Random replicators with high-order interactions

We use tools of the equilibrium statistical mechanics of disordered systems to study analytically the statistical properties of an ecosystem composed of N species interacting via random mutual interactions, as well as via deterministic self-interactions of order p>/=2. We show that the main effect of increasing the order of the interactions among the species is to make the system less competitive, in the sense that the fraction of extinct species is greatly reduced. In addition, we find that for p>2 there is a threshold value which gives a lower bound to the concentration of the surviving species, preventing then the existence of rare species and, consequently, increasing the robustness of the ecosystem to external perturbations.     

Self-assembled E(2)L(3) cryptands (E = P, As, Sb, Bi): transmetalation, homo- and heterometallic assemblies, and conformational isomerism

A series of Group 15-containing homometallic (E(2)L(3), E = P, As, Sb, Bi) and heterometallic (AsSbL(3), AsBiL(3), PSbL(3)) supramolecular cryptands were prepared by the self-assembly of pnictogen halides with dithiolate ligand or by direct transmetalation from a heavier congener. Structural characterization by single crystal X-ray diffraction shows that the E-S bond distances and S-E-S bond angles are significantly affected by the identity of the pnictogen. (1)H NMR spectroscopy reveals that the homometallic cryptands are dynamic in solution: surprisingly one ligand "flips", perturbing the C(3) symmetry of the complex and giving a new asymmetric conformer. Density functional theory calculations were carried out on both the symmetric and the asymmetric conformations of the cryptands, and the energies were compared to those observed by NMR spectroscopy. It was found that the relative stability of the asymmetric cryptand to its symmetric conformer increases with increasing size of the Group 15 element. Finally, it is reported that if two metals are present during the self-assembly process, heterometallic cryptands form. These supramolecular cryptands are reminiscent of their organic analogues, but result from a self-assembly process rather than a stepwise synthesis. Surprisingly, they possess conformational isomerism and exhibit dynamic transmetalation in their reactivity which provides access to otherwise unattainable assemblies.     

The negative sign and exponential expressions: Unveiling students’ persistent errors and misconceptions

The purpose of this study was to determine whether or not certain errors made when simplifying exponential expressions persist as students progress through their mathematical studies. College students enrolled in college algebra, pre-calculus, and first- and second-semester calculus mathematics courses were asked to simplify exponential expressions on an assessment. Persistent errors are identified and characterized. Using quantitative and qualitative methods, we found that the concept of negativity played a prominent role in most of the students’ errors. We theorize that an underdeveloped conception of additive and multiplicative inverses is the root of these errors.     

Diastereoselectivity in the self-assembly of As2L2Cl2 macrocycles is directed by the As-pi interaction

The As-pi interaction, in conjunction with reversible As-thiolate bond formation, is used to direct the self-assembly of dinuclear As2L2Cl2 (L = a dithiolate) macrocycles that exist as equilibrium mixtures of both syn and anti diastereomers. The diastereomeric excess of these self-assembly reactions is controlled in a predictable manner by prudent choice of different achiral, isomeric ligands. A general method for the preparation of As2L2Cl2 macrocycles is established, and strategies to control the diastereoselective self-assembly of regioisomeric macrocycles in solution and the crystalline state are described. A mechanism for the interconversion between diastereomers (a slow process on the NMR time scale) is suggested, and variable-temperature NMR spectroscopic data show that the diastereomeric excess (de) decreases with increasing temperature. anti-As2(L2,6)2Cl2 crystallizes in monoclinic space group P2(1)/n with a = 6.3949(13), b = 19.675(4), c = 10.967(2) A, beta = 106.817(3) degrees , and Z = 2. anti-As2(L1,5)2Cl2 crystallizes in monoclinic space group P2(1)/c with a = 6.813(4), b = 19.085(12), c = 10.277(6) A, beta = 107.788(10) degrees , and Z = 4. syn-As2(L1,4)2Cl2.CHCl3 crystallizes in triclinic space group P(-) with a = 19.313(4), b = 19.923(4), c = 24.508(5) A, alpha = 78.110(4) degrees , beta = 78.860(5) degrees , gamma = 89.183(5) degrees , and Z = 12. As2(L1,4)2Cl2.C6H6 crystallizes in monoclinic space group P2(1)/n with a = 10.3332(7), b = 34.375(2), c = 17.8593(12) A, beta = 98.9650(10) degrees , and Z = 8.     

