Characterization of the human SCF ubiquitin ligases - structure, function, and regulation

The SCF ubiquitin ligase complex of budding yeast triggers DNA replication by cata lyzi ng ubiquitination of the S phase CDK inhibitor SIC1. SCF is composed of several evolutionarily conserved proteins, including ySKP1, CDC53 (Cullin), and the F-box protein CDC4. We isolated hSKP1 in a two-hybrid screen with hCUL1, the human homologue of CDC53. We showed that hCUL1 associates with hSKP1 in vivo and directly interacts with hSKP1 and the human F-box protein SKP2 in vitro, forming an SCF-Iike particle. Moreover, hCUL1 complements the growth defect of yeast CDC53^(ts) mutants, associates with ubiquitination-promoting activity in human cell extracts, and can assemble into functional, chimeric ubiquitin ligase complexes with yeast SCF components. These data demonstrated that hCUL1 functions as part of an SCF ubiquitin ligase complex in human cells. However, purified human SCF complexes consisting of CUL1, SKP1, and SKP2 are inactive in vitro, suggesting that additional factors are required.

Subsequently, mammalian SCF ubiquitin ligases were shown to regulate various physiological processes by targeting important cellular regulators, like lĸBα, β-catenin, and p27, for ubiquitin-dependent proteolysis by the 26S proteasome. Little, however, is known about the regulation of various SCF complexes. By using sequential immunoaffinity purification and mass spectrometry, we identified proteins that interact with human SCF components SKP2 and CUL1 in vivo. Among them we identified two additional SCF subunits: HRT1, present in all SCF complexes, and CKS1, that binds to SKP2 and is likely to be a subunit of SCF5^(SKP2) complexes. Subsequent work by others demonstrated that these proteins are essential for SCF activity. We also discovered that COP9 Signalosome (CSN), previously described in plants as a suppressor of photomorphogenesis, associates with CUL1 and other SCF subunits in vivo. This interaction is evolutionarily conserved and is also observed with other Cullins, suggesting that all Cullin based ubiquitin ligases are regulated by CSN. CSN regulates Cullin Neddylation presumably through CSNS/JAB1, a stochiometric Signalosome subunit and a putative deneddylating enzyme. This work sheds light onto an intricate connection that exists between signal transduction pathways and protein degradation machinery inside the cell and sets stage for gaining further insights into regulation of protein degradation.

MicroRNA-132 is a physiological regulator of hematopoietic stem cell function and B-cell development

MicroRNAs are a class of small non-coding RNAs that negatively regulate gene expression. Several microRNAs have been implicated in altering hematopoietic cell fate decisions. Importantly, deregulation of many microRNAs can lead to deleterious consequences in the hematopoietic system, including the onset of cancer, autoimmunity, or a failure to respond effectively to infection. As such, microRNAs fine-tune the balance between normal hematopoietic output and pathologic consequences. In this work, we explore the role of two microRNAs, miR-132 and miR-125b, in regulating hematopoietic stem cell (HSC) function and B cell development. In particular, we uncover the role of miR-132 in maintaining the appropriate balance between self-renewal, differentiation, and survival in aging HSCs by buffering the expression of a critical transcription factor, FOXO3. By maintain this balance, miR-132 may play a critical role in preventing aging-associated hematopoietic conditions such as autoimmune disease and cancer. We also find that miR-132 plays a critical role in B cell development by targeting a key transcription factor, Sox4, that is responsible for the differentiation of pro-B cells into pre-B cells. We find that miR-132 regulates B cell apoptosis, and by delivering miR-132 to mice that are predisposed to developing B cell cancers, we can inhibit the formation of these cancers and improve the survival of these mice. In addition to miR-132, we uncovered the role of another critical microRNA, miR-125b, that potentiates hematopoietic stem cell function. We found that enforced expression of miR-125b causes an aggressive myeloid leukemia by downregulation of its target Lin28a. Importantly, miR-125b also plays a critical role in inhibiting the formation of pro-B cells. Thus, we have discovered two microRNAs with important roles in regulating normal hematopoiesis, and whose dregulation can lead to deleterious consequences such as cancer in the aging hematopoietic system. Both miR-132 and miR-125b may therefore be targeted for therapeutics to inhibit age-related immune diseases associated with the loss of HSC function and cancer progression.

