Maximal univalent disks of real rational functions and Hermite-Biehler polynomials

The well-known Hermite-Biehler theorem claims that a univariate monic polynomial s of degree k has all roots in the open upper half-plane if and only if s=p+iq where p and q are real polynomials of degree k and k-1 resp. with all real, simple and interlacing roots, and q has a negative leading coefficient. Considering roots of p as cyclically ordered on RP^1 we show that the open disk in CP^1 having a pair of consecutive roots of p as its diameter is the maximal univalent disk for the function R=\frac{q}{p}. This solves a special case of the so-called Hermite-Biehler problem.Comment: 10 pages, 4 figure

Molecular Imaging in Synthetic Biology, and Synthetic Biology in Molecular Imaging

Biomedical synthetic biology is an emerging field in which cells are engineered at the genetic level to carry out novel functions with relevance to biomedical and industrial applications. This approach promises new treatments, imaging tools, and diagnostics for diseases ranging from gastrointestinal inflammatory syndromes to cancer, diabetes, and neurodegeneration. As these cellular technologies undergo pre-clinical and clinical development, it is becoming essential to monitor their location and function in vivo, necessitating appropriate molecular imaging strategies, and therefore, we have created an interest group within the World Molecular Imaging Society focusing on synthetic biology and reporter gene technologies. Here, we highlight recent advances in biomedical synthetic biology, including bacterial therapy, immunotherapy, and regenerative medicine. We then discuss emerging molecular imaging approaches to facilitate in vivo applications, focusing on reporter genes for noninvasive modalities such as magnetic resonance, ultrasound, photoacoustic imaging, bioluminescence, and radionuclear imaging. Because reporter genes can be incorporated directly into engineered genetic circuits, they are particularly well suited to imaging synthetic biological constructs, and developing them provides opportunities for creative molecular and genetic engineering

Biogenic gas nanostructures as ultrasonic molecular reporters.

Ultrasound is among the most widely used non-invasive imaging modalities in biomedicine, but plays a surprisingly small role in molecular imaging due to a lack of suitable molecular reporters on the nanoscale. Here, we introduce a new class of reporters for ultrasound based on genetically encoded gas nanostructures from microorganisms, including bacteria and archaea. Gas vesicles are gas-filled protein-shelled compartments with typical widths of 45-250 nm and lengths of 100-600 nm that exclude water and are permeable to gas. We show that gas vesicles produce stable ultrasound contrast that is readily detected in vitro and in vivo, that their genetically encoded physical properties enable multiple modes of imaging, and that contrast enhancement through aggregation permits their use as molecular biosensors

Transcranial Focused Ultrasound Generates Skull-Conducted Shear Waves: Computational Model and Implications for Neuromodulation

Focused ultrasound (FUS) is an established technique for non-invasive surgery and has recently attracted considerable attention as a potential method for non-invasive neuromodulation. While the pressure waves in FUS procedures have been extensively studied in this context, the accompanying shear waves are often neglected due to the relatively high shear compliance of soft tissues. However, in bony structures such as the skull, acoustic pressure can also induce significant shear waves that could propagate outside the ultrasound focus. Here, we investigate wave propagation in the human cranium by means of a finite-element model that accounts for the anatomy, elasticity, and viscoelasticity of the skull and brain. We show that, when a region on the scalp is subjected to FUS, the skull acts as a waveguide for shear waves that propagate with a speed close to 1500 m/s, reaching off-target structures such as the cochlea. In particular, when a sharp onset of FUS is introduced in a zone proximal to the intersection of the parietal and temporal cranium, the bone-propagated shear waves reach the inner ear in about 40 μs, leading to cumulative displacements of about 1 μm. We further quantify the effect of ramped and sharp application of FUS on the cumulative displacements in the inner ear. Our results help explain the off-target auditory responses observed during neuromodulation experiments and inform the development of mitigation and sham control strategies

Ultrasonic Neuromodulation Causes Widespread Cortical Activation via an Indirect Auditory Mechanism

Ultrasound has received widespread attention as an emerging technology for targeted, non-invasive neuromodulation based on its ability to evoke electrophysiological and motor responses in animals. However, little is known about the spatiotemporal pattern of ultrasound-induced brain activity that could drive these responses. Here, we address this question by combining focused ultrasound with wide-field optical imaging of calcium signals in transgenic mice. Surprisingly, we find cortical activity patterns consistent with indirect activation of auditory pathways rather than direct neuromodulation at the ultrasound focus. Ultrasound-induced activity is similar to that evoked by audible sound. Furthermore, both ultrasound and audible sound elicit motor responses consistent with a startle reflex, with both responses reduced by chemical deafening. These findings reveal an indirect auditory mechanism for ultrasound-induced cortical activity and movement requiring careful consideration in future development of ultrasonic neuromodulation as a tool in neuroscience research

Genetically engineered sensors for non-invasive molecular imaging using MRI

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Biological Engineering, 2008.Cataloged from PDF version of thesis.Includes bibliographical references (p. 126-138).Technologies that provide information about the concentrations or activities of specific molecules in living subjects have the potential to greatly advance science and medicine. Magnetic resonance imaging (MRI) is a tool uniquely suited to this task because of its ability to image deep inside tissues at relatively high spatial and temporal resolution. However, the range of molecular phenomena currently accessible to MRI is limited by a lack of suitable molecular sensors. Most efforts to create such sensors have focused on synthetic contrast agents, whose complicated structures make them difficult to engineer, synthesize and deliver to target tissues. If MRI sensors could instead be made of proteins, a number of these difficulties could be mitigated. Here, we describe two platforms for the development of protein-based molecular sensors for MRI. The first is based on the heme domain of the bacterial cytochrome P450-BM3, which produces changes in TI contrast in MRI in response to small molecule binding. We developed a high-throughput assay that allowed us to evolve this protein into a sensor of the neurotransmitter dopamine (DA). We then used it to image DA release from cultured cells and cocaine-induced changes in DA transport in the brains of living rats. The second platform is based on the human iron storage protein ferritin (Ft), which enhances T2 contrast in MRI upon self-aggregation. We developed a system to express self-assembled Ft nanoparticles incorporating multiple surface functionalities, and used it to create a sensor for protein kinase A activity. Our results provide a proof of concept for two novel platforms for protein-based MRI sensor development, and highlight some key advantages of this approach over the synthetic methods used previously.by Mikhail G. Shapiro.Ph.D