore that the model is robust. The key property of the model, namely, the competitive dynamics of the enzymes, is preserved even if the model is modified to account for various regulatory mechanisms. Finally, the model has important implications for size regulation in development, since it suggests that protein dilution is one mechanism for coupling patterning and growth.Comment: Accepted, J Theoret Biol (47 pages

Variational theory of non-relativistic quantum electrodynamics

The ability to achieve ultra-strong coupling between light and matter promises to bring about new means to control material properties, new concepts for manipulating light at the atomic scale, and fundamentally new insights into quantum electrodynamics (QED). Thus, there is a need to develop quantitative theories of QED phenomena in complex electronic and photonic systems. In this Letter, we develop a variational theory of general non-relativistic QED systems of coupled light and matter. Essential to our ansatz is the notion of an effective photonic vacuum whose modes are different than the modes in the absence of light-matter coupling. This variational formulation leads to a set of general equations that can describe the ground state of multi-electron systems coupled to many photonic modes in real space. As a first step towards a new ab initio approach to ground and excited state energies in QED, we apply our ansatz to describe a multi-level emitter coupled to many optical modes, a system with no analytical solution. We find a compact semi-analytical formula which describes ground and excited state energies to less than 1% error in all regimes of coupling parameters allowed by sum rules. Additionally, our formulation provides essentially a non-perturbative theory of Lamb shifts and Casimir-Polder forces, as well as suggesting new physical concepts such as the Casimir energy of a single atom in a cavity. Our method should give rise to highly accurate descriptions of phenomena in general QED systems, such as Casimir forces, Lamb shifts, spontaneous emission, and other fluctuational electrodynamical effects.Comment: 6 pages, 2 figure

Towards "Intelligent Compression" in Streams: A Biased Reservoir Sampling based Bloom Filter Approach

With the explosion of information stored world-wide,data intensive computing has become a central area of research.Efficient management and processing of this massively exponential amount of data from diverse sources,such as telecommunication call data records,online transaction records,etc.,has become a necessity.Removing redundancy from such huge(multi-billion records) datasets resulting in resource and compute efficiency for downstream processing constitutes an important area of study. "Intelligent compression" or deduplication in streaming scenarios,for precise identification and elimination of duplicates from the unbounded datastream is a greater challenge given the realtime nature of data arrival.Stable Bloom Filters(SBF) address this problem to a certain extent.However,SBF suffers from a high false negative rate(FNR) and slow convergence rate,thereby rendering it inefficient for applications with low FNR tolerance.In this paper, we present a novel Reservoir Sampling based Bloom Filter,(RSBF) data structure,based on the combined concepts of reservoir sampling and Bloom filters for approximate detection of duplicates in data streams.Using detailed theoretical analysis we prove analytical bounds on its false positive rate(FPR),false negative rate(FNR) and convergence rates with low memory requirements.We show that RSBF offers the currently lowest FN and convergence rates,and are better than those of SBF while using the same memory.Using empirical analysis on real-world datasets(3 million records) and synthetic datasets with around 1 billion records,we demonstrate upto 2x improvement in FNR with better convergence rates as compared to SBF,while exhibiting comparable FPR.To the best of our knowledge,this is the first attempt to integrate reservoir sampling method with Bloom filters for deduplication in streaming scenarios.Comment: 11 pages, 8 figures, 5 table