Evolutionary Covariant Positions within Calmodulin EF-hand Sequences Promote Ligand Binding

Intracellular calcium signaling is an essential regulatory mechanism through calcium-mediated signal transduction pathways involved in many cell processes, such as exocytosis, motility, apoptosis, excitability, transcription, and muscle contraction. The calcium-binding, ubiquitous, and highly conserved protein calmodulin (CaM) is an important regulator of hundreds of target proteins involved in cellular calcium signaling. CaM comprises of two pairs of EF-hand calcium-binding domains and these structural regions of the protein are highly conserved. Studying the molecular mechanisms underlying the binding of calcium to the EF-hands of CaM is critical in understanding the calcium-mediated cellular processes and how improper binding of calcium can lead to various human pathologies. Previous site-specific binding measurements indicate that each of the four EF-hands of CaM have distinct affinities for calcium. In this study, we have utilized covariance patterns and site-specific mutagenesis to analyze calcium affinity in the two EF-hands of the N-lobe of CaM in order to determine the specific amino acids that are evolutionarily conserved to coordinate calcium. The specific amino acids in CaM that we studied are theorized to coevolve, which means that in their protein coding genes, when a mutation occurs, a compensatory mutation is likely to follow to conserve structure and function of CaM. Since CaM is a highly conserved protein with a known structure, covariance analyses will help in understanding which amino acid contacts are most important for the coordination of calcium in the EF-hands of CaM and to determine which amino acids are under evolutionary constraint. Covariance algorithms, multiple sequence analyses and accompanied protein structure analyses were used to identify the two high scoring amino acid pairs in the N-lobe EF-hands: positions 22 and 24 in EF-hand site 1 and positions 58 and 60 in EF-hand site 2. The amino acids in these locations were mutated and accompanied calcium binding was measured to better understand the effects of the mutations on calcium binding. We have found that both the D24N mutation in site 1 and the D58N mutation in site 2 disrupt binding likely due to the removal of a necessary aspartate in the binding site. However, the combined D58N and N60D mutations restore binding in site 2 by providing the necessary aspartate in the covariant location. The N60D mutation by itself has little impact on calcium binding in site 2. Therefore, it is evident that evolution conserves at least one aspartate in the covariant positions of the binding site and the presence of two aspartates in the covariant positions of the binding site has little affect on calcium binding. We are currently studying the covariant positions in site 1 and future work includes structurally analyzing the covariant positions in the C-lobe of CaM and studying covariance patterns of other calcium-binding proteins with EF-hand binding domains.Biochemistr

Theory of optimal orthonormal subband coders

The theory of the orthogonal transform coder and methods for its optimal design have been known for a long time. We derive a set of necessary and sufficient conditions for the coding-gain optimality of an orthonormal subband coder for given input statistics. We also show how these conditions can be satisfied by the construction of a sequence of optimal compaction filters one at a time. Several theoretical properties of optimal compaction filters and optimal subband coders are then derived, especially pertaining to behavior as the number of subbands increases. Significant theoretical differences between optimum subband coders, transform coders, and predictive coders are summarized. Finally, conditions are presented under which optimal orthonormal subband coders yield as much coding gain as biorthogonal ones for a fixed number of subbands

Orthonormal and biorthonormal filter banks as convolvers, and convolutional coding gain

Convolution theorems for filter bank transformers are introduced. Both uniform and nonuniform decimation ratios are considered, and orthonormal as well as biorthonormal cases are addressed. All the theorems are such that the original convolution reduces to a sum of shorter, decoupled convolutions in the subbands. That is, there is no need to have cross convolution between subbands. For the orthonormal case, expressions for optimal bit allocation and the optimized coding gain are derived. The contribution to coding gain comes partly from the nonuniformity of the signal spectrum and partly from nonuniformity of the filter spectrum. With one of the convolved sequences taken to be the unit pulse function,,e coding gain expressions reduce to those for traditional subband and transform coding. The filter-bank convolver has about the same computational complexity as a traditional convolver, if the analysis bank has small complexity compared to the convolution itself

Derivation of new and existing discrete-time Kharitonov theorems based on discrete-time reactances

The author first uses a discrete-time reactance approach to give a second proof of existing discrete-time Kharitonov-type results (1979). He then uses the same reactance language to derive a new discrete-time Kharitonov-type theorem which, in some sense, is a very close analog to the continuous-time case. He also points out the relation between discrete-time reactances and the technique of line-spectral pairs (LSP) used in speech compression

A new breakthrough in linear-system theory: Kharitonov's result

Given a real coefficient polynomial D(s), there exist several procedures for testing whether it is strictly Hurwitz (i.e., whether it has all its zeros in the open left-half plane). If the coefficients of D(s) are uncertain and belong to a known interval, such testing becomes more complicated because there is an infinitely large family of polynomials to which D(s) now belongs. It was shown by Kharitonov that in this case it is necessary and sufficient to test only four polynomials in order to know whether every polynomial in the family is strictly Hurwitz. An interpretation of this result in terms of reactance functions (i.e., LC impedances) was recently proposed. These results were also extended recently for the testing of positive real property of rational transfer functions with uncertain denominators. In this paper we review these results along with detailed proofs and discuss extensions to the discrete-time case

Perfect reconstruction QMF banks for two-dimensional applications

A theory is outlined whereby it is possible to design a M x N channel two-dimensional quadrature mirror filter bank which has perfect reconstruction property. Such a property ensures freedom from aliasing, amplitude distortion, and phase distortion. The method is based on a simple property of certain transfer matrices, namely the losslessness property

Genomics and proteomics: a signal processor's tour

The theory and methods of signal processing are becoming increasingly important in molecular biology. Digital filtering techniques, transform domain methods, and Markov models have played important roles in gene identification, biological sequence analysis, and alignment. This paper contains a brief review of molecular biology, followed by a review of the applications of signal processing theory. This includes the problem of gene finding using digital filtering, and the use of transform domain methods in the study of protein binding spots. The relatively new topic of noncoding genes, and the associated problem of identifying ncRNA buried in DNA sequences are also described. This includes a discussion of hidden Markov models and context free grammars. Several new directions in genomic signal processing are briefly outlined in the end

A note on general parallel QMF banks

Two issues concerning alias-free, parallel, quadrature mirror filter (QMF) banks are addressed in this correspondence. First, a property concerning alias-free analysis/synthesis systems is established; second, a scheme is proposed, by which a synthesis bank can be modified in order to take care of aliasing errors caused by linear channel-distortion in a simple manner. Applications of the stated results are outlined

Generalizations of the sampling theorem: Seven decades after Nyquist

The sampling theorem is one of the most basic and fascinating topics in engineering sciences. The most well-known form is Shannon's uniform-sampling theorem for bandlimited signals. Extensions of this to bandpass signals and multiband signals, and to nonuniform sampling are also well-known. The connection between such extensions and the theory of filter banks in DSP has been well established. This paper presents some of the less known aspects of sampling, with special emphasis on non bandlimited signals, pointwise stability of reconstruction, and reconstruction from nonuniform samples. Applications in multiresolution computation and in digital spline interpolation are also reviewed

On maximally-flat linear-phase FIR filters

An implementation for maximally-flat FIR filters is proposed that requires a much smaller number of multiplications than a direct form structure. The values of the multiplier coefficients in the implementation are conveniently small, and do not span a huge dynamic range, unlike in a direct form implementation