Organization and function of the phage Lambda chromosome

The process of prophage integration by phage λ and the function and structure of the chromosomal elements required for λ integration have been studied with the use of λ deletion mutants. Since att^φ, the substrate of the integration enzymes, is not essential for λ growth, and since att^φ resides in a portion of the λ chromosome which is not necessary for vegetative growth, viable λ deletion mutants were isolated and examined to dissect the structure of att^φ.

Deletion mutants were selected from wild type populations by treating the phage under conditions where phage are inactivated at a rate dependent on the DNA content of the particles. A number of deletion mutants were obtained in this way, and many of these mutants proved to have defects in integration. These defects were defined by analyzing the properties of Int-promoted recombination in these att mutants.

The types of mutants found and their properties indicated that att^φ has three components: a cross-over point which is bordered on either side by recognition elements whose sequence is specifically required for normal integration. The interactions of the recognition elements in Int-promoted recombination between att mutants was examined and proved to be quite complex. In general, however, it appears that the λ integration system can function with a diverse array of mutant att sites.

The structure of att^φ was examined by comparing the genetic properties of various att mutants with their location in the λ chromosome. To map these mutants, the techniques of heteroduplex DNA formation and electron microscopy were employed. It was found that integration cross-overs occur at only one point in att^φ and that the recognition sequences that direct the integration enzymes to their site of action are quite small, less than 2000 nucleotides each. Furthermore, no base pair homology was detected between att^φ and its bacterial analog, att^B. This result clearly demonstrates that λ integration can occur between chromosomes which have little, if any, homology. In this respect, λ integration is unique as a system of recombination since most forms of generalized recombination require extensive base pair homology.

An additional study on the genetic and physical distances in the left arm of the λ genome was described. Here, a large number of conditional lethal nonsense mutants were isolated and mapped, and a genetic map of the entire left arm, comprising a total of 18 genes, was constructed. Four of these genes were discovered in this study. A series of λdg transducing phages was mapped by heteroduplex electron microscopy and the relationship between physical and genetic distances in the left arm was determined. The results indicate that recombination frequency in the left arm is an accurate reflection of physical distances, and moreover, there do not appear to be any undiscovered genes in this segment of the genome.

Tissue engineering active biological machines : bio-inspired design, directed self-assembly, and characterization of muscular pumps simulating the embryonic heart

Biological machines are active devices that are comprised of cells and other biological components. These functional devices are best suited for physiological environments that support cellular function and survival. Biological machines have the potential to revolutionize the engineering of biomedical devices intended for implantation, where the human body can provide the required physiological environment. For engineering such cell-based machines, bio-inspired design can serve as a guiding platform as it provides functionally proven designs that are attainable by living cells. In the present work, a systematic approach was used to tissue engineer one such machine by exclusively using biological building blocks and by employing a bio-inspired design. Valveless impedance pumps were constructed based on the working principles of the embryonic vertebrate heart and by using cells and tissue derived from rats. The function of these tissue-engineered muscular pumps was characterized by exploring their spatiotemporal and flow behavior in order to better understand the capabilities and limitations of cells when used as the engines of biological machines.

Mathematical study of complex networks : brain, internet, and power grid

The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored, which are motivated by power systems. The first one is “flow optimization over a flow network” and the second one is “nonlinear optimization over a generalized weighted graph”. The results derived in this dissertation are summarized below.

Brain Networks: Neuroimaging data reveals the coordinated activity of spatially distinct brain regions, which may be represented mathematically as a network of nodes (brain regions) and links (interdependencies). To obtain the brain connectivity network, the graphs associated with the correlation matrix and the inverse covariance matrix—describing marginal and conditional dependencies between brain regions—have been proposed in the literature. A question arises as to whether any of these graphs provides useful information about the brain connectivity. Due to the electrical properties of the brain, this problem will be investigated in the context of electrical circuits. First, we consider an electric circuit model and show that the inverse covariance matrix of the node voltages reveals the topology of the circuit. Second, we study the problem of finding the topology of the circuit based on only measurement. In this case, by assuming that the circuit is hidden inside a black box and only the nodal signals are available for measurement, the aim is to find the topology of the circuit when a limited number of samples are available. For this purpose, we deploy the graphical lasso technique to estimate a sparse inverse covariance matrix. It is shown that the graphical lasso may find most of the circuit topology if the exact covariance matrix is well-conditioned. However, it may fail to work well when this matrix is ill-conditioned. To deal with ill-conditioned matrices, we propose a small modification to the graphical lasso algorithm and demonstrate its performance. Finally, the technique developed in this work will be applied to the resting-state fMRI data of a number of healthy subjects.

