• Korean Journal of Mathematics
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• 제32권2호
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• pp.213-218
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• 2024

Assume that at a certain locus there are three genotypes and that for every one progeny produced by an I^AI^A homozygote, the heterozygote I^AI^B produces. W. Choi found the adapted partial differential equations for the density and operator of the frequency for one gene and applied this adapted partial differential equations to several diploid model. Also, he found adapted partial differential equations for the diploid model against recessive homozygotes and in case that the alley frequency occurs after one generation of selection when there is no dominance. (see. [1, 2]). In this paper, we find the adapted partial equations for the model of selection against heterozygotes and in case that the allele frequency changes after one generation of selection when there is overdominance. Finally, we shall find the partial differential equation of general type of selection at diploid model and it also shall apply to actual examples. This is a very meaningful result in that it can be applied in any model.

• 대한수학회보
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• 제42권2호
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• pp.397-404
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• 2005

In this note, we characterize the limiting diffusion of a diploid model by defining the discrete generator for the resealed Markov chain. We conclude that this limiting diffusion model is with uncountable state space and mutation selection and special 'mutation or gene conversion rate'.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.241-246
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• 2013

Choi [1] identified and characterized the limiting diffusion of this diploid model by defining discrete generator for the rescaled Markov chain. In this note, we define the operator of projection $S_t$ on limiting diffusion and new measure $dQ=S_tdP$. We show the martingale property on this operator and measure. Also we conclude that the martingale problem for diffusion operator of projection is well-posed.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.1043-1048
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• 2011

W. Choi([1]) identified and characterized the limiting diffusion of this diploid model by defining discrete generator for the rescaled Markov chain. We denote by F the homozygosity and by S the average selection intensity. In this note, we define the Fleming-Viot process with generator of limiting diffusion and provide exact result for the relations of F and S.

• 한국가축번식학회지
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• 제13권1호
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• pp.49-55
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• 1989

The Results of colchicine and pretreatment time have shown that the cells of Coho Salmon(Oncorhynchus Kisutch) were effectively injected 6 hours prior to the harvest at a final concentration of 10$\mu\textrm{g}$/g body weight. The cell-density from 8,000 cells/㎣ (=8${\times}$106 ml) was found as ideal. The best effect of hypotonic solution in proportion to the cell is 20 : 1 and 50 minutes. The model number of diploid chromosome in this species was 2n=60. The karyotype analysis proved that the diploid complement consisted of 19 pairs of metacentric-, 4 pairs of submetacentric- and 7 paris of acrocentric-chromosomes. The diagrammatic representation proved that the diploid complement consisted of 7 pairs of metacentric-, 2 pairs of submetacentric- and 1 pair of acrocentric-chromosomes.

• Korean Journal of Mathematics
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• 제22권1호
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• pp.29-36
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• 2014

The limiting diffusion of special diploid model can be defined as a discrete generator for the rescaled Markov chain. Choi([2]) defined the operator of projection $S_t$ on limiting diffusion and new measure $dQ=S_tdP$. and showed the martingale property on this operator and measure. Let $P_{\rho}$ be the unique solution of the martingale problem for $\mathcal{L}_0$ starting at ${\rho}$ and ${\pi}_1,{\pi}_2,{\cdots},{\pi}_n$ the projection of $E^n$ on $x_1,x_2,{\cdots},x_n$. In this note we define $$dQ_{\rho}=S_tdP_{\rho}$$ and show that $Q_{\rho}$ solves the martingale problem for $\mathcal{L}_{\pi}$ starting at ${\rho}$.

• Plant Biotechnology Reports
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• 제5권3호
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• pp.265-271
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• 2011

The cultivated potato as well as its tuber-bearing relatives are considered model plants for cell and tissue culture, and therefore for exploiting the genetic variation induced by in vitro culture. The association between molecular stability and tissue culture in different genetic backgrounds and ploidy levels has already been explored. However, it still remains to be ascertained whether somaclonal variation differs between callus-derived chromosome-doubled and undoubled regenerants. Our research aimed at investigating, through amplified fragment length polymorphism (AFLP) markers, the genetic changes in marker-banding patterns of diploid and tetraploid regenerants obtained from one clone each of Solanum bulbocastanum Dunal and S. cardiophyllum Lindl (both 2n = 2x = 24) and tetraploids from cultivated S. tuberosum L. (2n = 4x = 48). Pairwise comparisons between the banding patterns of regenerants and parents allowed detecting considerable changes associated to in vitro culture both at diploid and tetraploid level. The percentages of polymorphic bands between diploid and tetraploid regenerants were, respectively, 57 and 69% in S. bulbocastanum and 58 and 63% in S. cardiophyllum. On average, the frequencies of lost parental fragments in regenerants were significantly higher than novel bands both in S. bulbocastanum (48 vs. 22%) and S. tuberosum (36 vs. 18%) regenerants. By contrast, in S. cardiophyllum, a similar incidence of the two events was detected (32 vs. 29%). Our results revealed that structural changes after tissue culture process strongly affected the genome of the species studied, but diploid and tetraploids regenerated plants responded equally.

