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APPL. V. 27, No. 4, pp. 930-951, 2006, Society for Industrial and Applied Mathematics.
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of Computer Science Carnegie Mellon University Pittsburgh, PA 15213, 1996.
6. V.P. Il�in, Mathematical Modeling. Part I. Continuous and Discrete Models. Novosibirsk: SBRAS Publ., 2017.
Programmed cell death regulation using rationally designed molecular probes
N. V. Ivanisenko
Institute of Cytology and Genetics SB RAS
Email: ivanisenko@bionet.nsc.ru
DOI 10.24412/9999-017A-2021-1-02-44
There are two types of apoptosis induction: intrinsic-mediated via mitochondria and extrinsic-mediated
via death receptor (DR) activation. CD95/Fas is one of the most studied members of the DR family. The induc-
tion of apoptosis via CD95 is largely controlled by the Death-Inducing Signaling Complex (DISC), which is
formed upon CD95 stimulation. The major components of the DISC complex include CD95, FADD, procaspases-
8/10 and c-FLIP (cellular FLICE inhibitory protein) proteins. Deregulation of the CD95 pathway accompanies a
variety of tumors and neurodegenerative diseases. Structural modeling of the key components of the DISC
complex and in silico screening of compounds targeting them have a great potential towards design of new
therapeutics and providing deep insights into molecular mechanisms of the signaling pathway functioning and
pathology development.
In the current study we applied structural modeling and virtual screening techniques of large databases of
chemical compounds to target the caspase-8/c-FLIPL complex. Designed chemical probe FLIPinB. was able to
target the heterodimerization interface leading to allosteric activation of the pro-apoptotic activity of the
complex. Kinetic mathematical model was further developed to analyze the observed effects of FLIPinB. on
DISC activation. Based on the modeling results we could predict that the stabilized FLIPinB./caspase-8/c-FLIPL
complex plays a major role at the very initial stages of the DISC assembly and procaspase-8 processing. Fur-
thermore, conducted structural analysis of the DISC complex suggests high therapeutic potential of c-FLIP tar-
geting compounds to enhance cell death in cancer cell lines that are characterized by high c-FLIP levels.
This work was supported by the Kurchatov Genomics Center of the Institute of Cytology & Genetics SB RAS (project
number: � 075-15-2019-1662).
Mesh conservation laws in filtration problems with discontinues solutions
M. I. Ivanov1, I. A. Kremer1,2, Yu. M. Laevsky1,2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email: laev@labchem.sscc.ru
DOI 10.24412/9999-017A-2021-1-00-21
We proposed new efficient computational algorithms for solving a number of filtration problems for a
two-phase fluid in porous and fractured-porous media. Main feature of the considered problems is in the
presence of discontinuous solutions which prohibits consideration of the mathematical model in the form of a
system of differential equations in the entire computational domain. We have considered a model in the form
of integral laws of mass conservation and momentum in arbitrary subdomains. In particular, we formulated
Darcy's law in a generalized form for the total velocity, and the phase velocities are given by the product of the
total velocity with some functions that are discontinuous in general [1]. The resulting problem formulation
naturally leads to a spatial approximation by the mixed finite element method for calculating the total velocity
and pressure, and the so-called centered finite volume method for calculating phase saturations. The time ap-
proximation of the saturation equation is based on the explicit upwind Euler scheme. We developed this ap-
proach both for one-porous and two-porous models describing flow in fractured-porous media using the mass
transfer function between pore blocks and fractures. In the case of a two-porous model, we built the upwind
scheme both within each medium and for the implementation of mass transfer between the media.
We considered the problem of gravitational segregation of a two-phase fluid in a porous medium [2]. We
constructed a new computational scheme for solving the multidimensional problem of gravitational segrega-
tion of a two-phase fluid in a porous medium. Unlike the currently well-known IHU (Implicit Hybrid Upwinding)
approach proposed in [3], we have developed an explicit version of this approach (EHU) which is not inferior to
IHU in accuracy and significantly exceeds IHU in performance. Otherwise, the algorithm with the standard up-
wind approximation is unable to adequately reproduce the filtration process. For the method we have con-
structed, we constructed a proof of the weak maximum principle with an explicit indication of the Courant-
Friedrichs-Levy condition that ensures the stability and monotonicity of the scheme. In this case, for the Buck-
ley-Leverett model where the saturation dynamics is described by a hyperbolic equation, the obtained condi-
tions are not restrictive in terms of the time step size, and the time step limiting factor is accuracy only. This
ensures the competitiveness of the EHU vs. IHU for the specified set of problems.
This work was supported by the Russian Science Foundation (grant 19-11-00048).
References
1. Ivanov �. I., Kremer I. A., Laevsky Yu. M. Oil reservoir simulation based on the conservation laws in integral form
// AIP Conference Proceedings. 2020. V. 2312. P. 050008.
2. Ivanov �. I., Kremer I. A., Laevsky Yu. M. Numerical model of gravity segregation of two-phase fluid in porous
media based on hybrid upwinding // Russian J. of Num. Analysis and Math. Modelling. 2021. V. 36, Is.1. P. 17-32.
3. Lee S. H, Efendiev Y., Tchelepi H. A. Hybrid upwind discretization of nonlinear two-phase flow with gravity // Ad-
vances in Water Resources. 2015. V. 82. P. 27-38.
3D inverse problems of magnetic susceptibility restoration from experimental data
I. I. Kolotov1, D. V. Lukyanenko1, Yanfei Wang2, A. G. Yagola1
1Lomonosov Moscow State University
2Institute of Geology and Geophysics, Chinese Academy of Sciences
Email: yagola@physics.msu.ru
DOI 10.24412/9999-017A-2021-1-01-98
Retrieval of magnetic parameters using magnetic tensor gradient measurements receives attention in re-
cent years. Traditional magnetic inversion is based on the total magnetic intensity data and solving the corre-
sponding mathematical physical model. In recent years, with the development of the advanced technology,
acquisition of the full tensor gradient data becomes available. In work [1], the problem of restoring magnetiza-
tion parameters has been solved. In this problem three scalar functions(components of the magnetization vec-
tor) were recovered using data by five scalar functions(independent components of the magnetic tensor). In
our work [2] we consider the problem of magnetic susceptibility restoration using magnetic tensor gradient
measurements. In this work we have recovered one scalar function (magnetic susceptibility) using data by five
scalar functions(components of the magnetic tensor). As we are dealing with the physically overdetermined
problem we expect to receive better results than if the problem was just physically determined. At the current
