Ricci Flow On Cohomogeneity One Manifolds

In the first part of this thesis, in joint work with Renato Bettiol, we show that the geometric property of nonnegative sectional curvature is not preserved under the Ricci flow on closed manifolds of dimension greater than or equal to 4. This is in contrast to the situation for 3 dimensional manifolds. The main strategy is to study the Ricci flow equation on certain 4 dimensional manifolds that admit an isometric group action of cohomogeneity one. Along the way we need to show that a certain canonical form for an invariant metric on a cohomogeneity one manifold, is preserved under the Ricci flow. In the particular situation of the above mentioned result, we prove the preservation of that canonical form using an ad hoc method. It is an interesting question whether this canonical form for a cohomogeneity one metric is preserved in general. In the second part of the thesis we present a strategy to tackle this problem, explain its geometric consequences, and also explain the challenges in carrying out the strategy, along with some partial results

1010-dimensional positively curved manifolds with T3T^3-symmetry

We show that ten-dimensional closed simply connected positively curved manifolds with isometric effective actions of three-dimensional tori are homotopy spheres or homotopy complex projective spaces.Comment: 16 page

Role of synergy and immunostimulation in design of chemotherapy combinations: An analysis of doxorubicin and camptothecin

Combination chemotherapy is often employed to improve therapeutic efficacies of drugs. However, traditional combination regimens often utilize drugs at or near-their maximum tolerated doses (MTDs), elevating the risk of dose-related toxicity and impeding their clinical success. Further, high doses of adjuvant or neoadjuvant chemotherapies can cause myeloablation, which compromises the immune response and hinders the efficacy of chemotherapy as well as accompanying treatments such as immunotherapy. Clinical outcomes can be improved if chemotherapy combinations are designed to reduce the overall doses without compromising their therapeutic efficacy. To this end, we investigated a combination of camptothecin (CPT) with doxorubicin (DOX) as a low-dose treatment option for breast cancer. DOX-CPT combinations were synergistic in several breast cancer cell lines in vitro and one particular ratio displayed extremely high synergy on human triple negative breast cancer cells (MDA-MB-231). This combination led to excellent long-term survival of mice bearing MDA-MB-231 tumors at doses roughly five-fold lower than the reported MTD values of its constituent drugs. Impact of low dose DOX-CPT treatment on local tumor immune environment was assessed in immunocompetent mice bearing breast cancer (4T1) tumors. The combination was not only superior in inhibiting the disease progression compared to individual drugs, but it also generated a more favorable antitumor immunogenic response. Engineering DOX and CPT ratios to manifest synergy enables treatment at doses much lower than their MTDs, which could ultimately facilitate their translation into the clinic as a promising combination for breast cancer treatment. </div

Shape effect in active targeting of nanoparticles to inflamed cerebral endothelium under static and flow conditions

Endothelial cells represent the first biological barrier for compounds, including nanoparticles, administered via the intravascular route. In the case of ischemic stroke and other vascular diseases, the endothelium overexpresses specific markers, which can be used as molecular targets to facilitate drug delivery and imaging. However, targeting these markers can be quite challenging due to the presence of blood flow and the associated hydrodynamic forces, reducing the likelihood of adhesion to the vessel wall. To overcome these challenges, various parameters including size, shape, charge or ligand coating have been explored to increase the targeting efficiency. Geometric shape can modulate nanoparticle binding to the cell, especially by counteracting part of the hydrodynamic forces of the bloodstream encountered by the classical spherical shape. In this study, the binding affinity of polystyrene nanoparticles with two different shapes, spherical and rod-shaped, were compared. First, vascular adhesion molecule-1 (VCAM-1) was evaluated as a vascular target of inflammation, induced by lipopolysaccharide (LPS) stimulation. To evaluate the effect of nanoparticle shape on particle adhesion, nanoparticles were coated with anti-VCAM-1 and tested under static conditions in cell culture dishes coated with cerebral microvasculature cells (bEnd.3) and under dynamic flow conditions in microfluidic channels lined with hCMEC/D3 cells. Effect of particle shape on accumulation was also assessed in two in vivo models including systemic inflammation and local brain inflammation. The elongated rod-shaped particles demonstrated greater binding ability in vitro, reaching a 2.5-fold increase in the accumulation for static cultures and 1.5-fold for flow conditions. Anti-VCAM-1 coated rods exhibited a 3.5-fold increase in the brain accumulation compared to control rods. These results suggest shape offers a useful parameter in future design of drug delivery nanosystems or contrast agents for neurovascular pathologies.This study has been partially supported by grants from Instituto de Salud Carlos III (PI13/00292 and PI17/0054), Spanish ResearchNetwork on Cerebrovascular Diseases RETICS-INVICTUS (RD12/0014),Fundación Mutua Madrileña. The Ministry of Economy and Competitiveness of Spain (SAF2017-84267-R). The European Union program FEDER and the European Regional Development Fund–ERDF, MADIA project No. 732678 to FC. Furthermore, F. Campos (CP14/00154) recipients a research contract from Miguel Servet Program of Instituto de Salud Carlos III. National Science Foundation Graduate Research Fellowship under Grant DGE-1745303S

A fig tree in a concrete jungle: fine-scale population genetic structure of the cluster fig Ficus racemosa in an urban environment

Urban vegetation is an essential requirement in cities for mitigating pollution, heat island effects and providing food and shelter to urban fauna. Efforts to conserve and augment green cover in cities, however, often lack data on the genetic diversity of urban trees, which could be crucial to the success of such programmes. We investigate the population genetics of the cluster fig Ficus racemosa, which occurs naturally in Indian cities and is a keystone species for urban fauna. Genetic analysis of 51 F. racemosa trees in urban Bangalore, India, shows no evidence of inbreeding; the overall inbreeding coefficient (F (is) ) across 12 microsatellite markers (0.0366) was non-significant with no evidence of heterozygote deficit. Spatial genetic structure (SGS) analysis of 47 trees showed an overall negative relationship between kinship coefficient and spatial distance, with strong SGS at distances < 1 km. The absence of heterozygote deficit is likely due to the fig's obligate mutualistic association with fig wasps which pollinate their flowers even across long distances. However, the strong SGS at short distances could result from clumped seed dispersal close to natal trees. Therefore, the pattern of population genetics for F. racemosa from urban Bangalore likely results from short-distance seed dispersal and long-distance pollen flow. Despite the scattered and fragmented nature of green areas within cities, these gene mobility factors maintain robust population genetics in F. racemosa even at low population densities. The same may not apply for Ficus species that are planted as vegetative cuttings in cities and therefore may have limited genetic diversity