Papers by Anirvan Sengupta
Additional file 9: Table S8. of Quantitative analysis of chromatin interaction changes upon a 4.3 Mb deletion at mouse 4E2
Combined DE genes of three + 129 /+ Bl6 and four Df/+â D Bl6 MEF revealed by RNA-Seq. (XLSX 170Â kb)
Additional file 3: Table S2. of Quantitative analysis of chromatin interaction changes upon a 4.3 Mb deletion at mouse 4E2
Summary of median magnitude of change, direction, and number of df DIRs for viewpoints 1, 2, 11, ... more Summary of median magnitude of change, direction, and number of df DIRs for viewpoints 1, 2, 11, and 12. Notice how viewpoint 1 displays an increase in contact probabilities with surrounding sequences (64 % of total detected regions), while viewpoints 2 and 11 show mostly a decrease in interactions (60 % for viewpoint 2, and 95 % for viewpoint 11). Viewpoint 12 has both increase and decrease in interactions in approximately the same magnitude (~50 %). (XLSX 10 kb)
Additional file 2: Table S1. of Quantitative analysis of chromatin interaction changes upon a 4.3 Mb deletion at mouse 4E2
(a) Positions and (b) C57Bl6/J-129S5/SvEvBrd SNP information for analyzed PE-4Cseq viewpoints on ... more (a) Positions and (b) C57Bl6/J-129S5/SvEvBrd SNP information for analyzed PE-4Cseq viewpoints on chromosome 4. Primers used for Sanger sequencing are shown. (XLSX 26Â kb)
Additional file 8: Table S7. of Quantitative analysis of chromatin interaction changes upon a 4.3 Mb deletion at mouse 4E2
BACS used for selected PE-4Cseq and chromatin decompaction regions. a) Location of BACs used in 3... more BACS used for selected PE-4Cseq and chromatin decompaction regions. a) Location of BACs used in 3D DNA FISH experiments for the validation of df PE-4Cseq DIRs and chromatin decompaction. b) Number of CTCF, Med1, Med12, and Smc1 protein binding sites33 overlapping each BAC used for 3D DNA FISH experiments. c) Proportions of CTCF, Med1, Med12, and Smc133 protein binding sites overlapping each BAC used for 3D DNA FISH experiments normalized by BAC size. (XLSX 377 kb)
Additional file 7: Table S6. of Quantitative analysis of chromatin interaction changes upon a 4.3 Mb deletion at mouse 4E2
Sequencing LAD (sLAD) positions detected for the terminal part of chromosome 4. Data derived from... more Sequencing LAD (sLAD) positions detected for the terminal part of chromosome 4. Data derived from 3 T3 MEFs40. Marked in yellow is the extensive sequence stretch bordering the CNV devoid of sLADs. Marked in green are the sLAD regions inside the CNV. (XLSX 11 kb)
Additional file 11: Table S10. of Quantitative analysis of chromatin interaction changes upon a 4.3 Mb deletion at mouse 4E2
129S5/SvEvBrd allele-specific DE genes of three + 129 /+ Bl6 and four Df/+â D Bl6 MEF revealed by... more 129S5/SvEvBrd allele-specific DE genes of three + 129 /+ Bl6 and four Df/+â D Bl6 MEF revealed by RNA-Seq. (XLSX 40Â kb)
Additional file 13: Table S12. of Quantitative analysis of chromatin interaction changes upon a 4.3 Mb deletion at mouse 4E2
Candidate genes associated with different Monosomy 1p36 phenotypes. Their corresponding mouse hom... more Candidate genes associated with different Monosomy 1p36 phenotypes. Their corresponding mouse homologues are shown in column 3, together with their chromosomal positions (columns 5,6). Their overlaps with df DIRs are displayed in columns 7–9, as well as the direction of change of the contact probabilities (1 = increase,–1 = decrease. Both compared to + 129 ). RNA-Seq derived expression in Df/+ Bl6 MEFs is shown in columns 11,12. Mouse gene coordinates are expressed in NCBI37/mm9 assembly, while human is GRCh38. (XLSX 11 kb)
Additional file 10: Table S9. of Quantitative analysis of chromatin interaction changes upon a 4.3 Mb deletion at mouse 4E2
GO â condensed nuclear chromosomeâ table of DE genes in df/+ Bl6 MEFs. (XLSX 12Â kb)
Neural computation, 2018
Modeling self-organization of neural networks for unsupervised learning using Hebbian and anti-He... more Modeling self-organization of neural networks for unsupervised learning using Hebbian and anti-Hebbian plasticity has a long history in neuroscience. Yet derivations of single-layer networks with such local learning rules from principled optimization objectives became possible only recently, with the introduction of similarity matching objectives. What explains the success of similarity matching objectives in deriving neural networks with local learning rules? Here, using dimensionality reduction as an example, we introduce several variable substitutions that illuminate the success of similarity matching. We show that the full network objective may be optimized separately for each synapse using local learning rules in both the offline and online settings. We formalize the long-standing intuition of the rivalry between Hebbian and anti-Hebbian rules by formulating a min-max optimization problem. We introduce a novel dimensionality reduction objective using fractional matrix exponents...
