Generalisation of the Perron–Frobenius theory to matrix pencils

AbstractWe present a new extension of the well-known Perron–Frobenius theorem to regular matrix pairs (E, A). The new extension is based on projector chains and is motivated from the solution of positive differential-algebraic systems or descriptor systems. We present several examples where the new condition holds, whereas conditions in previous literature are not satisfied

Bounded real lemmas for positive descriptor systems

A well known result in the theory of linear positive systems is the existence of positive definite diagonal matrix (PDDM) solutions to some well known linear matrix inequalities (LMIs). In this paper, based on the positivity characterization, a novel bounded real lemma for continuous positive descriptor systems in terms of strict LMI is first established by the separating hyperplane theorem. The result developed here provides a necessary and sufficient condition for systems to possess H?H? norm less than ? and shows the existence of PDDM solution. Moreover, under certain condition, a simple model reduction method is introduced, which can preserve positivity, stability and H?H? norm of the original systems. An advantage of such method is that systems? matrices of the reduced order systems do not involve solving of LMIs conditions. Then, the obtained results are extended to discrete case. Finally, a numerical example is given to illustrate the effectiveness of the obtained results

A direct method to obtain a realization of a polynomial matrix and its applications

[EN] In this paper we present a Silverman-Ho algorithm-based method to obtain a realization of a polynomial matrix. This method provides the final formulation of a minimal realization directly from a full rank factorization of a specific given matrix. Also, some classical problems in control theory such as model reduction in singular systems or the positive realization problem in standard systems are solved with this method.Work supported by the Spanish DGI grant MTM2017-85669-P-AR.Cantó Colomina, R.; Moll López, SE.; Ricarte Benedito, B.; Urbano Salvador, AM. (2020). A direct method to obtain a realization of a polynomial matrix and its applications. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(2):1-15. https://doi.org/10.1007/s13398-020-00819-1S1151142Anderson, B.D.O., Bongpanitlerd, S.: Network Analysis and Synthesis, A Modern Systems Theory Approach. Prentice-Hall Inc., New Jersey (1968)Benvenuti, L., Farina, L.: A tutorial on the positive realization problem. IEEE Trans. Autom. Control 49(5), 651–664 (2004). https://doi.org/10.1109/TAC.2004.826715Bru, R., Coll, C., Sánchez, E.: Structural properties of positive linear time-invariant difference-algebraic equations. Linear Algebra Appl. 349, 1–10 (2002). https://doi.org/10.1016/S0024-3795(02)00277-XCantó, R., Ricarte, B., Urbano, A.M.: Positive realizations of transfer matrices with real poles. IEEE Trans. Circuits Syst. II Expr. Br. 54(6), 517–521 (2007). https://doi.org/10.1109/TCSII.2007.894408Cantó, R., Ricarte, B., Urbano, A.M.: On positivity of discrete-time singular systems and the realization problem. Lect. Notes Control Inf. Sci. 389, 251–258 (2009). https://doi.org/10.1007/978-3-642-02894-6_24Climent, J., Napp, D., Requena, V.: Block Toeplitz matrices for burst-correcting convolutional codes. RACSAM 114, 38 (2020). https://doi.org/10.1007/s13398-019-00744-yDai, L.: Singular Control Systems. Lecture Notes in Control and Information Sciences. Springer-Verlag, New York (1989)Golub, G.H., Van Loan, C.F.: Matrix Computations, Fourth edn. Johns Hopkins University Press, Baltimore (2013)Henrion, D., Šebek, M.: Polynomial and matrix fraction description. In: Control Systems, Robotics and Automation, vol. 7, pp. 211-231, (2009). http://www.eolss.net/Sample-Chapters/C18/E6-43-13-05.pdfHo, B.L., Kalman, R.E.: Effective construction of linear state-variable models from mput/output functions. Regelungstechnik 14(12), 545–548 (1966)Kaczorek, T.: Weakly positive continuous-time linear systems. Lect. Notes Control Inf. Sci. 243, 3–16 (1999)Kaczorek, T.: Positive 1D and 2D Systems, vol. 431. Springer, London (2002)Kaczorek, T.: Externally and internally positive singular discrete-time linear systems. Int. J. Appl. Math. Comput. Sci. 12(2), 197–202 (2002)MATLAB, The Math Works, Inc., Natick, Massachusetts, United States. Official website: http://www.mathworks.comMcCrory, C., Parusinski, A.: The weight filtration for real algebraic varieties II: classical homology. RACSAM 108, 63–94 (2014). https://doi.org/10.1007/s13398-012-0098-ySilverman, L.: Realization of linear dynamical systems. IEEE Trans. Autom. Control 16(6), 554–567 (1971)Virnik, E.: Stability analysis of positive descriptor systems. Linear Algebra Appl. 429(10), 2640–2659 (2008