• Korean Journal of Mathematics
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• 제30권1호
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• pp.67-72
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• 2022

For a locus with two alleles (I^A and I^B), the frequencies of the alleles are represented by $$p=f(I^A)={\frac{2N_{AA}+N_{AB}}{2N},\;q=f(I^B)={\frac{2N_{BB}+N_{AB}}{2N}$$ where N_AA, N_AB and N_BB are the numbers of I^AI^A, I^AI^B and I^BI^B respectively and N is the total number of populations. The frequencies of the genotypes expected are calculated by using p², 2pq and q². Choi showed the method of whether some genotypes is in these probabalities. Also he calculate the probability generating function for offspring number of genotype under a diploid model( [1]). In this paper, let x(t, p) be the probability that I^A become fixed in the population by time t-th generation, given that its initial frequency at time t = 0 is p. We find adapted equations for x using the mean change of frequence of alleles and fitness of genotype. Also we apply this adapted equations to several diploid model and it also will apply to actual examples.

• 미생물학회지
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• 제52권4호
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• pp.406-414
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• 2016

대장균에서 6개의 Leu 코돈중 가장 흔한 코돈은 CUG이다. 이 코돈을 인식하는 tRNA는 4개의 유전자에 의해 합성되는데, leuPQV와 leuT 2개의 locus로 나누어져 있다. 이 CUG를 인식하는 모든 tRNA가 결핍된 균주를 만들기 위해, 우선 leuPQV가 삭제된 균주(${\Delta}leuPQV$)와, leuT의 anticodon CAG를 GAG로 돌연변이시킨 균주[$Km^R$, $leuT^*$(GAG)]를 각각 만들었다. 이 두 돌연변이 유전자를 모으기 위해 ${\Delta}leuPQV$ 균주를 recipient로, $leuT^*$(GAG) 균주를 donor로하는 transduction을 수행한 결과, 콜로니 크기가 큰 것과 작은 것 두 종류의 transductant를 얻었다. PCR 후 염기서열 분석 결과 큰 콜로니는 예측한 recombinant로 판명됐으나, 작은 콜로니는 donor와 recipient 염색체 간의 상호교환재조합(reciprocal recombination)으로는 설명이 되지 않는, 돌연변이 유전자[$leuT^*$(GAG)]와 야생형 유전자(leuT(CAG)]를 모두 가진 균주로 밝혀졌다. 이 heterozygous diploid는 광학현미경으로 관찰시 세포의 형태와 크기에서 특이점이 발견되지 않았으나, 영양배지에서 야생형에 비해 생장이 한참 느리면서, 선형생장곡선(linear growth curve)이라는 예측하지 못한 생장특성을 보였다. 이 2배체 균주는 선택배지에서는 항상 작은 균일한 콜로니를 형성하였으나, 배지에 선택항생제 없을 경우, $leuT^*$(GAG) 유전자형 세포와 leuT(CAG) 유전자형 세포로 분리가 일어났다. 우리의 결과를 종합해볼 때, 이 2배체 균주는, $leuT^*$(GAG)와 leuT(CAG) 부분만 2배체로 갖는 부분이배체(merodiploid)라기 보다는, $leuT^*$(GAG)와 leuT(CAG)가 서로 다른 염색체에 있는 완전이배체라는 모델을 지지했다. 우리는 이러한 2배체가 어떻게 생성되었으며, 어떻게 분리되는지, 또 이 균주는 왜 선형생장곡선을 보이는지 등에 대한 모델을 토론하였다.

• 환경생물
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• 제26권1호
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• pp.1-7
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• 2008

A mathematical model for the synergistic interaction of physical and chemical environmental agents was suggested for quantitative prediction of irreversibly damaged cells after combined exposures. The model took into account the synergistic interaction of agents and was based on the supposition that additional effective damages responsible for the synergy are irreversible and originated from an interaction of ineffective sublesions. The experimental results regarding the irreversible component of radiation damage of diploid yeast cells simultaneous exposed to heat with ionizing radiation ($^{60}Co$) or UV light (254 nm) are presented. It was shown that the cell ability of the liquid holding recovery decreased with an increase in the temperature, at which the exposure was occurred. A good correspondence between experimental results and model prediction was demonstrated. The importance of the results obtained for the interpretation of the mechanism of synergistic interaction of various environmental factors is discussed.