Communication Networks: Congestion control techniques aim to adjust the transmission rates of competing users in the Internet in such a way that the network resources are shared efficiently. Despite the progress in the analysis and synthesis of the Internet congestion control, almost all existing fluid models of congestion control assume that every link in the path of a flow observes the original source rate. To address this issue, a more accurate model is derived in this work for the behavior of the network under an arbitrary congestion controller, which takes into account of the effect of buffering (queueing) on data flows. Using this model, it is proved that the well-known Internet congestion control algorithms may no longer be stable for the common pricing schemes, unless a sufficient condition is satisfied. It is also shown that these algorithms are guaranteed to be stable if a new pricing mechanism is used.

Electrical Power Networks: Optimal power flow (OPF) has been one of the most studied problems for power systems since its introduction by Carpentier in 1962. This problem is concerned with finding an optimal operating point of a power network minimizing the total power generation cost subject to network and physical constraints. It is well known that OPF is computationally hard to solve due to the nonlinear interrelation among the optimization variables. The objective is to identify a large class of networks over which every OPF problem can be solved in polynomial time. To this end, a convex relaxation is proposed, which solves the OPF problem exactly for every radial network and every meshed network with a sufficient number of phase shifters, provided power over-delivery is allowed. The concept of “power over-delivery” is equivalent to relaxing the power balance equations to inequality constraints.

Flow Networks: In this part of the dissertation, the minimum-cost flow problem over an arbitrary flow network is considered. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which always finds the optimal injections. A primary application of this work is in the OPF problem. The results of this work on GNF prove that the relaxation on power balance equations (i.e., load over-delivery) is not needed in practice under a very mild angle assumption.

Generalized Weighted Graphs: Motivated by power optimizations, this part aims to find a global optimization technique for a nonlinear optimization defined over a generalized weighted graph. Every edge of this type of graph is associated with a weight set corresponding to the known parameters of the optimization (e.g., the coefficients). The motivation behind this problem is to investigate how the (hidden) structure of a given real/complex valued optimization makes the problem easy to solve, and indeed the generalized weighted graph is introduced to capture the structure of an optimization. Various sufficient conditions are derived, which relate the polynomial-time solvability of different classes of optimization problems to weak properties of the generalized weighted graph such as its topology and the sign definiteness of its weight sets. As an application, it is proved that a broad class of real and complex optimizations over power networks are polynomial-time solvable due to the passivity of transmission lines and transformers.

Optimal uncertainty quantification via convex optimization and relaxation

Many engineering applications face the problem of bounding the expected value of a quantity of interest (performance, risk, cost, etc.) that depends on stochastic uncertainties whose probability distribution is not known exactly. Optimal uncertainty quantification (OUQ) is a framework that aims at obtaining the best bound in these situations by explicitly incorporating available information about the distribution. Unfortunately, this often leads to non-convex optimization problems that are numerically expensive to solve.

This thesis emphasizes on efficient numerical algorithms for OUQ problems. It begins by investigating several classes of OUQ problems that can be reformulated as convex optimization problems. Conditions on the objective function and information constraints under which a convex formulation exists are presented. Since the size of the optimization problem can become quite large, solutions for scaling up are also discussed. Finally, the capability of analyzing a practical system through such convex formulations is demonstrated by a numerical example of energy storage placement in power grids.

When an equivalent convex formulation is unavailable, it is possible to find a convex problem that provides a meaningful bound for the original problem, also known as a convex relaxation. As an example, the thesis investigates the setting used in Hoeffding's inequality. The naive formulation requires solving a collection of non-convex polynomial optimization problems whose number grows doubly exponentially. After structures such as symmetry are exploited, it is shown that both the number and the size of the polynomial optimization problems can be reduced significantly. Each polynomial optimization problem is then bounded by its convex relaxation using sums-of-squares. These bounds are found to be tight in all the numerical examples tested in the thesis and are significantly better than Hoeffding's bounds.