Rapid extraction and preservation of genomic DNA from human samples

Simple and rapid extraction of human genomic DNA remains a bottleneck for genome analysis and disease diagnosis. Current methods using microfilters require cumbersome, multiple handling steps in part because salt conditions must be controlled for attraction and elution of DNA in porous silica. We report a novel extraction method of human genomic DNA from buccal swab and saliva samples. DNA is attracted onto a gold-coated microchip by an electric field and capillary action while the captured DNA is eluted by thermal heating at 70 °C. A prototype device was designed to handle four microchips, and a compatible protocol was developed. The extracted DNA using microchips was characterized by qPCR for different sample volumes, using different lengths of PCR amplicon, and nuclear and mitochondrial genes. In comparison with a commercial kit, an equivalent yield of DNA extraction was achieved with fewer steps. Room-temperature preservation for 1 month was demonstrated for captured DNA, facilitating straightforward collection, delivery, and handling of genomic DNA in an environment-friendly protocol.

A De Novo Designed Metalloenzyme for the Hydration of CO2

Protein design will ultimately allow for the creation of artificial enzymes with novel functions and unprecedented stability. To test our current mastery of nature’s approach to catalysis, a Zn^II metalloenzyme was prepared using de novo design. α₃DH₃ folds into a stable single‐stranded three‐helix bundle and binds Zn^II with high affinity using His₃O coordination. The resulting metalloenzyme catalyzes the hydration of CO₂ better than any small molecule model of carbonic anhydrase and with an efficiency within 1400‐fold of the fastest carbonic anhydrase isoform, CAII, and 11‐fold of CAIII.     

Maturation of auditory temporal integration and inhibition assessed with event-related potentials (ERPs)

Background

We examined development of auditory temporal integration and inhibition by assessing electrophysiological responses to tone pairs separated by interstimulus intervals (ISIs) of 25, 50, 100, 200, 400, and 800 ms in 28 children aged 7 to 9 years, and 15 adults.

Results

In adults a distinct neural response was elicited to tones presented at ISIs of 25 ms or longer, whereas in children this was only seen in response to tones presented at ISIs above 100 ms. In adults, late N1 amplitude was larger for the second tone of the tone pair when separated by ISIs as short as 100 ms, consistent with the perceptual integration of successive stimuli within the temporal window of integration. In contrast, children showed enhanced negativity only when tone pairs were separated by ISIs of 200 ms. In children, the amplitude of the P1 component was attenuated at ISIs below 200 ms, consistent with a refractory process.

Conclusions

These results indicate that adults integrate sequential auditory information into smaller temporal segments than children. These results suggest that there are marked maturational changes from childhood to adulthood in the perceptual processes underpinning the grouping of incoming auditory sensory information, and that electrophysiological measures provide a sensitive, non-invasive method allowing further examination of these changes.     

Host-guest interactions in a series of self-assembled As2L2Cl2 macrocycles

The reaction of AsCl3 with H2L (where L = a rigid dithiolate) results in the self-assembly of As2L2Cl2 supramolecular macrocycles. For ligands 4,4'-bis(mercaptomethyl)biphenyl (H2), 4,4'-bis(mercaptomethyl)-trans-stilbene (H2), and 1,4-dimethoxy-2,5-bis(mercaptomethyl)benzene (H2), the macrocyclic cavities of the resulting assemblies are large enough to host aromatic solvent molecules, as revealed by single crystal X-ray structures of the inclusion complexes. As2L2Cl(2) macrocycles form in solution as a mixture of diastereomers, but the diastereomers can be selectively crystallized and separated. Crystallization of syn- or anti-As(2)3(2)Cl2 can be controlled using host-guest interactions by the prudent choice of crystallization solvents. anti-As(2)3(2)Cl2 crystallizes exclusively from chloroform and benzene, while a [(syn-As(2)(2)Cl(2))(2).p-xylene] dimer crystallizes from p-xylene and a mixture of [(syn-As(2)3(2)Cl(2))(anti-As(2)3(2)Cl2) x toluene] and [(syn-As(2)3(2)Cl2)2 x toluene] dimers crystallize from toluene.