The biological sense of smell: olfactory search behavior and a metabolic view for olfactory perception

Part I of the thesis describes the olfactory searching and scanning behaviors of rats in a wind tunnel, and a detailed movement analysis of terrestrial arthropod olfactory scanning behavior. Olfactory scanning behaviors in rats may be a behavioral correlate to hippocampal place cell activity.

Part II focuses on the organization of olfactory perception, what it suggests about a natural order for chemicals in the environment, and what this in tum suggests about the organization of the olfactory system. A model of odor quality space (analogous to the "color wheel") is presented. This model defines relationships between odor qualities perceived by human subjects based on a quantitative similarity measure. Compounds containing Carbon, Nitrogen, or Sulfur elicit odors that are contiguous in this odor representation, which thus allows one to predict the broad class of odor qualities a compound is likely to elicit. Based on these findings, a natural organization for olfactory stimuli is hypothesized: the order provided by the metabolic process. This hypothesis is tested by comparing compounds that are structurally similar, perceptually similar, and metabolically similar in a psychophysical cross-adaptation paradigm. Metabolically similar compounds consistently evoked shifts in odor quality and intensity under cross-adaptation, while compounds that were structurally similar or perceptually similar did not. This suggests that the olfactory system may process metabolically similar compounds using the same neural pathways, and that metabolic similarity may be the fundamental metric about which olfactory processing is organized. In other words, the olfactory system may be organized around a biological basis.

The idea of a biological basis for olfactory perception represents a shift in how olfaction is understood. The biological view has predictive power while the current chemical view does not, and the biological view provides explanations for some of the most basic questions in olfaction, that are unanswered in the chemical view. Existing data do not disprove a biological view, and are consistent with basic hypotheses that arise from this viewpoint.

Wide Field-of-view Microscopes and Endoscopes for Time-lapse Imaging and High-throughput Screening

Wide field-of-view (FOV) microscopy is of high importance to biological research and clinical diagnosis where a high-throughput screening of samples is needed. This thesis presents the development of several novel wide FOV imaging technologies and demonstrates their capabilities in longitudinal imaging of living organisms, on the scale of viral plaques to live cells and tissues.

The ePetri Dish is a wide FOV on-chip bright-field microscope. Here we applied an ePetri platform for plaque analysis of murine norovirus 1 (MNV-1). The ePetri offers the ability to dynamically track plaques at the individual cell death event level over a wide FOV of 6 mm × 4 mm at 30 min intervals. A density-based clustering algorithm is used to analyze the spatial-temporal distribution of cell death events to identify plaques at their earliest stages. We also demonstrate the capabilities of the ePetri in viral titer count and dynamically monitoring plaque formation, growth, and the influence of antiviral drugs.

We developed another wide FOV imaging technique, the Talbot microscope, for the fluorescence imaging of live cells. The Talbot microscope takes advantage of the Talbot effect and can generate a focal spot array to scan the fluorescence samples directly on-chip. It has a resolution of 1.2 μm and a FOV of ~13 mm². We further upgraded the Talbot microscope for the long-term time-lapse fluorescence imaging of live cell cultures, and analyzed the cells’ dynamic response to an anticancer drug.

We present two wide FOV endoscopes for tissue imaging, named the AnCam and the PanCam. The AnCam is based on the contact image sensor (CIS) technology, and can scan the whole anal canal within 10 seconds with a resolution of 89 μm, a maximum FOV of 100 mm × 120 mm, and a depth-of-field (DOF) of 0.65 mm. We also demonstrate the performance of the AnCam in whole anal canal imaging in both animal models and real patients. In addition to this, the PanCam is based on a smartphone platform integrated with a panoramic annular lens (PAL), and can capture a FOV of 18 mm × 120 mm in a single shot with a resolution of 100─140 μm. In this work we demonstrate the PanCam’s performance in imaging a stained tissue sample.

Improving the biological activity of pyrrole-imidazole polyamides

DNA is nature’s blueprint, holding within it the genetic code that defines the structure and function of an organism. A complex network of DNA-binding proteins called transcription factors can largely control the flow of information from DNA, so modulating the function of transcription factors is a promising approach for treating many diseases. Pyrrole-imidazole (Py-Im) polyamides are a class of DNA-binding oligomers, which can be synthetically programmed to bind a target sequence of DNA. Due to their unique shape complementarity and a series of favorable hydrogen bonding interactions that occur upon DNA-binding, Py-Im polyamides can bind to the minor groove of DNA with affinities comparable to transcription factors. Previous studies have demonstrated that these cell-permeable small molecules can enter cell nuclei and disrupt the transcription factor-DNA interface, thereby repressing transcription. As the use of Py-Im polyamides has significant potential as a type of modular therapeutic platform, the need for polyamides with extremely favorable biological properties and high potency will be essential. Described herein, a variety of studies have been performed aimed at improving the biological activity of Py-Im polyamides. To improve the biological potency and cellular uptake of these compounds, we have developed a next-generation class of polyamides bearing aryl-turn moieties, a simple structural modification that allows significant improvements in cellular uptake. This strategy was also applied to a panel of high-affinity cyclic Py-Im polyamides, again demonstrating the remarkable effect minor structural changes can have on biological activity. The solubility properties of Py-Im polyamides and use of formulating reagents with their treatment have also been examined. Finally, we describe the study of Py-Im polyamides as a potential artificial transcription factor.

