Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and thomas-kuhn sum rules

Successfully predicting the frequency dispersion of electronic hyperpolarizabilities is an unresolved challenge in materials science and electronic structure theory. We show that the generalized Thomas-Kuhn sum rules, combined with linear absorption data and measured hyperpolarizability at one or two frequencies, may be used to predict the entire frequency-dependent electronic hyperpolarizability spectrum. This treatment includes two- and three-level contributions that arise from the lowest two or three excited electronic state manifolds, enabling us to describe the unusual observed frequency dispersion of the dynamic hyperpolarizability in high oscillator strength M-PZn chromophores, where (porphinato)zinc(II) (PZn) and metal(II)polypyridyl (M) units are connected via an ethyne unit that aligns the high oscillator strength transition dipoles of these components in a head-to-tail arrangement. We show that some of these structures can possess very similar linear absorption spectra yet manifest dramatically different frequency dependent hyperpolarizabilities, because of three-level contributions that result from excited state-to excited state transition dipoles among charge polarized states. Importantly, this approach provides a quantitative scheme to use linear optical absorption spectra and very limited individual hyperpolarizability measurements to predict the entire frequency-dependent nonlinear optical response. Copyright © 2010 American Chemical Society.

Analytic expressions for the constitutive parameters of magnetoelectric metamaterials

Electromagnetic metamaterials are artificially structured media typically composed of arrays of resonant electromagnetic circuits, the dimension and spacing of which are considerably smaller than the free-space wavelengths of operation. The constitutive parameters for metamaterials, which can be obtained using full-wave simulations in conjunction with numerical retrieval algorithms, exhibit artifacts related to the finite size of the metamaterial cell relative to the wavelength. Liu showed that the complicated, frequency-dependent forms of the constitutive parameters can be described by a set of relatively simple analytical expressions. These expressions provide useful insight and can serve as the basis for more intelligent interpolation or optimization schemes. Here, we show that the same analytical expressions can be obtained using a transfer-matrix formalism applied to a one-dimensional periodic array of thin, resonant, dielectric, or magnetic sheets. The transfer-matrix formalism breaks down, however, when both electric and magnetic responses are present in the same unit cell, as it neglects the magnetoelectric coupling between unit cells. We show that an alternative analytical approach based on the same physical model must be applied for such structures. Furthermore, in addition to the intercell coupling, electric and magnetic resonators within a unit cell may also exhibit magnetoelectric coupling. For such cells, we find an analytical expression for the effective index, which displays markedly characteristic dispersion features that depend on the strength of the coupling coefficient. We illustrate the applicability of the derived expressions by comparing to full-wave simulations on magnetoelectric unit cells. We conclude that the design of metamaterials with tailored simultaneous electric and magnetic response-such as negative index materials-will generally be complicated by potentially unwanted magnetoelectric coupling. © 2010 The American Physical Society.

Time-dependent transport through molecular junctions.

We investigate transport properties of molecular junctions under two types of bias--a short time pulse or an ac bias--by combining a solution for Green's functions in the time domain with electronic structure information coming from ab initio density functional calculations. We find that the short time response depends on lead structure, bias voltage, and barrier heights both at the molecule-lead contacts and within molecules. Under a low frequency ac bias, the electron flow either tracks or leads the bias signal (resistive or capacitive response) depending on whether the junction is perfectly conducting or not. For high frequency, the current lags the bias signal due to the kinetic inductance. The transition frequency is an intrinsic property of the junctions.

