448 research outputs found
Topological interactions between ring polymers: Implications for chromatin loops
Chromatin looping is a major epigenetic regulatory mechanism in higher
eukaryotes. Besides its role in transcriptional regulation, chromatin loops
have been proposed to play a pivotal role in the segregation of entire
chromosomes. The detailed topological and entropic forces between loops still
remain elusive. Here, we quantitatively determine the potential of mean force
between the centers of mass of two ring polymers, i.e. loops. We find that the
transition from a linear to a ring polymer induces a strong increase in the
entropic repulsion between these two polymers. On top, topological interactions
such as the non-catenation constraint further reduce the number of accessible
conformations of close-by ring polymers by about 50%, resulting in an
additional effective repulsion. Furthermore, the transition from linear to ring
polymers displays changes in the conformational and structural properties of
the system. In fact, ring polymers adopt a markedly more ordered and aligned
state than linear ones. The forces and accompanying changes in shape and
alignment between ring polymers suggest an important regulatory function of
such a topology in biopolymers. We conjecture that dynamic loop formation in
chromatin might act as a versatile control mechanism regulating and maintaining
different local states of compaction and order.Comment: 12 pages, 11 figures. The article has been accepted by The Journal Of
Chemical Physics. After it is published, it will be found at
http://jcp.aip.or
Π‘Π΅ΠΉΡΠΌΠΎΡΠ°ΡΠΈΠ°Π»ΡΠ½ΡΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΡΠΎΠ΄ΡΠΊΡΠΈΠ²Π½ΡΡ ΠΎΡΠ»ΠΎΠΆΠ΅Π½ΠΈΠΉ ΡΡΡ ΠΠ΅ΡΡΠΎΠ²ΠΎΠ³ΠΎ ΠΌΠ΅ΡΡΠΎΡΠΎΠΆΠ΄Π΅Π½ΠΈΡ
Π‘Π΅ΠΉΡΠΌΠΎΡΠ°ΡΠΈΠ°Π»ΡΠ½ΠΎΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ Π½Π° ΠΠ΅ΡΡΠΎΠ²ΠΎΠΌ Π½Π΅ΡΡΠ΅Π³Π°Π·ΠΎΠ²ΠΎΠΌ ΠΌΠ΅ΡΡΠΎΡΠΎΠΆΠ΄Π΅Π½ΠΈΠΈ Π²ΡΠΏΠΎΠ»Π½Π΅Π½ΠΎ ΠΏΠΎ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ°ΠΌ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠΉ ΡΠ΅ΠΉΡΠΌΠΎΡΠ°Π·Π²Π΅Π΄ΠΊΠΈ Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΠΌΠ°ΡΠ΅ΡΠΈΠ°Π»ΠΎΠ² Π³Π΅ΠΎΡΠΈΠ·ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ ΡΠΊΠ²Π°ΠΆΠΈΠ½ ΠΈ Π΄Π°Π½Π½ΡΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΊΠ΅ΡΠ½Π°. Π‘Π΅ΠΉΡΠΌΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΡΡΡΠΊΡΡΡΠ½ΡΠ΅ ΠΈ Π»ΠΈΡΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΠΎΠ·Π²ΠΎΠ»ΠΈΠ»ΠΈ ΡΡΠΎΡΠ½ΠΈΡΡ ΡΠ°ΡΠΈΠ°Π»ΡΠ½ΡΡ ΠΏΡΠΈΡΠΎΠ΄Ρ ΠΊΠΎΠ»Π»Π΅ΠΊΡΠΎΡΠΎΠ² ΡΡΡΠΊΠΈΡ
ΠΎΡΠ»ΠΎΠΆΠ΅Π½ΠΈΠΉ, ΠΌΠ°Π»ΠΎ ΠΈΠ·ΡΡΠ΅Π½Π½ΡΡ
ΠΈ ΠΏΠ΅ΡΡΠΏΠ΅ΠΊΡΠΈΠ²Π½ΠΎ Π½Π΅ΡΡΠ΅Π³Π°Π·ΠΎΠ½ΠΎΡΠ½ΡΡ
Π½Π° ΠΌΠ΅ΡΡΠΎΡΠΎΠΆΠ΄Π΅Π½ΠΈΠΈ. ΠΠΎ ΠΌΠ°ΡΠ΅ΡΠΈΠ°Π»Π°ΠΌ ΡΠ΅ΠΉΡΠΌΠΎΠ³Π΅ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΎΡΠ»Π΅ΠΆΠ΅Π½Ρ ΠΊΠΎΠ½ΡΡΡΡ ΠΏΠ°Π»Π΅ΠΎΡΡΡΠ»ΠΎΠ²ΡΡ
ΠΎΡΠ»ΠΎΠΆΠ΅Π½ΠΈΠΉ, ΡΠ²Π»ΡΡΡΠΈΠ΅ΡΡ Π½Π° ΠΌΠ΅ΡΡΠΎΡΠΎΠΆΠ΄Π΅Π½ΠΈΠΈ Π²ΡΡΠΎΠΊΠΎΠ΄Π΅Π±ΠΈΡΠ½ΡΠΌΠΈ ΠΊΠΎΠ»Π»Π΅ΠΊΡΠΎΡΠ°ΠΌΠΈ. Π’ΠΈΠΏ ΡΠ°ΡΠΈΠΉ ΠΏΡΠΎΠ΄ΡΠΊΡΠΈΠ²Π½ΡΡ
ΠΎΡΠ»ΠΎΠΆΠ΅Π½ΠΈΠΉ ΡΡΠΎΡΠ½ΡΠ½ ΠΏΠΎ Π΄Π°Π½Π½ΡΠΌ Π»ΠΈΡΠΎΡΠ°ΡΠΈΠ°Π»ΡΠ½ΡΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ ΠΏΠΎ ΠΊΠ΅ΡΠ½Ρ ΡΠΊΠ²Π°ΠΆΠΈΠ½
A simple algorithm for distance estimation without radar and stereo vision based on the bionic principle of bee eyes
Simple navigation algorithms are needed for small autonomous unmanned aerial vehicles (UAVs). These algorithms can be implemented in a small microprocessor with low power consumption. This will help to reduce the weight of the UAVs computing equipment and to increase the flight range. The proposed algorithm uses only the number of opaque channels (ommatidia in bees) through which a target can be seen by moving an observer from location 1 to 2 toward the target. The distance estimation is given relative to the distance between locations 1 and 2. The simple scheme of an appositional compound eye to develop calculation formula is proposed. The distance estimation error analysis shows that it decreases with an increase of the total number of opaque channels to a certain limit. An acceptable error of about 2 % is achieved with the angle of view from 3 to 10Β° when the total number of opaque channels is 21600
Π‘ΠΈΡΡΠ΅ΠΌΠ° ΠΊΠΎΠ½ΡΡΠΎΠ»Ρ ΠΊΠ°ΡΠ΅ΡΡΠ²Π° ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π° ΠΊΠ°Π±Π΅Π»ΡΠ½ΡΡ ΠΈΠ·Π΄Π΅Π»ΠΈΠΉ
Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½Π° Π²ΠΈΡΡΡΠ°Π»ΡΠ½Π°Ρ ΠΏΠ°Π½Π΅Π»Ρ, ΠΎΡΠΎΠ±ΡΠ°ΠΆΠ°ΡΡΠ°Ρ Π² ΡΠ΅Π°Π»ΡΠ½ΠΎΠΌ ΠΌΠ°ΡΡΡΠ°Π±Π΅ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ Π²Π΅ΡΡ ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠΉ ΠΏΡΠΎΡΠ΅ΡΡ ΠΈΠ·Π³ΠΎΡΠΎΠ²Π»Π΅Π½ΠΈΡ ΠΊΠ°Π±Π΅Π»ΡΠ½ΡΡ
ΠΈΠ·Π΄Π΅Π»ΠΈΠΉ. ΠΡΠ΅Π΄ΡΡΠΌΠΎΡΡΠ΅Π½Π° Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΠΊΠΎΠ½ΡΡΠΎΠ»Ρ Π»ΡΠ±ΠΎΠ³ΠΎ ΠΊΠΎΠ½ΠΊΡΠ΅ΡΠ½ΠΎΠ³ΠΎ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠ° ΠΊΠ°Π±Π΅Π»Ρ ΠΏΡΠΈ ΠΏΠΎΠΌΠΎΡΠΈ ΠΌΠ½ΠΎΠ³ΠΎΠΎΠΊΠΎΠ½Π½ΠΎΠ³ΠΎ ΡΠ΅ΠΆΠΈΠΌΠ°. Π ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΠΎΠΌ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΠΈ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½Π° Π½Π΅ΡΠ΅ΡΠΊΠ°Ρ Π»ΠΎΠ³ΠΈΠΊΠ°, ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡΠ°Ρ ΠΎΡΡΠ»Π΅ΠΆΠΈΠ²Π°ΡΡ Π½Π°ΡΡΡΠ΅Π½ΠΈΡ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ ΠΏΡΠΎΡΠ΅ΡΡΠ° ΠΈ ΠΊΠΎΡΡΠ΅ΠΊΡΠΈΡΠΎΠ²Π°ΡΡ Π΄Π΅ΠΉΡΡΠ²ΠΈΡ ΠΎΠΏΠ΅ΡΠ°ΡΠΎΡΠ°
ΠΠ± ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠ°Ρ Π²Π΅ΡΠ΅ΡΡΠ²Π° Π·ΠΎΠ»ΠΎΡΠΎΡΡΠ΄Π½ΡΡ ΠΌΠ΅ΡΡΠΎΡΠΎΠΆΠ΄Π΅Π½ΠΈΠΉ ΠΈ ΠΈΡ Π²ΠΎΠ΄Π½ΡΡ ΠΏΠΎΡΠΎΠΊΠΎΠ² ΡΠ°ΡΡΠ΅ΡΠ½ΠΈΡ
ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΠΎΠΏΠΎΡΡΠ°Π²Π»Π΅Π½ΠΈΡ ΡΠ°Π·Π½ΠΎΡΡΠ΅ΠΉ ΠΊΠ»Π°ΡΠΊΠΎΠ² ΡΡΠ΄ΠΎΠ²ΠΌΠ΅ΡΠ°ΡΡΠΈΡ
ΠΏΠΎΡΠΎΠ΄ Ρ ΠΊΠ»Π°ΡΠΊΠ°ΠΌΠΈ Π³ΡΠ°Π½ΠΈΡΠΎΠ² ΡΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΡΠΎ Π² Π·ΠΎΠ»ΠΎΡΠΎΡΡΠ΄Π½ΡΡ
ΠΌΠ΅ΡΡΠΎΡΠΎΠΆΠ΄Π΅Π½ΠΈΡΡ
ΠΈ ΠΈΡ
Π²ΠΎΠ΄Π½ΡΡ
ΠΏΠΎΡΠΎΠΊΠ°Ρ
Π²ΡΡΡΠ΅ΡΠ°ΡΡΡΡ ΡΠΎΠ»ΡΠΊΠΎ ΡΠ΅ ΡΠ»Π΅ΠΌΠ΅Π½ΡΡ, Π΄Π»Ρ ΠΊΠΎΡΠΎΡΡΡ
ΡΡΠ° ΡΠ°Π·Π½ΠΎΡΡΡ ΠΏΠΎΠ»ΠΎΠΆΠΈΡΠ΅Π»ΡΠ½Π°. ΠΡΡΠΎΠΊΠ°Ρ ΠΊΠΎΡΡΠ΅Π»ΡΡΠΈΡ Π·Π½Π°ΡΠ΅Π½ΠΈΠΉ ΡΡΠΈΡ
ΡΠ°Π·Π½ΠΎΡΡΠ΅ΠΉ Ρ Π°Π½ΠΎΠΌΠ°Π»ΡΠ½ΡΠΌΠΈ ΡΠΎΠ΄Π΅ΡΠΆΠ°Π½ΠΈΡΠΌΠΈ ΡΠ»Π΅ΠΌΠ΅Π½ΡΠΎΠ² Π² ΡΡΠ΄Π°Ρ
ΠΈ Π²ΠΎΠ΄Π½ΡΡ
ΠΏΠΎΡΠΎΠΊΠ°Ρ
ΡΠ°ΡΡΠ΅ΡΠ½ΠΈΡ ΠΏΠΎΠΊΠ°Π·ΡΠ²Π°Π΅Ρ, ΡΡΠΎ ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠΎΠΌ ΡΡΠΈΡ
ΡΠ»Π΅ΠΌΠ΅Π½ΡΠΎΠ² ΡΠ²Π»ΡΡΡΡΡ Π²ΠΌΠ΅ΡΠ°ΡΡΠΈΠ΅ Π³ΠΎΡΠ½ΡΠ΅ ΠΏΠΎΡΠΎΠ΄Ρ. ΠΠ°Π»ΠΈΡΠΈΠ΅ Π² ΡΡΡΡΠΊΡΡΡΠ΅ Π²ΡΠ΅Ρ
ΠΈΠ·ΡΡΠ΅Π½Π½ΡΡ
ΠΌΠ΅ΡΡΠΎΡΠΎΠΆΠ΄Π΅Π½ΠΈΠΉ ΠΏΠΎΠ»Π΅ΠΉ Π³ΡΠ°Π½ΠΈΡΠΈΠ·Π°ΡΠΈΠΈ ΠΏΠΎΠΊΠ°Π·ΡΠ²Π°Π΅Ρ, ΡΡΠΎ ΠΈΠ·Π²Π»Π΅ΡΠ΅Π½ΠΈΠ΅ ΡΠ»Π΅ΠΌΠ΅Π½ΡΠΎΠ² ΠΈΠ· Π²ΠΌΠ΅ΡΠ°ΡΡΠΈΡ
ΠΏΠΎΡΠΎΠ΄ ΠΏΡΠΎΠΈΡΡ
ΠΎΠ΄ΠΈΡ Π² ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΠΈΡ
Π³ΡΠ°Π½ΠΈΡΠΈΠ·Π°ΡΠΈΠΈ. ΠΡΠ΅Π΄ΠΏΠΎΠ»Π°Π³Π°Π΅ΡΡΡ, ΡΡΠΎ ΠΏΠ΅ΡΠ΅Π½ΠΎΡ ΡΠ»Π΅ΠΌΠ΅Π½ΡΠΎΠ² ΠΎΡΡΡΠ΅ΡΡΠ²Π»ΡΠ΅ΡΡΡ ΠΏΠΎΡΠΎΠ²ΡΠΌΠΈ ΡΠ°ΡΡΠ²ΠΎΡΠ°ΠΌΠΈ, Π° ΠΈΡ
ΠΎΡΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ - Π² ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ Π½Π΅ΡΠ°Π²Π½ΠΎΠ²Π΅ΡΠ½ΠΎΠ³ΠΎ ΡΠΎΡΡΠΎΡΠ½ΠΈΡ ΠΌΠ΅ΠΆΠ΄Ρ ΠΏΠΎΡΠΎΠ²ΡΠΌΠΈ ΠΈ Π³ΡΠ°Π²ΠΈΡΠ°ΡΠΈΠΎΠ½Π½ΡΠΌΠΈ Π²ΠΎΠ΄Π°ΠΌΠΈ
ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΏΠΎ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΠΌΠΎΠ»ΠΈΠ±Π΄Π΅Π½Π° ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΏΠΎΠ»ΡΡΠΎΠ³ΡΠ°ΡΠΈΠΈ Ρ Π½Π°ΠΊΠΎΠΏΠ»Π΅Π½ΠΈΠ΅ΠΌ
ΠΠΏΡΡ ΡΠΎΠ·Π΄Π°Π½ΠΈΡ Π±Π°ΡΠΎΠ²ΡΡ Π·Π΅ΠΌΠ»Π΅ΡΠ΅Π·Π½ΡΡ ΠΌΠ°ΡΠΈΠ½ Π½Π° Π±Π°Π·Π΅ ΡΡΠ°Π½ΡΠ΅ΠΉΠ½ΡΡ ΡΠΊΡΠΊΠ°Π²Π°ΡΠΎΡΠΎΠ²
Conformational properties of compact polymers
Monte Carlo simulations of coarse-grained polymers provide a useful tool to
deepen the understanding of conformational and statistical properties of
polymers both in physical as well as in biological systems. In this study we
sample compact conformations on a cubic LxLxL lattice with different occupancy
fractions by modifying a recently proposed algorithm. The system sizes studied
extend up to N=256000 monomers, going well beyond the limits of older
publications on compact polymers. We analyze several conformational properties
of these polymers, including segment correlations and screening of excluded
volume. Most importantly we propose a scaling law for the end-to-end distance
distribution and analyze the moments of this distribution. It shows
universality with respect to different occupancy fractions, i.e. system
densities. We further analyze the distance distribution between intrachain
segments, which turns out to be of great importance for biological experiments.
We apply these new findings to the problem of chromatin folding inside
interphase nuclei and show that -- although chromatin is in a compacted state
-- the classical theory of compact polymers does not explain recent
experimental results
Π Π°Π·Π²ΠΈΡΠΈΠ΅ ΠΊΠΈΠ±Π΅ΡΠΏΡΠΈΡ ΠΎΠ»ΠΎΠ³ΠΈΠΈ ΠΊΠ°ΠΊ ΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΈΠ· Π²ΠΈΠ΄ΠΎΠ² ΡΡΠ΄Π΅Π±Π½ΠΎ-ΠΏΡΠΈΡ ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠΊΡΠΏΠ΅ΡΡΠΈΠ·Ρ
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