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.

Synthesis and biological activity of anticoagulant heparan sulfate glycopolymers

Heparin has been used as an anticoagulant drug for more than 70 years. The global distribution of contaminated heparin in 2007, which resulted in adverse clinical effects and over 100 deaths, emphasizes the necessity for safer alternatives to animal-sourced heparin. The structural complexity and heterogeneity of animal-sourced heparin not only impedes safe access to these biologically active molecules, but also hinders investigations on the significance of structural constituents at a molecular level. Efficient methods for preparing new synthetic heparins with targeted biological activity are necessary not only to ensure clinical safety, but to optimize derivative design to minimize potential side effects. Low molecular weight heparins have become a reliable alternative to heparin, due to their predictable dosages, long half-lives, and reduced side effects. However, heparin oligosaccharide synthesis is a challenging endeavor due to the necessity for complex protecting group manipulation and stereoselective glycosidic linkage chemistry, which often result in lengthy synthetic routes and low yields. Recently, chemoenzymatic syntheses have produced targeted ultralow molecular weight heparins with high-efficiency, but continue to be restricted by the substrate specificities of enzymes.

To address the need for access to homogeneous, complex glycosaminoglycan structures, we have synthesized novel heparan sulfate glycopolymers with well-defined carbohydrate structures and tunable chain length through ring-opening metathesis polymerization chemistry. These polymers recapitulate the key features of anticoagulant heparan sulfate by displaying the sulfation pattern responsible for heparin’s anticoagulant activity. The use of polymerization chemistry greatly simplifies the synthesis of complex glycosaminoglycan structures, providing a facile method to generate homogeneous macromolecules with tunable biological and chemical properties. Through the use of in vitro chromogenic substrate assays and ex vivo clotting assays, we found that the HS glycopolymers exhibited anticoagulant activity in a sulfation pattern and length-dependent manner. Compared to heparin standards, our short polymers did not display any activity. However, our longer polymers were able to incorporate in vitro and ex vivo characteristics of both low-molecular-weight heparin derivatives and heparin, displaying hybrid anticoagulant properties. These studies emphasize the significance of sulfation pattern specificity in specific carbohydrate-protein interactions, and demonstrate the effectiveness of multivalent molecules in recapitulating the activity of natural polysaccharides.

Earthquakes of the Nepal Himalaya : towards a physical model of the seismic cycle