Succinate:ubiquinone oxidoreductase from Paracoccus denitrificans and particulate methane monooxygenase from Methylococcus capsulatus (Bath): experimental and theoretical EPR studies of the metal cofactors

This thesis summarizes the application of conventional and modern electron paramagnetic resonance (EPR) techniques to establish proximity relationships between paramagnetic metal centers in metalloproteins and between metal centers and magnetic ligand nuclei in two important and timely membrane proteins: succinate:ubiquinone oxidoreductase (SQR) from Paracoccus denitrificans and particulate methane monooxygenase (pMMO) from Methylococcus capsulatus. Such proximity relationships are thought to be critical to the biological function and the associated biochemistry mediated by the metal centers in these proteins. A mechanistic understanding of biological function relies heavily on structure-function relationships and the knowledge of how molecular structure and electronic properties of the metal centers influence the reactivity in metalloenzymes. EPR spectroscopy has proven to be one of the most powerful techniques towards obtaining information about interactions between metal centers as well as defining ligand structures. SQR is an electron transport enzyme wherein the substrates, organic and metallic cofactors are held relatively far apart. Here, the proximity relationships of the metallic cofactors were studied through their weak spin-spin interactions by means of EPR power saturation and electron spin-lattice (T_1) measurements, when the enzyme was poised at designated reduction levels. Analysis of the electron T_1 measurements for the S-3 center when the b-heme is paramagnetic led to a detailed analysis of the dipolar interactions and distance determination between two interacting metal centers. Studies of ligand environment of the metal centers by electron spin echo envelope modulation (ESEEM) spectroscopy resulted in the identication of peptide nitrogens as coupled nuclei in the environment of the S-1 and S-3 centers.

Finally, an EPR model was developed to describe the ferromagnetically coupled trinuclear copper clusters in pMMO when the enzyme is oxidized. The Cu(II) ions in these clusters appear to be strongly exchange coupled, and the EPR is consistent with equilateral triangular arrangements of type 2 copper ions. These results offer the first glimpse of the magneto-structural correlations for a trinuclear copper cluster of this type, which, until the work on pMMO, has had no precedent in the metalloprotein literature. Such trinuclear copper clusters are even rare in synthetic models.

The C. elegans ALA neuron : its transcriptome and role in inducing sleep

A long-standing yet to be accomplished task in understanding behavior is to dissect the function of each gene involved in the development and function of a neuron. The C. elegans ALA neuron was chosen in this study for its known function in sleep, an ancient but less understood animal behavior. Single-cell transcriptome profiling identified 8,133 protein-coding genes in the ALA neuron, of which 57 are neuropeptide-coding genes. The most enriched genes are also neuropeptides. In combination with gain-of-function and loss-of-function assays, here I showed that the ALA-enriched FMRFamide neuropeptides, FLP-7, FLP-13, and FLP-24, are sufficient and necessary for inducing C. elegans sleep. These neuropeptides act as neuromodulators through GPCRs, NPR-7, and NPR-22. Further investigation in zebrafish indicates that FMRFamide neuropeptides are sleep-promoting molecules in animals. To correlate the behavioral outputs with genomic context, I constructed a gene regulatory network of the relevant genes controlling C. elegans sleep behavior through EGFR signaling in the ALA neuron. First, I identified an ALA cell-specific motif to conduct a genome-wide search for possible ALA-expressed genes. I then filtered out non ALA-expressed genes by comparing the motif-search genes with ALA transcriptomes from single-cell profiling. In corroborating with ChIP-seq data from modENCODE, I sorted out direct interaction of ALA-expressed transcription factors and differentiation genes in the EGFR sleep regulation pathway. This approach provides a network reference for the molecular regulation of C. elegans sleep behavior, and serves as an entry point for the understanding of functional genomics in animal behaviors.

Convex Relaxation for Low-Dimensional Representation: Phase Transitions and Limitations

There is a growing interest in taking advantage of possible patterns and structures in data so as to extract the desired information and overcome the curse of dimensionality. In a wide range of applications, including computer vision, machine learning, medical imaging, and social networks, the signal that gives rise to the observations can be modeled to be approximately sparse and exploiting this fact can be very beneficial. This has led to an immense interest in the problem of efficiently reconstructing a sparse signal from limited linear observations. More recently, low-rank approximation techniques have become prominent tools to approach problems arising in machine learning, system identification and quantum tomography.