Ketorolak-dekstran konjugati: sinteza, in vitro i in vivo vrednovanje

Ketorolac is a non-steroidal anti-inflammatory drug. Dextran conjugates of ketorolac (KD) were synthesized and characterized to improve ketorolac aqueous solubility and reduce gastrointestinal side effects. An N-acylimidazole derivative of ketorolac (KAI) was condensed with a model carrier polymer, dextran of different molecular masses (40000, 60000, 110000 and 200000). IR spectral data confirmed formation of ester bonding. Ketorolac contents were evaluated by UV-spectrophotometric analysis. The molecular mass was determined by measuring viscosity using the Mark-Howink-Sakurada equation. In vitro hydrolysis studies were performed in aqueous buffers (pH 1.2, 7.4, 9) and in 80% (V/V) human plasma (pH 7.4). At pH 9, a higher rate of ketorolac release from KD was observed as compared to aqueous buffer of pH 7.4 and 80% human plasma (pH 7.4), following first-order kinetics. In vivo biological screening in mice and rats indicated that conjugates retained analgesic and anti-inflammatory activities with significantly reduced ulcerogenicity compared to the parent drug.U radu je opisana sinteza konjugata dektrana i protuupalnog lijeka ketorolaka (KD). Konjugati su pripravljeni da bi se povećala topljivost ketorolaka u vodi i smanjila njegova nusdjelovanja u gastrointestinanom traktu. Ketorak je prvo preveden u N-acilimidazolni derivat (KAI) koji je kondenziran s polimernim nosačem, dekstranom različitih molekulskih masa (40000, 60000, 110000 i 200000). IR-spektri potvrdili su nastajanje esterske veze. Udio ketorolaka u konjugatu određen je UV-spektrofotometrijskom analizom. Molekulske mase određene su mjerenjem viskoznosti koristeći Mark-Howink-Sakurada jednadžbu. Hidroliza in vitro praćena je u puferskim otopinama (pH 1,2, 7,4 i 9) i u 80% V/V humanoj plazmi (pH 7,4). Pri pH 9 primjećeno je značajno brže oslobađanje ketorolaka iz KD nego u puferskoj otopini pH 7,4 i krvnoj plazmi. Oslobađanje je prati kinetiku prvog reda. In vivo biološka ispitivanja na miševima i štakorima ukazuju da konjugati imaju analgetsko i protuupalno djelovanje, a značajno smanjeno ulcerogeno djelovanje

The antiparallel loops in gal DNA

Interactions between proteins bound to distant sites along a DNA molecule require bending and twisting deformations in the intervening DNA. In certain systems, the sterically allowed protein–DNA and protein–protein interactions are hypothesized to produce loops with distinct geometries that may also be thermodynamically and biologically distinct. For example, theoretical models of Gal repressor/HU-mediated DNA-looping suggest that the antiparallel DNA loops, A1 and A2, are thermodynamically quite different. They are also biologically different, since in experiments using DNA molecules engineered to form only one of the two loops, the A2 loop failed to repress in vitro transcription. Surprisingly, single molecule measurements show that both loop trajectories form and that they appear to be quite similar energetically and kinetically

The replication of plastid minicircles involves rolling circle intermediates

Plastid genomes of peridinin-containing dinoflagellates are unique in that its genes are found on multiple circular DNA molecules known as ‘minicircles’ of ∼2–3 kb in size, carrying from one to three genes. The non-coding regions (NCRs) of these minicircles share a conserved core region (250–500 bp) that are AT-rich and have several inverted or direct repeats. Southern blot analysis using an NCR probe, after resolving a dinoflagellate whole DNA extract in pulsed-field gel electrophoresis (PFGE), revealed additional positive bands (APBs) of 6–8 kb in size. APBs preferentially diminished from cells treated with the DNA-replication inhibitor aphidicolin, when compared with 2–3 kb minicircles, implicating they are not large minicircles. The APBs are also exonuclease III-sensitive, implicating the presence of linear DNA. These properties and the migration pattern of the APBs in a 2D-gel electrophoresis were in agreement with a rolling circle type of replication, rather than the bubble-forming type. Atomic force microscopy of 6–8 kb DNA separated by PFGE revealed DNA intermediates with rolling circle shapes. Accumulating data thus supports the involvement of rolling circle intermediates in the replication of the minicircles

