Stability of Vector Bundles and Rational Curves

This thesis is based on two research papers, each addressing distinct but interconnected topics within algebraic geometry. In the first part, we study the stability of general kernel bundles on projective space P^n. Let a, b, d > 0 be integers. A kernel bundle E_{a,b} on P^n is defined as the kernel of a surjective map φ from O_{P^n}(-d)^a to O_{P^n}^b. Here, φ is represented by a b×a matrix (f_{ij}), where the entries f_{ij} are polynomials of degree d. We give sufficient conditions for semistability of a general kernel bundle on P^n, in terms of its Chern class. In the second part, we study whether a given morphism f from the tangent bundle of P^1 to a balanced vector bundle of degree (n+1)d is induced by the restriction of the tangent bundle T_{P^n} to a rational curve of degree d in P^n. We propose a conjecture on this problem based on Mathematica computations of some examples and provide computer-assisted proof of the conjecture for certain values of n and d

<i>Switching Go</i>̅<i>‑Martini</i> for Investigating Protein Conformational Transitions and Associated Protein–Lipid Interactions

Proteins are dynamic biomolecules that can transform between different conformational states when exerting physiological functions, which is difficult to simulate using all-atom methods. Coarse-grained (CG) Go̅-like models are widely used to investigate large-scale conformational transitions, which usually adopt implicit solvent models and therefore cannot explicitly capture the interaction between proteins and surrounding molecules, such as water and lipid molecules. Here, we present a new method, named Switching Go̅-Martini, to simulate large-scale protein conformational transitions between different states, based on the switching Go̅ method and the CG Martini 3 force field. The method is straightforward and efficient, as demonstrated by the benchmarking applications for multiple protein systems, including glutamine binding protein (GlnBP), adenylate kinase (AdK), and β2-adrenergic receptor (β2AR). Moreover, by employing the Switching Go̅-Martini method, we can not only unveil the conformational transition from the E2Pi-PL state to E1 state of the type 4 P-type ATPase (P4-ATPase) flippase ATP8A1-CDC50 but also provide insights into the intricate details of lipid transport

Real-Time Monitoring of the Activity and Kinetics of T4 Polynucleotide Kinase by a Singly Labeled DNA-Hairpin Smart Probe Coupled with λ Exonuclease Cleavage

We describe a novel method for real-time monitoring of the activity and kinetics of T4 polynucleotide kinase (PNK) by use of a singly fluorophore-labeled DNA-hairpin smart probe (SP) coupled with λ exonuclease (λ exo) cleavage. The method was performed in a sealed reaction tube and offered more sensitive, fast, high-throughput, and cost-effective detection. The SP was designed with a fluorophore at the 3′-end, and the fluorescence was quenched by a GGG-triplet at the 5′-end without any other additional quenchers. The 5′-hydroxyl group of the SP was phosphorylated by T4 PNK in the presence of ATP, and the resulting 5′-phosphoryl end product was promptly cleaved by λ exo, which caused significant enhancement of fluorescence. A fast and accurate method for assaying the kinase activity of T4 PNK was developed with a wide linear detection range from 0.022 to 5.6 nM s−1. The phosphorylation reaction was monitored at varying substrate concentrations at the molecular level, and Km, Vmax, and Kcat values were all calculated. Furthermore, the effects of ATP concentration and salts were investigated. The developed method can be easily adapted to the detection of many other nucleic acid enzymes and may find widespread applications

<i>Switching Go</i>̅<i>‑Martini</i> for Investigating Protein Conformational Transitions and Associated Protein–Lipid Interactions

Proteins are dynamic biomolecules that can transform between different conformational states when exerting physiological functions, which is difficult to simulate using all-atom methods. Coarse-grained (CG) Go̅-like models are widely used to investigate large-scale conformational transitions, which usually adopt implicit solvent models and therefore cannot explicitly capture the interaction between proteins and surrounding molecules, such as water and lipid molecules. Here, we present a new method, named Switching Go̅-Martini, to simulate large-scale protein conformational transitions between different states, based on the switching Go̅ method and the CG Martini 3 force field. The method is straightforward and efficient, as demonstrated by the benchmarking applications for multiple protein systems, including glutamine binding protein (GlnBP), adenylate kinase (AdK), and β2-adrenergic receptor (β2AR). Moreover, by employing the Switching Go̅-Martini method, we can not only unveil the conformational transition from the E2Pi-PL state to E1 state of the type 4 P-type ATPase (P4-ATPase) flippase ATP8A1-CDC50 but also provide insights into the intricate details of lipid transport

Intrinsic Ion Selectivity of Narrow Hydrophobic Pores

We show that narrow hydrophobic pores have an intrinsic ion selectivity by using single-walled carbon nanotube membranes as a model. We examined pores of radius 3.4−6.1 Å, and conducted molecular dynamics simulations to show that Na+, K+, and Cl− face different free energy barriers when entering hydrophobic pores. Most of the differences result from the different dehydration energies of the ions; however, changes in the solvation shell structure in the confined nanotube interior and van der Waals interactions in the small tubes can both play a role. Molecular dynamics simulations conducted under hydrostatic pressure show that carbon nanotube membranes can act as ion sieves, with the pore radius and pressure determining which ions will permeate through the membrane. This work suggests that the intrinsic ion selectivity of biological pores of differing radii might also play a role in determining their selectivity, in addition to the more common explanations based on electrostatic effects. In addition, “hydrophobic gating” can arise in continuous water-filled pores

<i>Switching Go</i>̅<i>‑Martini</i> for Investigating Protein Conformational Transitions and Associated Protein–Lipid Interactions