Regulating Looping in
9Th European Conference on Mathematical and Theoretical Biology, Jun 9, 2014
Regions of the chromosome that are many thousands of bases away often have to come in contact for... more Regions of the chromosome that are many thousands of bases away often have to come in contact for turning some genes on or off. The specificity of such contacts is maintained by interposed boundaries or insulators, which are able to block these long distance interactions. The physical basis for the control of chromatin contact is still not well understood. We model the chromatin fiber as a semi-flexible polymer to explain how 'distant' regulatory interaction happens and how it is controlled by other sequence elements. There appears be region in the of parameters space of where mesoscopic attractive polymers fold to form branched polymer like structures, which are key to understanding our results. We will explore the connection between this regime and disordered systems treated by large N expansion. We finish by discussing how we could use the polymer model of chromatin to analyze data related to chromatin conformation and learn about regulatory contacts.
On convergence of parallel rays after specular reflection from plane curves and surfaces
Physical review letters, Jan 24, 2015
The dynamics of proteins in the unfolded state can be quantified in computer simulations by calcu... more The dynamics of proteins in the unfolded state can be quantified in computer simulations by calculating a spectrum of relaxation times which describes the time scales over which the population fluctuations decay to equilibrium. If the unfolded state space is discretized, we can evaluate the relaxation time of each state. We derive a simple relation that shows the mean first passage time to any state is equal to the relaxation time of that state divided by the equilibrium population. This explains why mean first passage times from state to state within the unfolded ensemble can be very long but the energy landscape can still be smooth (minimally frustrated). In fact, when the folding kinetics is two-state, all of the unfolded state relaxation times within the unfolded free energy basin are faster than the folding time. This result supports the well-established funnel energy landscape picture and resolves an apparent contradiction between this model and the recently proposed kinetic h...
Biophysical Journal, 2014
The packaging of chromatin within the nucleus of eukaryotic cells is achieved through several lev... more The packaging of chromatin within the nucleus of eukaryotic cells is achieved through several levels of spatial organization. The lowest levels give rise to nucleosomes and the 30-nm chromatin fiber while the higher levels involve folding of the chromatin fiber into chromosomes. These higher levels, often referred to as the higher order organization of chromatin, are still poorly understood but are actively being investigated through a new class of experiments known as chromatin conformation capture (3C), and its high-throughput derivative called Hi-C. These experiments detect contacts between different genomic loci, yielding contact probabilities (CPs) that may be used to elucidate the higher order organization of chromatin. Here we present a computational method for recovering chromatin conformation ensembles from reference CPs (Meluzzi D and Arya G. Nucleic Acids Research. 2013 41:63). The conformations are generated by simulating a bead-chain polymer model that represents the 30-nm chromatin fiber. Selected parameters of this polymer model are optimized iteratively until the CPs estimated from the conformation ensembles match the reference CPs. To minimize the size of ensembles required to reliably compute the CPs, we have developed a method that estimates CPs by fitting the extended generalized lambda distribution to simulated inter-bead distances. We show that our overall approach enables the recovery of conformation ensembles for genomic lengths on the order of 1 Mbp and that these ensembles can be used to investigate the shape and spatial properties of biologically relevant chromatin domains.
Physical Review B, 2000
I consider models with an impurity spin coupled to a fluctuating gaussian field with or without a... more I consider models with an impurity spin coupled to a fluctuating gaussian field with or without additional Kondo coupling of the conventional sort. In the case of isotropic fluctuations, the renormalisation group flows for these models have controlled fixed points when the autocorrelation of the gaussian field h(t), < T h(t)h(0) >∼ 1 t 2−ǫ with small positive ǫ. In absence of any additional Kondo coupling, I get powerlaw decay of spin correlators, < T S(t)S(0) >∼ 1 t ǫ. For negative ǫ, the spin autocorrelation is constant in long time limit. The results agree with calculations in Schwinger Boson mean field theory. In presence of a Kondo coupling to itinerant electrons, the model shows a phase transition from a Kondo phase to a field fluctuation dominated phase. These models are good starting points for understanding behaviour of impurities in a system near a zero-temperature magnetic transition. They are also useful for understanding the dynamical local mean field theory of Kondo lattice with Heisenberg (spin-glass type) magnetic interactions.