In sparse and low-rank estimation problems, the challenge is the inherent intractability of the objective function, and one needs efficient methods to capture the low-dimensionality of these models. Convex optimization is often a promising tool to attack such problems. An intractable problem with a combinatorial objective can often be "relaxed" to obtain a tractable but almost as powerful convex optimization problem. This dissertation studies convex optimization techniques that can take advantage of low-dimensional representations of the underlying high-dimensional data. We provide provable guarantees that ensure that the proposed algorithms will succeed under reasonable conditions, and answer questions of the following flavor:

More specifically, i) Focusing on linear inverse problems, we generalize the classical error bounds known for the least-squares technique to the lasso formulation, which incorporates the signal model. ii) We show that intuitive convex approaches do not perform as well as expected when it comes to signals that have multiple low-dimensional structures simultaneously. iii) Finally, we propose convex relaxations for the graph clustering problem and give sharp performance guarantees for a family of graphs arising from the so-called stochastic block model. We pay particular attention to the following aspects. For i) and ii), we aim to provide a general geometric framework, in which the results on sparse and low-rank estimation can be obtained as special cases. For i) and iii), we investigate the precise performance characterization, which yields the right constants in our bounds and the true dependence between the problem parameters.

On the Role of Delays in Biological Systems : Analysis and Design

This work quantifies the nature of delays in genetic regulatory networks and their effect on system dynamics. It is known that a time lag can emerge from a sequence of biochemical reactions. Applying this modeling framework to the protein production processes, delay distributions are derived in a stochastic (probability density function) and deterministic setting (impulse function), whilst being shown to be equivalent under different assumptions. The dependence of the distribution properties on rate constants, gene length, and time-varying temperatures is investigated. Overall, the distribution of the delay in the context of protein production processes is shown to be highly dependent on the size of the genes and mRNA strands as well as the reaction rates. Results suggest longer genes have delay distributions with a smaller relative variance, and hence, less uncertainty in the completion times, however, they lead to larger delays. On the other hand large uncertainties may actually play a positive role, as broader distributions can lead to larger stability regions when this formalization of the protein production delays is incorporated into a feedback system.

Furthermore, evidence suggests that delays may play a role as an explicit design into existing controlling mechanisms. Accordingly, the reccurring dual-feedback motif is also investigated with delays incorporated into the feedback channels. The dual-delayed feedback is shown to have stabilizing effects through a control theoretic approach. Lastly, a distributed delay based controller design method is proposed as a potential design tool. In a preliminary study, the dual-delayed feedback system re-emerges as an effective controller design.

A theory of strong and weak scintillations with applications to astrophysics

The propagation of waves in an extended, irregular medium is studied under the "quasi-optics" and the "Markov random process" approximations. Under these assumptions, a Fokker-Planck equation satisfied by the characteristic functional of the random wave field is derived. A complete set of the moment equations with different transverse coordinates and different wavenumbers is then obtained from the characteristic functional. The derivation does not require Gaussian statistics of the random medium and the result can be applied to the time-dependent problem. We then solve the moment equations for the phase correlation function, angular broadening, temporal pulse smearing, intensity correlation function, and the probability distribution of the random waves. The necessary and sufficient conditions for strong scintillation are also given.

We also consider the problem of diffraction of waves by a random, phase-changing screen. The intensity correlation function is solved in the whole Fresnel diffraction region and the temporal pulse broadening function is derived rigorously from the wave equation.

The method of smooth perturbations is applied to interplanetary scintillations. We formulate and calculate the effects of the solar-wind velocity fluctuations on the observed intensity power spectrum and on the ratio of the observed "pattern" velocity and the true velocity of the solar wind in the three-dimensional spherical model. The r.m.s. solar-wind velocity fluctuations are found to be ~200 km/sec in the region about 20 solar radii from the Sun.

We then interpret the observed interstellar scintillation data using the theories derived under the Markov approximation, which are also valid for the strong scintillation. We find that the Kolmogorov power-law spectrum with an outer scale of 10 to 100 pc fits the scintillation data and that the ambient averaged electron density in the interstellar medium is about 0.025 cm^-3. It is also found that there exists a region of strong electron density fluctuation with thickness ~10 pc and mean electron density ~7 cm^-3 between the PSR 0833-45 pulsar and the earth.

On certain discrete inequalities and their continous analogues

In a 1955 paper, Ky Fan, Olga Taussky, and John Todd presented discrete analogues of inequalities of Wirtinger type, and by taking limits they were able to recover the continuous inequalities. We generalize their techniques to mixed and higher derivatives and inequalities with weight functions in the integrals. We have also considered analogues of inequalities of Müller and Redheffer and have used these inequalities to derive a necessary and sufficient condition on ordered pairs of numbers so that the first number is the square norm of the k^th derivative of some periodic function and the second number is the square norm of the m^th derivative of the same periodic function.