Home to hundreds of millions of souls and land of excessiveness, the Himalaya is also the locus of a unique seismicity whose scope and peculiarities still remain to this day somewhat mysterious. Having claimed the lives of kings, or turned ancient timeworn cities into heaps of rubbles and ruins, earthquakes eerily inhabit Nepalese folk tales with the fatalistic message that nothing lasts forever. From a scientific point of view as much as from a human perspective, solving the mysteries of Himalayan seismicity thus represents a challenge of prime importance. Documenting geodetic strain across the Nepal Himalaya with various GPS and leveling data, we show that unlike other subduction zones that exhibit a heterogeneous and patchy coupling pattern along strike, the last hundred kilometers of the Main Himalayan Thrust fault, or MHT, appear to be uniformly locked, devoid of any of the “creeping barriers” that traditionally ward off the propagation of large events. The approximately 20 mm/yr of reckoned convergence across the Himalaya matching previously established estimates of the secular deformation at the front of the arc, the slip accumulated at depth has to somehow elastically propagate all the way to the surface at some point. And yet, neither large events from the past nor currently recorded microseismicity nearly compensate for the massive moment deficit that quietly builds up under the giant mountains. Along with this large unbalanced moment deficit, the uncommonly homogeneous coupling pattern on the MHT raises the question of whether or not the locked portion of the MHT can rupture all at once in a giant earthquake. Univocally answering this question appears contingent on the still elusive estimate of the magnitude of the largest possible earthquake in the Himalaya, and requires tight constraints on local fault properties. What makes the Himalaya enigmatic also makes it the potential source of an incredible wealth of information, and we exploit some of the oddities of Himalayan seismicity in an effort to improve the understanding of earthquake physics and cipher out the properties of the MHT. Thanks to the Himalaya, the Indo-Gangetic plain is deluged each year under a tremendous amount of water during the annual summer monsoon that collects and bears down on the Indian plate enough to pull it away from the Eurasian plate slightly, temporarily relieving a small portion of the stress mounting on the MHT. As the rainwater evaporates in the dry winter season, the plate rebounds and tension is increased back on the fault. Interestingly, the mild waggle of stress induced by the monsoon rains is about the same size as that from solid-Earth tides which gently tug at the planets solid layers, but whereas changes in earthquake frequency correspond with the annually occurring monsoon, there is no such correlation with Earth tides, which oscillate back-and-forth twice a day. We therefore investigate the general response of the creeping and seismogenic parts of MHT to periodic stresses in order to link these observations to physical parameters. First, the response of the creeping part of the MHT is analyzed with a simple spring-and-slider system bearing rate-strengthening rheology, and we show that at the transition with the locked zone, where the friction becomes near velocity neutral, the response of the slip rate may be amplified at some periods, which values are analytically related to the physical parameters of the problem. Such predictions therefore hold the potential of constraining fault properties on the MHT, but still await observational counterparts to be applied, as nothing indicates that the variations of seismicity rate on the locked part of the MHT are the direct expressions of variations of the slip rate on its creeping part, and no variations of the slip rate have been singled out from the GPS measurements to this day. When shifting to the locked seismogenic part of the MHT, spring-and-slider models with rate-weakening rheology are insufficient to explain the contrasted responses of the seismicity to the periodic loads that tides and monsoon both place on the MHT. Instead, we resort to numerical simulations using the Boundary Integral CYCLes of Earthquakes algorithm and examine the response of a 2D finite fault embedded with a rate-weakening patch to harmonic stress perturbations of various periods. We show that such simulations are able to reproduce results consistent with a gradual amplification of sensitivity as the perturbing period get larger, up to a critical period corresponding to the characteristic time of evolution of the seismicity in response to a step-like perturbation of stress. This increase of sensitivity was not reproduced by simple 1D-spring-slider systems, probably because of the complexity of the nucleation process, reproduced only by 2D-fault models. When the nucleation zone is close to its critical unstable size, its growth becomes highly sensitive to any external perturbations and the timings of produced events may therefore find themselves highly affected. A fully analytical framework has yet to be developed and further work is needed to fully describe the behavior of the fault in terms of physical parameters, which will likely provide the keys to deduce constitutive properties of the MHT from seismological observations.

Design, synthesis, and biological activity of rhodium metalloinsertors

Deficiencies in the mismatch repair (MMR) pathway are associated with several types of cancers, as well as resistance to commonly used chemotherapeutics. Rhodium metalloinsertors have been found to bind DNA mismatches with high affinity and specificity in vitro, and also exhibit cell-selective cytotoxicity, targeting MMR-deficient cells over MMR-proficient cells.

Here we examine the biological fate of rhodium metalloinsertors bearing dipyridylamine ancillary ligands. These complexes are shown to exhibit accelerated cellular uptake which permits the observation of various cellular responses, including disruption of the cell cycle and induction of necrosis, which occur preferentially in the MMR-deficient cell line. These cellular responses provide insight into the mechanisms underlying the selective activity of this novel class of targeted anti-cancer agents.

In addition, ten distinct metalloinsertors with varying lipophilicities are synthesized and their mismatch binding affinities and biological activities studied. While they are found to have similar binding affinities, their cell-selective antiproliferative and cytotoxic activities vary significantly. Inductively coupled plasma mass spectrometry (ICP-MS) experiments show that all of these metalloinsertors localize in the nucleus at sufficient concentrations for binding to DNA mismatches. Furthermore, metalloinsertors with high rhodium localization in the mitochondria show toxicity that is not selective for MMR-deficient cells. This work supports the notion that specific targeting of the metalloinsertors to nuclear DNA gives rise to their cytotoxic and antiproliferative activities that are selective for cells deficient in MMR.

To explore further the basis of the unique selectivity of the metlloinsertors in targeting MMR-deficient cells, experiments were conducted using engineered NCI-H23 lung adenocarcinoma cells that contain a doxycycline-inducible shRNA which suppresses the expression of the MMR gene MLH1. Here we use this new cell line to further validate rhodium metalloinsertors as compounds capable of differentially inhibiting the proliferation of MMR-deficient cancer cells over isogenic MMR-proficient cells. General DNA damaging agents, such as cisplatin and etoposide, in contrast, are less effective in the induced cell line defective in MMR.

Finally, we describe a new subclass of metalloinsertors with enhanced potency and selectivity, in which the complexes show Rh-O coordination. In particular, it has been found that both Δ and Λ enantiomers of [Rh(chrysi)(phen)(DPE)]²⁺ bind to DNA with similar affinities, suggesting a possible different binding conformation than previous metalloinsertors. Remarkably, all members of this new family of compounds have significantly increased potency in a range of cellular assays; indeed, all are more potent than the FDA-approved anticancer drugs cisplatin and MNNG. Moreover, these activities are coupled with high levels of selectivity for MMR-deficient cells.