The Ontogeny of Mucosal and Systemic Antibody Responses to HIV-1 Infection

The humoral immune system plays a critical role in the clearance of numerous pathogens. In the setting of HIV-1 infection, the virus infects, integrates its genome into the host's cells, replicates, and establishes a reservoir of virus-infected cells. The initial antibody response to HIV-1 infection is targeted to non-neutralizing epitopes on HIV-1 Env gp41, and when a neutralizing response does develop months after transmission, it is specific for the autologous founder virus and the virus escapes rapidly. After continuous waves of antibody mediated neutralization and viral escape, a small subset of infected individuals eventually develop broad and potent heterologous neutralizing antibodies years after infection. In this dissertation, I have studied the ontogeny of mucosal and systemic antibody responses to HIV-1 infection by means of three distinct aims: 1. Determine the origin of the initial antibody response to HIV-1 infection. 2. Characterize the role of restricted VH and VL gene segment usage in shaping the antibody response to HIV-1 infection. 3. Determine the role of persistence of B cell clonal lineages in shaping the mutation frequencies of HIV-1 reactive antibodies.

After the introduction (Chapter 1) and methods (Chapter 2), Chapter 3 of this dissertation describes a study of the antibody response of terminal ileum B cells to HIV-1 envelope (Env) in early and chronic HIV-1 infection and provides evidence for the role of environmental antigens in shaping the repertoire of B cells that respond to HIV-1 infection. Previous work by Liao et al. demonstrated that the initial plasma cell response in the blood to acute HIV-1 infection is to gp41 and is derived from a polyreactive memory B cell pool. Many of these antibodies cross-reacted with commensal bacteria, Therefore, in Chapter 3, the relationship of intestinal B cell reactivity with commensal bacteria to HIV-1 infection-induced antibody response was probed using single B cell sorting, reverse transcription and nested polymerase chain reaction (RT- PCR) methods, and recombinant antibody technology. The dominant B cell response in the terminal ileum was to HIV-1 envelope (Env) gp41, and 82% of gp41- reactive antibodies cross-reacted with commensal bacteria whole cell lysates. Pyrosequencing of blood B cells revealed HIV-1 antibody clonal lineages shared between ileum and blood. Mutated IgG antibodies cross-reactive with both Env gp41 and commensal bacteria could also be isolated from the terminal ileum of HIV-1 uninfected individuals. Thus, the antibody response to HIV-1 can be shaped by intestinal B cells stimulated by commensal bacteria prior to HIV-1 infection to develop a pre-infection pool of memory B cells cross-reactive with HIV-1 gp41.

Chapter 4 details the study of restricted VH and VL gene segment usage for gp41 and gp120 antibody induction following acute HIV-1 infection; mutations in gp41 lead to virus enhanced neutralization sensitivity. The B cell repertoire of antibodies induced in a HIV-1 infected African individual, CAP206, who developed broadly neutralizing antibodies (bnAbs) directed to the HIV-1 envelope gp41 membrane proximal external region (MPER), is characterized. Understanding the selection of virus mutants by neutralizing antibodies is critical to understanding the role of antibodies in control of HIV-1 replication and prevention from HIV-1 infection. Previously, an MPER neutralizing antibody, CAP206-CH12, with the binding footprint identical to that of MPER broadly neutralizing antibody 4E10, that like 4E10 utilized the VH1-69 and VK3-20 variable gene segments was isolated from this individual (Morris et al., 2011). Using single B cell sorting, RT- PCR methods, and recombinant antibody technology, Chapter 4 describes the isolation of a VH1-69, Vk3-20 glycan-dependent clonal lineage from CAP206, targeted to gp120, that has the property of neutralizing a neutralization sensitive CAP206 transmitted/founder (T/F) and heterologous viruses with mutations at amino acids 680 or 681 in the MPER 4E10/CH12 binding site. These data demonstrate sites within the MPER bnAb epitope (aa 680-681) in which mutations can be selected that lead to viruses with enhanced sensitivity to autologous and heterologous neutralizing antibodies.

