Role of feedback and dynamics in a gene regulatory network

Cells exhibit a diverse repertoire of dynamic behaviors. These dynamic functions are implemented by circuits of interacting biomolecules. Although these regulatory networks function deterministically by executing specific programs in response to extracellular signals, molecular interactions are inherently governed by stochastic fluctuations. This molecular noise can manifest as cell-to-cell phenotypic heterogeneity in a well-mixed environment. Single-cell variability may seem like a design flaw but the coexistence of diverse phenotypes in an isogenic population of cells can also serve a biological function by increasing the probability of survival of individual cells upon an abrupt change in environmental conditions. Decades of extensive molecular and biochemical characterization have revealed the connectivity and mechanisms that constitute regulatory networks. We are now confronted with the challenge of integrating this information to link the structure of these circuits to systems-level properties such as cellular decision making. To investigate cellular decision-making, we used the well studied galactose gene-regulatory network in \textit{Saccharomyces cerevisiae}. We analyzed the mechanism and dynamics of the coexistence of two stable on and off states for pathway activity. We demonstrate that this bimodality in the pathway activity originates from two positive feedback loops that trigger bistability in the network. By measuring the dynamics of single-cells in a mixed sugar environment, we observe that the bimodality in gene expression is a transient phenomenon. Our experiments indicate that early pathway activation in a cohort of cells prior to galactose metabolism can accelerate galactose consumption and provide a transient increase in growth rate. Together these results provide important insights into strategies implemented by cells that may have been evolutionary advantageous in competitive environments.

I. Spectroscopic evidence for slow vibrational relaxation in excited electronic states of diatomics in rare gas solids. II. Static crystal field effects in the electronic spectra of isotopically mixed benzene crystals

Part I

Studies of vibrational relaxation in excited electronic states of simple diatomic molecules trapped in solid rare-gas matrices at low temperatures are reported. The relaxation is investigated by monitoring the emission intensity from vibrational levels of the excited electronic state to vibrational levels of the ground electronic state. The emission was in all cases excited by bombardment of the doped rare-gas solid with X-rays.

The diatomics studied and the band systems seen are: N₂, Vegard-Kaplan and Second Positive systems; O₂, Herzberg system; OH and OD, A ²Σ⁺ - X²II_i system. The latter has been investigated only in solid Ne, where both emission and absorption spectra were recorded; observed fine structure has been partly interpreted in terms of slightly perturbed rotational motion in the solid. For N₂, OH, and OD emission occurred from v' > 0, establishing a vibrational relaxation time in the excited electronic state of the order, of longer than, the electronic radiative lifetime. The relative emission intensity and decay times for different v' progressions in the Vegard-Kaplan system are found to depend on the rare-gas host and the N₂ concentration, but are independent of temperature in the range 1.7°K to 30°K.

Part II

Static crystal field effects on the absorption, fluorescence, and phosphorescence spectra of isotopically mixed benzene crystals were investigated. Evidence is presented which demonstrate that in the crystal the ground, lowest excited singlet, and lowest triplet states of the guest deviate from hexagonal symmetry. The deviation appears largest in the lowest triplet state and may be due to an intrinsic instability of the ³B_1u state. High resolution absorption and phospho- rescence spectra are reported and analyzed in terms of site-splitting of degenerate vibrations and orientational effects. The guest phosphorescence lifetime for various benzene isotopes in C₆D₆ and sym-C₆H₃D₃ hosts is presented and discussed.

Functionalization of Si(111) surfaces and the formation of mixed monolayers for the covalent attachment of molecular catalysts in photoelectrochemical devices

The functionalization of silicon surfaces with molecular catalysts for proton reduction is an important part of the development of a solar-powered, water-splitting device for solar fuel formation. The covalent attachment of these catalysts to silicon without damaging the underlying electronic properties of silicon that make it a good photocathode has proven difficult. We report the formation of mixed monolayer-functionalized surfaces that incor- porate both methyl and vinylferrocenyl or vinylbipyridyl (vbpy) moieties. The silicon was functionalized using reaction conditions analogous to those of hydrosilylation, but instead of a H-terminated Si surface, a chlorine-terminated Si precursor surface was used to produce the linked vinyl-modified functional group. The functionalized surfaces were characterized by time-resolved photoconductivity decay, X-ray photoelectron spectroscopy (XPS), electro- chemical, and photoelectrochemical measurements. The functionalized Si surfaces were well passivated, exhibited high surface coverage and few remaining reactive Si atop sites, had a very low surface recombination velocity, and displayed little initial surface oxidation. The surfaces were stable toward atmospheric and electrochemical oxidation. The surface coverage of ferrocene or bipyridine was controllably varied from 0 up to 30% of a monolayer without loss of the underlying electronic properties of the silicon. Interfacial charge transfer to the attached ferrocene group was relatively rapid, and a photovoltage of 0.4 V was generated upon illumination of functionalized n-type silicon surfaces in CH₃CN. The immobilized bipyridine ligands bound transition metal ions, and thus enabled the assembly of metal complexes on the silicon surface. XPS studies demonstrated that [Cp∗Rh(vbpy)Cl]Cl, [Cp∗Ir(vbpy)Cl]Cl, and Ru(acac)₂vbpy were assembled on the surface. For the surface prepared with iridium, x-ray absorption spectroscopy at the Ir L_III edge showed an edge energy and post-edge features virtually identical to a powder sample of [Cp∗Ir(bipy)Cl]Cl (bipy is 2,2 ́-bipyridyl). Electrochemical studies on these surfaces confirmed that the assembled complexes were electrochemically active.

