• Honam Mathematical Journal
• /
• v.45 no.2
• /
• pp.231-247
• /
• 2023

In this study, we mean that timelike q-helices are curves whose q-frame fields make a constant angle with a non-zero fixed axis. We present the necessary and sufficient conditions for timelike curves via the q-frame to be q-helices in Lorentz-Minkowski 3-space. Then we find some results of the relations between q-helices and Darboux q-helices. Furthermore, we portray Darboux q-helices as special curves whose Darboux vector makes a constant angle with a non-zero fixed axis by choosing the curve as one of the types of q-helices, and also the general case.

• Honam Mathematical Journal
• /
• v.40 no.2
• /
• pp.305-314
• /
• 2018

In this paper, we investigate the notions of helix and slant helices in the lightlike cone. Using the asymptotic orthonormal frame we present some characterizations of helices and slant helices.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.885-899
• /
• 2013

In this paper, we study null helices, null slant helices and Cartan slant helices in $\mathb{E}^3_1$. Using some associated curves, we characterize the null helices and the Cartan slant helices and construct them. Also, we study a space-like curve with the principal normal vector field which is a degenerate plane curve.

• Bulletin of the Korean Chemical Society
• /
• v.24 no.6
• /
• pp.824-828
• /
• 2003

Our previous quantum mechanical calculations using polyalanine model systems showed that the monodipolemacrodipoleinteractions selectively stabilize α-helices and make it possible for α-helices to be formed inhydrophobic environment where the solvent effect is not available. The monodipole-macrodipole interactionsin α-helices were studied molecular mechanically using various point-charge systems available. The resultsshow that all the point-charge systems used in the calculations produce the monodipole-macrodipoleinteractions up to about 60% compared to the results of the quantum mechanical calculations. The results ofmolecular mechanical calculations are explained and discussed compared to the results of the quantummechanical calculations.

• Honam Mathematical Journal
• /
• v.44 no.3
• /
• pp.310-324
• /
• 2022

In this paper, we define timelike curves in R⁴₂ and characterize such curves in terms of Frenet frame. Also, we examine the timelike helices of R⁴₂, taking into account their curvatures. In addition, we study timelike slant helices, timelike B₁-slant helices, timelike B₂-slant helices in four dimensional semi-Euclidean space, R⁴₂. And then we obtain an approximate solution for the timelike B₁ slant helix with Taylor matrix collocation method.

• BMB Reports
• /
• v.40 no.2
• /
• pp.261-269
• /
• 2007

The structure and dynamics of a 37-residue antimicrobial peptide gaegurin 4 (GGN4) isolated from the skin of the native Korean frog, Rana rugosa, was determined in SDS micelles by NMR spectroscopy. The solution structure of the peptide in SDS micelles was determined from 352 NOE-derived distance constraints and 22 backbone torsion angle constraints. Dynamic properties for the amide backbone were characterized by $^1H-^{15}N $heteronuclear NOE experiments. The structural study revealed two amphipathic helices spanning residues 2-10 and 16-32 and that the helices were connected by a flexible loop. An intraresidue disulfide bridge was formed between residues Cys31 and Cys37 near the C-terminus. The loop region (11-15) connecting the two helices are were slightly more flexible than these helices themselves. From the fact that since there is no contact NOEs between two helices, it is implied that the GGN4 peptide shows an independent motion of both helices which has an angle of about $ 60^{\circ}-120^{\circ}$ from each other.

• KIPS Transactions on Software and Data Engineering
• /
• v.3 no.4
• /
• pp.163-168
• /
• 2014

In a protein molecule, ${\alpha}$-helices are important for protein structure, function, and binding to other proteins, so the analysis on the structure of helices has been researched. Since an interaction between two helices is evaluated based on their axes, massive errors in protein structure analysis would be caused if a curved or kinked long ${\alpha}$-helix is considered as a linear one. In this paper, we present an algorithm to reconstruct ${\alpha}$-helices in a protein molecule as a sequence of straight helices under given threshold.

• BMB Reports
• /
• v.50 no.10
• /
• pp.522-527
• /
• 2017

A large number of transcriptional activation domains (TADs) are intrinsically unstructured, meaning they are devoid of a three-dimensional structure. The fact that these TADs are transcriptionally active without forming a 3-D structure raises the question of what features in these domains enable them to function. One of two TADs in human glucocorticoid receptor (hGR) is located at its N-terminus and is responsible for ~70% of the transcriptional activity of hGR. This 58-residue intrinsically-disordered TAD, named tau1c in an earlier study, was shown to form three helices under trifluoroethanol, which might be important for its activity. We carried out heteronuclear multi-dimensional NMR experiments on hGR tau1c in a more physiological aqueous buffer solution and found that it forms three helices that are ~30% pre-populated. Since pre-populated helices in several TADs were shown to be key elements for transcriptional activity, the three pre-formed helices in hGR tau1c delineated in this study should be critical determinants of the transcriptional activity of hGR. The presence of pre-structured helices in hGR tau1c strongly suggests that the existence of pre-structured motifs in target-unbound TADs is a very broad phenomenon.

• Journal of the Korean Mathematical Society
• /
• v.54 no.4
• /
• pp.1331-1343
• /
• 2017

A curve ${\gamma}$ immersed in the three-dimensional sphere ${\mathbb{S}}^3$ is said to be a slant helix if there exists a Killing vector field V(s) with constant length along ${\gamma}$ and such that the angle between V and the principal normal is constant along ${\gamma}$. In this paper we characterize slant helices in ${\mathbb{S}}^3$ by means of a differential equation in the curvature ${\kappa}$ and the torsion ${\tau}$ of the curve. We define a helix surface in ${\mathbb{S}}^3$ and give a method to construct any helix surface. This method is based on the Kitagawa representation of flat surfaces in ${\mathbb{S}}^3$. Finally, we obtain a geometric approach to the problem of solving natural equations for slant helices in the three-dimensional sphere. We prove that the slant helices in ${\mathbb{S}}^3$ are exactly the geodesics of helix surfaces.

• Honam Mathematical Journal
• /
• v.36 no.2
• /
• pp.233-251
• /
• 2014

In this paper, position vector of a spacelike slant helix with respect to standard frame are deduced in Minkowski space $E^3_1$. Some new characterizations of a spacelike slant helices are presented. Also, a vector differential equation of third order is constructed to determine position vector of an arbitrary spacelike curve. In terms of solution, we determine the parametric representation of the spacelike slant helices from the intrinsic equations. Thereafter, we apply this method to find the parametric representation of some special spacelike slant helices such as: Salkowski and anti-Salkowski curves.