Proteins are dynamic biomolecules that can transform between different conformational states when exerting physiological functions, which is difficult to simulate using all-atom methods. Coarse-grained (CG) Go̅-like models are widely used to investigate large-scale conformational transitions, which usually adopt implicit solvent models and therefore cannot explicitly capture the interaction between proteins and surrounding molecules, such as water and lipid molecules. Here, we present a new method, named Switching Go̅-Martini, to simulate large-scale protein conformational transitions between different states, based on the switching Go̅ method and the CG Martini 3 force field. The method is straightforward and efficient, as demonstrated by the benchmarking applications for multiple protein systems, including glutamine binding protein (GlnBP), adenylate kinase (AdK), and β2-adrenergic receptor (β2AR). Moreover, by employing the Switching Go̅-Martini method, we can not only unveil the conformational transition from the E2Pi-PL state to E1 state of the type 4 P-type ATPase (P4-ATPase) flippase ATP8A1-CDC50 but also provide insights into the intricate details of lipid transport

Schematic depiction of binocular rivalry and experimental paradigms.

<p>(A) To induce binocular rivalry, a pair of orthogonal gratings (tilted +45° and −45° away from the vertical) were separately presented to the two eyes of the human subjects, and subjects experienced the alternating dominance between one grating and the other. Between the stimulus onset and the first percept, there existed a short period during which subjects experienced the fusion of the two gratings, rather than the complete dominance of one grating over the other. (B) and (C) To measure the first percept and its latency, rivalry stimuli were briefly presented for a duration varied from 10 msec to 500 msec, and subjects reported their perception through a three-alternative forced choice (+45° grating, the −45° grating, or the fusion of two gratings). The trails in which subjects reported the fusion perception were taken into account only when we calcualted the latency of the first percept, and different conditions of stimulus duration were combined in the analyses except for calculating this latency.</p

Influence of contrast imbalance on the latency of the first percept.

<p>(A) For each contrast imbalance, the latency of the first percept was quantified as the stimulus duration that corresponded to 33% of fusion perception. Error bars represent 1 SEM (n = 7). (B) The latency of the first percept shortens as the contrast imbalance increases from 0% to 20% (*, Wilcoxon rank-sum test, p<0.05), from 20% to 40% (**, Wilcoxon rank-sum test, p<0.02), and from 40% to 60% (*, Wilcoxon rank-sum test, p<0.05). Error bars represent 1 SEM (n = 7).</p

Influence of contrast imbalance on percept sequence versus percept duration.

<p>(A) and (B) There is no bias in the percept sequence (Wilcoxon signed-rank test, p>0.9) when the contrast imbalance is 0%. When the contrast imbalance is at or above 20%, the percept sequence is biased to begin with the higher-contrast stimulus (**, Wilcoxon signed-rank test, p<0.02). There is no bias in the percept duration (Wilcoxon signed-rank test, p>0.1) when the contrast imbalance is at or below 20%. When the contrast imbalance is at or above 40%, the percept duration is biased and the higher-contrast stimulus enjoys a longer percept duration (**, Wilcoxon signed-rank test, p<0.02). Compared with the percept duration, the percept sequence can detect a smaller contrast imbalance and has a much larger degree of bias. Error bars represent 1 SEM (n = 7). (C) When the contrast imbalance increases from 0% to 20%, the probability of being the first percept significantly changes (***, Kruskal-Wallis test, p<0.002), but the average percept duration does not (Kruskal-Wallis test, p>0.5). When the contrast imbalance increases from 20% to 80%, the average percept duration significantly changes (*, Kruskal-Wallis test, p<0.05), but the probability of being the first percept does not (Kruskal-Wallis test, p>0.1). Error bars represent 1 SEM (n = 7). (D) When the contrast imbalance increases from 0% to 20%, the degree of bias in the percept sequence significantly increases (***, Kruskal-Wallis test, p<0.002), but that in the percept duration does not (Kruskal-Wallis test, p>0.1). When the contrast imbalance increases from 20% to 80%, the degree of bias in the percept duration significantly increases (**, Kruskal-Wallis test, p<0.02), but that in the percept sequence does not (Kruskal-Wallis test, p>0.1). Error bars represent 1 SEM (n = 7).</p

Electrospun Liquid-Infused Membranes for Emulsified Oil/Water Separation

From an environmental perspective, microfiltration membranes are attractive for the separation of emulsified oils from contaminated water. However, fouling of the membrane is a major drawback of the technology. “Liquid-infused membranes” (LIMs) have the potential to eliminate membrane fouling. Here, we demonstrate the practical application of LIMs for the separation of oil from a stable oil-in-water emulsion and characterize their resistance to fouling. The base membrane is an electrospun nonwoven fibrous layer of the fluorinated copolymer poly­(vinylidene fluoride-co-hexafluoropropylene) (PVDF-co-HFP). The surface energy of the PVDF-co-HFP fibers was lowered by the covalent attachment of a fluorinated silane (PFOCTS), and then, the membrane was infused with a perfluoropolyether. The membrane was then challenged with model emulsions of dodecane in water in a cross-flow configuration. This PFOCTS-modified LIM showed better infused liquid stability, permeation selectivity, higher permeate flux than the unmodified LIM, and better anti-fouling properties than the bare membrane without infused liquid. We also examine the mechanism for transport of the dispersed oil phase through the liquid-infused membrane. We find a linear relationship between the dodecane flux and dodecane concentration in the feed and a higher dodecane flux through the PFOCTS-modified membrane than the unmodified one, which suggests that the capture of dodecane droplets from the feed plays an important role in determining the overall rate of permeation. Other factors such as lower viscosity of the infused liquid, larger pore size, and higher operating pressure also improved the permeate flux through the LIMs. Overall, this work provides some guidelines on the design of composite membranes comprising infused liquids and the choice of operating conditions for the filtration process