Smooth sets for borel equivalence relations and the covering property for σ-ideals of compact sets

This thesis is divided into three chapters. In the first chapter we study the smooth sets with respect to a Borel equivalence realtion E on a Polish space X. The collection of smooth sets forms σ-ideal. We think of smooth sets as analogs of countable sets and we show that an analog of the perfect set theorem for Σ¹₁ sets holds in the context of smooth sets. We also show that the collection of Σ¹₁ smooth sets is ∏¹₁ on the codes. The analogs of thin sets are called sparse sets. We prove that there is a largest ∏¹₁ sparse set and we give a characterization of it. We show that in L there is a ∏¹₁ sparse set which is not smooth. These results are analogs of the results known for the ideal of countable sets, but it remains open to determine if large cardinal axioms imply that ∏¹₁ sparse sets are smooth. Some more specific results are proved for the case of a countable Borel equivalence relation. We also study I(E), the σ-ideal of closed E-smooth sets. Among other things we prove that E is smooth iff I(E) is Borel.

In chapter 2 we study σ-ideals of compact sets. We are interested in the relationship between some descriptive set theoretic properties like thinness, strong calibration and the covering property. We also study products of σ-ideals from the same point of view. In chapter 3 we show that if a σ-ideal I has the covering property (which is an abstract version of the perfect set theorem for Σ¹₁ sets), then there is a largest ∏¹₁ set in I^int (i.e., every closed subset of it is in I). For σ-ideals on 2^ω we present a characterization of this set in a similar way as for C₁, the largest thin ∏¹₁ set. As a corollary we get that if there are only countable many reals in L, then the covering property holds for Σ¹₂ sets.

Biological Activity of Rhodium Metalloinsertors and the Design of Bifunctional Conjugates

The Barton laboratory has established that octahedral rhodium complexes bearing the sterically expansive 5,6-chrysene diimine ligand can target thermodynamically destabilized sites, such as base pair mismatches, in DNA with high affinity and selectivity. These complexes approach DNA from the minor groove, ejecting the mismatched base pairs from the duplex in a binding mode termed metalloinsertion. In recent years, we have shown that these metalloinsertor complexes also exhibit cytotoxicity preferentially in cancer cells that are deficient in the mismatch repair (MMR) machinery.

Here, we establish that a sensitive structure-activity relationship exists for rhodium metalloinsertors. We studied the relationship between the chemical structures of metalloinsertors and their effect on biological activity for ten complexes with similar DNA binding affinities, but wide variation in their lipophilicity. Drastic differences were observed in the selectivities of the complexes for MMR-deficient cells. Compounds with hydrophilic ligands were highly selective, exhibiting preferential cytotoxicity in MMR-deficient cells at low concentrations and short incubation periods, whereas complexes with lipophilic ligands displayed poor cell-selectivity. It was discovered that all of the complexes localized to the nucleus in concentrations sufficient for mismatch binding; however, highly lipophilic complexes also exhibited high mitochondrial uptake. Significantly, these results support the notion that mitochondrial DNA is not the desired target for our metalloinsertor complexes; instead, selectivity stems from targeting mismatches in genomic DNA.

We have also explored the potential for metalloinsertors to be developed into more complex structures with multiple functionalities that could either enhance their overall potency or impart mismatch selectivity onto other therapeutic cargo. We have constructed a family of bifunctional metalloinsertor conjugates incorporating cis-platinum, each unique in its chemical structure, DNA binding interactions, and biological activity. The study of these complexes in MMR-deficient cells has established that the cell-selective biological activity of rhodium metalloinsertors proceeds through a critical cellular pathway leading to necrosis.

We further explored the underlying mechanisms surrounding the biological response to mismatch recognition by metalloinsertors in the genome. Immunofluorescence assays of MMR-deficient and MMR-proficient cells revealed that a critical biomarker for DNA damage, phosphorylation of histone H2AX (γH2AX) rapidly accumulates in response to metalloinsertor treatment, signifying the induction of double strand breaks in the genome. Significantly, we have discovered that our metalloinsertor complexes selectively inhibit transcription in MMR-deficient cells, which may be a crucial checkpoint in the eventual breakdown of the cell via necrosis. Additionally, preliminary in vivo studies have revealed the capability of these compounds to traverse the complex environments of multicellular organisms and accumulate in MMR-deficient tumors. Our ever-increasing understanding of metalloinsertors, as well as the development of new generations of complexes both monofunctional and bifunctional, enables their continued progress into the clinic as promising new chemotherapeutic agents.