Enhanced Thermoelectric Performance at the Superionic Phase Transitions of Mixed Ion-Electron Conducting Materials

The quality of a thermoelectric material is judged by the size of its temperature de- pendent thermoeletric-figure-of-merit (zT ). Superionic materials, particularly Zn₄Sb₃ and Cu₂Se, are of current interest for the high zT and low thermal conductivity of their disordered, superionic phase. In this work it is reported that the super-ionic materials Ag₂Se, Cu₂Se and Cu_1.97Ag_0.03Se show enhanced zT in their ordered, normal ion-conducting phases. The zT of Ag₂Se is increased by 30% in its ordered phase as compared to its disordered phase, as measured just below and above its first order phase transition. The zT ’s of Cu₂Se and Cu_1.97Ag_0.03Se both increase by more than 100% over a 30 K temperatures range just below their super-ionic phase transitions. The peak zT of Cu₂Se is 0.7 at 406 K and of Cu_1.97Ag_0.03Se is 1.0 at 400 K. In all three materials these enhancements are due to anomalous increases in their Seebeck coefficients, beyond that predicted by carrier concentration measurements and band structure modeling. As the Seebeck coefficient is the entropy transported per carrier, this suggests that there is an additional quantity of entropy co-transported with charge carriers. Such co-transport has been previously observed via co-transport of vibrational entropy in bipolaron conductors and spin-state entropy in Na_xCo₂O₄. The correlation of the temperature profile of the increases in each material with the nature of their phase transitions indicates that the entropy is associated with the thermodynamcis of ion-ordering. This suggests a new mechanism by which high thermoelectric performance may be understood and engineered.

DNA-Mediated Charge Transport Devices for Protein Detection

Detection of biologically relevant targets, including small molecules, proteins, DNA, and RNA, is vital for fundamental research as well as clinical diagnostics. Sensors with biological elements provide a natural foundation for such devices because of the inherent recognition capabilities of biomolecules. Electrochemical DNA platforms are simple, sensitive, and do not require complex target labeling or expensive instrumentation. Sensitivity and specificity are added to DNA electrochemical platforms when the physical properties of DNA are harnessed. The inherent structure of DNA, with its stacked core of aromatic bases, enables DNA to act as a wire via DNA-mediated charge transport (DNA CT). DNA CT is not only robust over long molecular distances of at least 34 nm, but is also especially sensitive to anything that perturbs proper base stacking, including DNA mismatches, lesions, or DNA-binding proteins that distort the π-stack. Electrochemical sensors based on DNA CT have previously been used for single-nucleotide polymorphism detection, hybridization assays, and DNA-binding protein detection. Here, improvements to (i) the structure of DNA monolayers and (ii) the signal amplification with DNA CT platforms for improved sensitivity and detection are described.

First, improvements to the control over DNA monolayer formation are reported through the incorporation of copper-free click chemistry into DNA monolayer assembly. As opposed to conventional film formation involving the self-assembly of thiolated DNA, copper-free click chemistry enables DNA to be tethered to a pre-formed mixed alkylthiol monolayer. The total amount of DNA in the final film is directly related to the amount of azide in the underlying alkylthiol monolayer. DNA monolayers formed with this technique are significantly more homogeneous and lower density, with a larger amount of individual helices exposed to the analyte solution. With these improved monolayers, significantly more sensitive detection of the transcription factor TATA binding protein (TBP) is achieved.

Using low-density DNA monolayers, two-electrode DNA arrays were designed and fabricated to enable the placement of multiple DNA sequences onto a single underlying electrode. To pattern DNA onto the primary electrode surface of these arrays, a copper precatalyst for click chemistry was electrochemically activated at the secondary electrode. The location of the secondary electrode relative to the primary electrode enabled the patterning of up to four sequences of DNA onto a single electrode surface. As opposed to conventional electrochemical readout from the primary, DNA-modified electrode, a secondary microelectrode, coupled with electrocatalytic signal amplification, enables more sensitive detection with spatial resolution on the DNA array electrode surface. Using this two-electrode platform, arrays have been formed that facilitate differentiation between well-matched and mismatched sequences, detection of transcription factors, and sequence-selective DNA hybridization, all with the incorporation of internal controls.