In Chapter 5, I have completed a comparison of evolution of B cell clonal lineages in two HIV-1 infected individuals who have a predominant VH1-69 response to HIV-1 infection--one who produces broadly neutralizing MPER-reactive mAbs and one who does not. Autologous neutralization in the plasma takes ~12 weeks to develop (Gray et al., 2007; Tomaras et al., 2008b). Only a small subset of HIV-1 infected individuals develops high plasma levels of broad and potent heterologous neutralization, and when it does occur, it typically takes 3-4 years to develop (Euler et al., 2010; Gray et al., 2007; 2011; Tomaras et al., 2011). The HIV-1 bnAbs that have been isolated to date have a number of unusual characteristics including, autoreactivity and high levels of somatic hypermutations, which are typically tightly regulated by immune control mechanisms (Haynes et al., 2005; 2012b; Kwong and Mascola, 2012; Scheid et al., 2009a). The VH mutation frequencies of bnAbs average ~15% but have been shown to be as high as 32% (reviewed in Mascola and Haynes, 2013; Kwong and Mascola, 2012). The high frequency of somatic hypermutations suggests that the B cell clonal lineages that eventually produce bnAbs undergo high-levels of affinity maturation, implying prolonged germinal center (GC) reactions and high levels of T cell help. To study the duration of HIV-1- reactive B cell clonal persistence, HIV-1 reactive and non HIV-1- reactive B cell clonal lineages were isolated from an HIV-1 infected individual that produces bnAbs, CAP206, and an HIV-1 infected individual who does not produce bnAbs, 004-0. Single B cell sorting, RT-PCR and recombinant antibody technology was used to isolate and produce monoclonal antibodies from multiple time points from each individual. B cell sequences clonally related to mAbs isolated by single cell PCR were identified within pyrosequences of longitudinal samples of these two individuals. Both individuals produced long-lived B cell clones that persisted from 0-232 weeks in CAP206, and 0-238 weeks in 004-0. The average length of persistence of clones containing members isolated from two separate time points was 91.5 weeks both individuals. Examples of the continued evolution of clonal lineages were observed in both the bnAb and non-bnAb individual. These data indicated that the ability to generate persistent and evolving B cell clonal lineages occurs in both bnAb and non-bnAb individuals, suggesting that some alternative host or viral factor is critical for the generation of highly mutated broadly neutralizing antibodies.

Together the studies described in Chapter 3-5 show that multiple factors influence the antibody response to HIV-1 infection. The initial antibody response to HIV-1 Env gp41 can be shaped by a B cell response to intestinal commensal bacteria prior to HIV-1 infection. VH and VL gene segment restriction can impact the B cell response to multiple HIV-1 antigens, and virus escape mutations in the MPER can confer enhanced neutralization sensitivity to autologous and heterologous antibodies. Finally, the ability to generate long-lived HIV-1 clonal lineages in and of itself does not confer on the host the ability to produce bnAbs.

Calcium/Calmodulin-Dependent Protein Kinase II Serves as a Biochemical Integrator of Calcium Signals for the Induction of Synaptic Plasticity

Repetitive Ca2+ transients in dendritic spines induce various forms of synaptic plasticity by transmitting information encoded in their frequency and amplitude. CaMKII plays a critical role in decoding these Ca2+ signals to initiate long-lasting synaptic plasticity. However, the properties of CaMKII that mediate Ca2+ decoding in spines remain elusive. Here, I measured CaMKII activity in spines using fast-framing two-photon fluorescence lifetime imaging. Following each repetitive Ca2+ elevations, CaMKII activity increased in a stepwise manner. This signal integration, at the time scale of seconds, critically depended on Thr286 phosphorylation. In the absence of Thr286 phosphorylation, only by increasing the frequency of repetitive Ca2+ elevations could high peak CaMKII activity or plasticity be induced. In addition, I measured the association between CaMKII and Ca2+/CaM during spine plasticity induction. Unlike CaMKII activity, association of Ca2+/CaM to CaMKII plateaued at the first Ca2+ elevation event. This result indicated that integration of Ca2+ signals was initiated by the binding of Ca2+/CaM and amplified by the subsequent increases in Thr286-phosphorylated form of CaMKII. Together, these findings demonstrate that CaMKII functions as a leaky integrator of repetitive Ca2+ signals during the induction of synaptic plasticity, and that Thr286 phosphorylation is critical for defining the frequencies of such integration.