Computational Mathematics, 2002
Quantum search is a quantum mechanical technique for searching N possibilities in only √ N steps.... more Quantum search is a quantum mechanical technique for searching N possibilities in only √ N steps. We show that the algorithm can be described as a resonance phenomenon. A similar algorithm applies in a purely classical setting when there are N oscillators, one of which is of a different resonant frequency. We could identify which one this is by measuring the oscillation frequency of each oscillator, a procedure that would take about N cycles. We show, how by coupling the oscillators together in a very simple way, it is possible to identify the different one in only √ N cycles.
Physical Review B, 1996
We consider the single channel Kondo problem with the Kondo coupling between a spin S impurity an... more We consider the single channel Kondo problem with the Kondo coupling between a spin S impurity and conduction electrons with spin j. These problems arise as multicritical points in the parameter spaces of two-and higher-level tunneling systems, and some impurity models of heavy fermion compounds. In contrast to the previous Bethe-anstaz conjectures, it turns out that the dynamics of the spin sector is the same as that of a spin S impurity coupled to k(j) channels of spin 1/2 electrons with k(j) = 2j(j + 1)(2j + 1)/3. As a result, for 2S < k(j), the system shows non-Fermi liquid behavior with the same exponents for the thermodynamic quantities as those of k(j) channel Kondo problem. However, both the finite-size spectrum and the operator content are different due to the presence of the other sectors and can be obtained by conformal field theory techniques.
Regions of the chromosome that are many thousands of bases away often have to come in contact for... more Regions of the chromosome that are many thousands of bases away often have to come in contact for turning some genes on or off. To discover the specific and highly regulated contacts, we need to have a good statistical description of the strength of non-specific ones. We model the chromatin fiber as a potentially heterogeneous polymer and discuss how to use such a model in the analysis of chromatin conformation capture data.
Proceedings of the National Academy of Sciences, 2002
Chromosomal instability (CIN) is a defining characteristic of most human cancers. Mutation of CIN... more Chromosomal instability (CIN) is a defining characteristic of most human cancers. Mutation of CIN genes increases the probability that whole chromosomes or large fractions of chromosomes are gained or lost during cell division. The consequence of CIN is an imbalance in the number of chromosomes per cell (aneuploidy) and an enhanced rate of loss of heterozygosity. A major question of cancer genetics is to what extent CIN, or any genetic instability, is an early event and consequently a driving force for tumor progression. In this article, we develop a mathematical framework for studying the effect of CIN on the somatic evolution of cancer. Specifically, we calculate the conditions for CIN to initiate the process of colorectal tumorigenesis before the inactivation of tumor suppressor genes.
PLoS Computational Biology, 2011
Although many of the core components of the embryonic cell-cycle network have been elucidated, th... more Although many of the core components of the embryonic cell-cycle network have been elucidated, the question of how embryos achieve robust, synchronous cellular divisions post-fertilization remains unexplored. What are the different schemes that could be implemented by the embryo to achieve synchronization? By extending a cell-cycle model previously developed for embryos of the frog Xenopus laevis to include the spatial dimensions of the embryo, we establish a novel role for the rapid, fertilization-initiated calcium wave that triggers cell-cycle oscillations. Specifically, in our simulations a fast calcium wave results in synchronized cell cycles, while a slow wave results in full-blown spatio-temporal chaos. We show that such chaos would ultimately lead to an unpredictable patchwork of cell divisions across the embryo. Given this potential for chaos, our results indicate a novel design principle whereby the fast calcium-wave trigger following embryo fertilization synchronizes cell divisions.
Physical Review Letters, 1995
We solve the two-impurity two-channel Kondo model using a combination of conformal invariance and... more We solve the two-impurity two-channel Kondo model using a combination of conformal invariance and bosonisation techniques. The odd-even symmetric case is analysed in detail. The RKKY interaction turns out to be exactly marginal, resulting in a line of non-Fermi liquid fixed points. Explicit formulae are given for the critical exponents and for the finite-size spectrum, which depend continuously on a single parameter. The marginal line spans a range of values of the RKKY coupling I which goes from the infinitely strong ferromagnetic point I = −∞ (associated with a 4-channel spin-1 Kondo model) to a finite antiferromagnetic critical value I c > 0 beyond which a Fermi liquid is recovered. We also find that, when the odd-even symmetry is broken, the marginal line is unstable for ferromagnetic I, while for antiferromagnetic I it extends into a manifold of fixed points.
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Papers by Anirvan Sengupta