For effective clinical detection, the two working electrode platform was multiplexed to contain two complementary arrays, each with fifteen electrodes. This platform, coupled with low density DNA monolayers and electrocatalysis with readout from a secondary electrode, enabled even more sensitive detection from especially small volumes (4 μL per well). This multiplexed platform has enabled the simultaneous detection of two transcription factors, TBP and CopG, with surface dissociation constants comparable to their solution dissociation constants.

With the sensitivity and selectivity obtained from the multiplexed, two working electrode array, an electrochemical signal-on assay for activity of the human methyltransferase DNMT1 was incorporated. DNMT1 is the most abundant human methyltransferase, and its aberrant methylation has been linked to the development of cancer. However, current methods to monitor methyltransferase activity are either ineffective with crude samples or are impractical to develop for clinical applications due to a reliance on radioactivity. Electrochemical detection of methyltransferase activity, in contrast, circumvents these issues. The signal-on detection assay translates methylation events into electrochemical signals via a methylation-specific restriction enzyme. Using the two working electrode platform combined with this assay, DNMT1 activity from tumor and healthy adjacent tissue lysate were evaluated. Our electrochemical measurements revealed significant differences in methyltransferase activity between tumor tissue and healthy adjacent tissue.

As differential activity was observed between colorectal tumor tissue and healthy adjacent tissue, ten tumor sets were subsequently analyzed for DNMT1 activity both electrochemically and by tritium incorporation. These results were compared to expression levels of DNMT1, measured by qPCR, and total DNMT1 protein content, measured by Western blot. The only trend detected was that hyperactivity was observed in the tumor samples as compared to the healthy adjacent tissue when measured electrochemically. These advances in DNA CT-based platforms have propelled this class of sensors from the purely academic realm into the realm of clinically relevant detection.

Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.

Feedback communication using orthogonal signals

This research is concerned with block coding for a feedback communication system in which the forward and feedback channels are independently disturbed by additive white Gaussian noise and average power constrained. Two coding schemes are proposed in which the messages to be coded for transmission over the forward channel are realized as a set of orthogonal waveforms. A finite number of forward and feedback transmissions (iterations) per message is made. Information received over the feedback channel is used to modify the waveform transmitted on successive forward iterations in such a way that the expected value of forward signal energy is zero on all iterations after the first. Similarly, information is sent over the feedback channel in such a way that the expected value of feedback signal energy is also zero on all iterations after the first. These schemes are shown to achieve a lower probability of error than the best one-way coding scheme at all rates up to the forward channel capacity, provided only that the feedback channel capacity be greater than the forward channel capacity. These schemes make more efficient use of the available feedback power than existing feedback coding schemes, and therefore require less feedback power to achieve a given error performance.

The global optimization of phase-incoherent signals

The problem of global optimization of M phase-incoherent signals in N complex dimensions is formulated. Then, by using the geometric approach of Landau and Slepian, conditions for optimality are established for N = 2 and the optimal signal sets are determined for M = 2, 3, 4, 6, and 12.

The method is the following: The signals are assumed to be equally probable and to have equal energy, and thus are represented by points ṡ_i, i = 1, 2, …, M, on the unit sphere S₁ in C^N. If W_ik is the halfspace determined by ṡ_i and ṡ_k and containing ṡ_i, i.e. W_ik = {ṙϵC^N:| ≥ | ˂ṙ, ṡ_k˃|}, then the Ʀ_i = ∩/k≠i W_ik, i = 1, 2, …, M, the maximum likelihood decision regions, partition S₁. For additive complex Gaussian noise ṅ and a received signal ṙ = ṡ_ie^jϴ + ṅ, where ϴ is uniformly distributed over [0, 2π], the probability of correct decoding is P_C = 1/π^N ∞/ʃ/0 r^2N-1e^-(r2+1)U(r)dr, where U(r) = 1/M M/Ʃ/i=1 Ʀ_i ʃ/∩ S₁ I₀(2r | ˂ṡ, ṡ_i˃|)dσ(ṡ), and r = ǁṙǁ.

For N = 2, it is proved that U(r) ≤ ʃ/C_α I₀(2r|˂ṡ, ṡ_i˃|)dσ(ṡ) – 2K/M. h(1/2K [Mσ(C_α)-σ(S₁)]), where C_α = {ṡϵS₁:|˂ṡ, ṡ_i˃| ≥ α}, K is the total number of boundaries of the net on S₁ determined by the decision regions, and h is the strictly increasing strictly convex function of σ(C_α∩W), (where W is a halfspace not containing ṡ_i), given by h = ʃ/C_α∩W I₀ (2r|˂ṡ, ṡ_i˃|)dσ(ṡ). Conditions for equality are established and these give rise to the globally optimal signal sets for M = 2, 3, 4, 6, and 12.