The replication of plastid minicircles involves rolling circle intermediates

Plastid genomes of peridinin-containing dinoflagellates are unique in that its genes are found on multiple circular DNA molecules known as ‘minicircles’ of ∼2–3 kb in size, carrying from one to three genes. The non-coding regions (NCRs) of these minicircles share a conserved core region (250–500 bp) that are AT-rich and have several inverted or direct repeats. Southern blot analysis using an NCR probe, after resolving a dinoflagellate whole DNA extract in pulsed-field gel electrophoresis (PFGE), revealed additional positive bands (APBs) of 6–8 kb in size. APBs preferentially diminished from cells treated with the DNA-replication inhibitor aphidicolin, when compared with 2–3 kb minicircles, implicating they are not large minicircles. The APBs are also exonuclease III-sensitive, implicating the presence of linear DNA. These properties and the migration pattern of the APBs in a 2D-gel electrophoresis were in agreement with a rolling circle type of replication, rather than the bubble-forming type. Atomic force microscopy of 6–8 kb DNA separated by PFGE revealed DNA intermediates with rolling circle shapes. Accumulating data thus supports the involvement of rolling circle intermediates in the replication of the minicircles

Interplay of Protein and DNA Structure Revealed in Simulations of the lac Operon

The E. coli Lac repressor is the classic textbook example of a protein that attaches to widely spaced sites along a genome and forces the intervening DNA into a loop. The short loops implicated in the regulation of the lac operon suggest the involvement of factors other than DNA and repressor in gene control. The molecular simulations presented here examine two likely structural contributions to the in-vivo looping of bacterial DNA: the distortions of the double helix introduced upon association of the highly abundant, nonspecific nucleoid protein HU and the large-scale deformations of the repressor detected in low-resolution experiments. The computations take account of the three-dimensional arrangements of nucleotides and amino acids found in crystal structures of DNA with the two proteins, the natural rest state and deformational properties of protein-free DNA, and the constraints on looping imposed by the conformation of the repressor and the orientation of bound DNA. The predicted looping propensities capture the complex, chain-length-dependent variation in repression efficacy extracted from gene expression studies and in vitro experiments and reveal unexpected chain-length-dependent variations in the uptake of HU, the deformation of repressor, and the folding of DNA. Both the opening of repressor and the presence of HU, at levels approximating those found in vivo, enhance the probability of loop formation. HU affects the global organization of the repressor and the opening of repressor influences the levels of HU binding to DNA. The length of the loop determines whether the DNA adopts antiparallel or parallel orientations on the repressor, whether the repressor is opened or closed, and how many HU molecules bind to the loop. The collective behavior of proteins and DNA is greater than the sum of the parts and hints of ways in which multiple proteins may coordinate the packaging and processing of genetic information. © 2013 Czapla et al

Do Femtonewton Forces Affect Genetic Function? A Review

Protein-Mediated DNA looping is intricately related to gene expression. Therefore any mechanical constraint that disrupts loop formation can play a significant role in gene regulation. Polymer physics models predict that less than a piconewton of force may be sufficient to prevent the formation of DNA loops. Thus, it appears that tension can act as a molecular switch that controls the much larger forces associated with the processive motion of RNA polymerase. Since RNAP can exert forces over 20 pN before it stalls, a ‘substrate tension switch’ could offer a force advantage of two orders of magnitude. Evidence for such a mechanism is seen in recent in vitro micromanipulation experiments. In this article we provide new perspective on existing theory and experimental data on DNA looping in vitro and in vivo . We elaborate on the connection between tension and a variety of other intracellular mechanical constraints including sequence specific curvature and supercoiling. In the process, we emphasize that the richness and versatility of DNA mechanics opens up a whole new paradigm of gene regulation to explore.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41816/1/10867_2005_Article_9002.pd