Robersy Sanchez

New horizons for genomic mathematics are glimpsed in the Post-Genomic Era. However, communication of the basic results on genomic mathematics to the scientific community not familiar with mathematical biology and to a wider audience is a challenge. We are living times in which there are so many interesting things to see and to learn that there is almost no time to discover the beauty of nature in those things that require the lens of mathematics to be observed.

The best is yet to come

The genetic-code cube. Although the genetic code is not universal (almost universal), the genetic code cube is universal, since it is unique up to isomorphism. Click to read more ...

 The genetic code is the cornerstone of life on earth, the fundamental set of biochemical rules that distinguish living organisms from non-living matter. The quantitative relationships between the DNA bases in the codons permit the description of the genetic code as a cube inserted in the three dimensional space.

The Hasse diagram shows the lattice structure of the Genetic Code Boolean algebra. Hence, bases, codons, and DNA sequences can be represented in the binary alphabet of 0s and 1s. Click to read more ...

The genetic code can be represented as Boolean lattice as well, which is in directed correspondence with a graph called Hasse diagram. The role of the hydrophobicity in the distribution of codons assigned to each amino acid is reflected on Hasse diagram symmetry.

Methyl-IT approach was designed to discriminate methylation regulatory signal from background noise induced by molecular stochastic fluctuations. Click to read more ...

Methyl-IT R package. A signal detection based approach for methylation analysis. Since the biological signal created within the dynamic methylome environment characteristic of living organisms is not free of background noise, application of signal detection theory is required (get Methyl-IT here).

The probability of fixations of immunogenic proteins in the pathogen populations can be estimated on statistical thermodynamics basis in the framework of the symmetric group of genetic-code group. Click to read more ...

To know in advance the fixation probability of immune escape epitopes is essential to build successful vaccines. The fixation probabilities of mutational events on viral proteins can be estimated in a thermodynamics framework of the symmetric group of genetic-code cubes (get Computational Document Format (CDF) here)

Non-linear Fit of Mixture Distributions

Fitting Mixture Distributions 1. Background Mixture Distributions were introduced in a previous post.  Basically, it is said that a distribution $f(x)$ is a mixture of k components distributions $f_1(x), ..., f_k(x)$ if: $f(x) = sum_{i=1}^k pi_i f_i(x)$ where $pi_i$ are the so called mixing weights, $0 le pi_i le 1$, and $pi_1 + ... + […]

Sampling from a Mixture of Distributions

Sampling from a Mixture of Distributions It is said that a distribution $f(x)$ is a mixture of k components distributions $f_1(x), ..., f_k(x)$ if: $f(x) = sum_{i=1}^k pi_i f_i(x)$ where $pi_i$ are the so called mixing weights, $0 le pi_i le 1$, and $pi_1 + ... + pi_k = 1$. Here, new data points from […]

PCA and LDA with Methyl-IT

Principal Components and Linear Discriminant Downstream Methylation Analyses with Methyl-IT When methylation analysis is intended for diagnostic/prognostic purposes, for example, in clinical applications for patient diagnostics, to know whether the patient would be in healthy or disease stage we would like to have a good predictor tool in our side. It turns out that classical […]

The Binary Alphabet of DNA

On the DNA Computer Binary Code In any finite set we can define a partial order, a binary operation in different ways. But here, a partial order is defined in the set of four DNA bases in such a manner that a Boolean lattice structure is obtained. A Boolean lattice is an algebraic structure that […]

Monte-Carlo Goodness of Fit Test

Goodness of fit with large Sample size 1. Background The goodness of fit (GOF) tests frequently fail with real datasets when the sample size goes beyond 100. This issue is critical when working with experimental data where enviromental random noise cannot be prevented. Fortunately, permutation and Monte Carlo approaches for GOF could help to confront […]

Methylation analysis with Methyl-IT. Part 3

An example of methylation analysis with simulated datasets Part 3: Estimation of an optimal cutpoint for the methylation signal  Methylation analysis with Methyl-IT is illustrated on simulated datasets of methylated and unmethylated read counts with relatively high average of  methylation levels: 0.15 and 0.286 for control and treatment groups, respectively. Herein, the detection of the methylation signal […]