scholarly journals Erratum to “Writhe of DNA induced by a terminal twist” [Bull. Math. Biol. 67 (2005) 197–209]

2005 ◽  
Vol 67 (5) ◽  
pp. 1155-1155 ◽  
Author(s):  
K HU
Keyword(s):  
Math Biol

scholarly journals An Inverse Problem Involving a Viscous Eikonal Equation with Applications in Electrophysiology

2021 ◽  
Author(s):  
Karl Kunisch ◽  
Philip Trautmann
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Eikonal Equation ◽  
State Equation ◽  
High Accuracy ◽  
Well Posedness ◽  
Numerical Examples ◽  
Marquardt Method ◽  
Math Biol ◽  
Levenberg Marquardt

AbstractIn this work we discuss the reconstruction of cardiac activation instants based on a viscous Eikonal equation from boundary observations. The problem is formulated as a least squares problem and solved by a projected version of the Levenberg–Marquardt method. Moreover, we analyze the well-posedness of the state equation and derive the gradient of the least squares functional with respect to the activation instants. In the numerical examples we also conduct an experiment in which the location of the activation sites and the activation instants are reconstructed jointly based on an adapted version of the shape gradient method from (J. Math. Biol. 79, 2033–2068, 2019). We are able to reconstruct the activation instants as well as the locations of the activations with high accuracy relative to the noise level.

scholarly journals Emergence of protocellular growth laws

2007 ◽  
Vol 362 (1486) ◽  
pp. 1841-1845 ◽  
Author(s):  
Tristan Rocheleau ◽  
Steen Rasmussen ◽  
Peter E Nielsen ◽  
Martin N Jacobi ◽  
Hans Ziock
Keyword(s):  
Kinetic Studies ◽  
Product Inhibition ◽  
Replication Process ◽  
Gene Replication ◽  
Math Biol ◽  
Curr Opin Cell Biol ◽  
Growth Laws ◽  
Internal Gene ◽  
The Many ◽  
The Individual

Template-directed replication is known to obey a parabolic growth law due to product inhibition (Sievers & Von Kiedrowski 1994 Nature 369 , 221; Lee et al . 1996 Nature 382 , 525; Varga & Szathmáry 1997 Bull. Math. Biol . 59 , 1145). We investigate a template-directed replication with a coupled template catalysed lipid aggregate production as a model of a minimal protocell and show analytically that the autocatalytic template–container feedback ensures balanced exponential replication kinetics; both the genes and the container grow exponentially with the same exponent. The parabolic gene replication does not limit the protocellular growth, and a detailed stoichiometric control of the individual protocell components is not necessary to ensure a balanced gene–container growth as conjectured by various authors (Gánti 2004 Chemoton theory ). Our analysis also suggests that the exponential growth of most modern biological systems emerges from the inherent spatial quality of the container replication process as we show analytically how the internal gene and metabolic kinetics determine the cell population's generation time and not the growth law (Burdett & Kirkwood 1983 J. Theor. Biol . 103 , 11–20; Novak et al . 1998 Biophys. Chem . 72 , 185–200; Tyson et al . 2003 Curr. Opin. Cell Biol . 15 , 221–231). Previous extensive replication reaction kinetic studies have mainly focused on template replication and have not included a coupling to metabolic container dynamics (Stadler et al . 2000 Bull. Math. Biol . 62 , 1061–1086; Stadler & Stadler 2003 Adv. Comp. Syst . 6 , 47). The reported results extend these investigations. Finally, the coordinated exponential gene–container growth law stemming from catalysis is an encouraging circumstance for the many experimental groups currently engaged in assembling self-replicating minimal artificial cells (Szostak 2001 et al . Nature 409 , 387–390; Pohorille & Deamer 2002 Trends Biotech . 20 123–128; Rasmussen et al . 2004 Science 303 , 963–965; Szathmáry 2005 Nature 433 , 469–470; Luisi et al . 2006 Naturwissenschaften 93 , 1–13). 1

scholarly journals Generalized principal eigenvalues for heterogeneous road–field systems

2019 ◽  
Vol 22 (01) ◽  
pp. 1950013 ◽  
Author(s):  
Henri Berestycki ◽  
Romain Ducasse ◽  
Luca Rossi
Keyword(s):  
Nonlinear Evolution Equation ◽  
Ecological Niche ◽  
Nonlinear Evolution ◽  
Principal Eigenvalue ◽  
Reaction Diffusion ◽  
Fast Diffusion ◽  
Reaction Diffusion Model ◽  
Math Biol ◽  
Field Systems ◽  
System Coupling

This paper develops the notion and properties of the generalized principal eigenvalue for an elliptic system coupling an equation in a plane with one on a line in this plane, together with boundary conditions that express exchanges taking place between the plane and the line. This study is motivated by the reaction–diffusion model introduced by Berestycki, Roquejoffre and Rossi [The influence of a line with fast diffusion on Fisher–KPP propagation, J. Math. Biol. 66(4–5) (2013) 743–766] to describe the effect on biological invasions of networks with fast diffusion imbedded in a field. Here we study the eigenvalue associated with heterogeneous generalizations of this model. In a forthcoming work [Influence of a line with fast diffusion on an ecological niche, preprint (2018)] we show that persistence or extinction of the associated nonlinear evolution equation is fully accounted for by this generalized eigenvalue. A key element in the proofs is a new Harnack inequality that we establish for these systems and which is of independent interest.

scholarly journals STATIONARY SOLUTIONS TO FOREST KINEMATIC MODEL

2009 ◽  
Vol 51 (1) ◽  
pp. 1-17 ◽  
Author(s):  
LE HUY CHUAN ◽  
TOHRU TSUJIKAWA ◽  
ATSUSHI YAGI
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Infinite Number ◽  
Kinematic Model ◽  
Stationary Solutions ◽  
Cross Diffusion ◽  
Stability And Instability ◽  
Math Biol ◽  
Forest Boundary ◽  
Boundary Dynamics

AbstractWe continue the study of a mathematical model for a forest ecosystem which has been presented by Y. A. Kuznetsov, M. Y. Antonovsky, V. N. Biktashev and A. Aponina (A cross-diffusion model of forest boundary dynamics, J. Math. Biol. 32 (1994), 219–232). In the preceding two papers (L. H. Chuan and A. Yagi, Dynamical systemfor forest kinematic model, Adv. Math. Sci. Appl. 16 (2006), 393–409; L. H. Chuan, T. Tsujikawa and A. Yagi, Aysmptotic behavior of solutions for forest kinematic model, Funkcial. Ekvac. 49 (2006), 427–449), the present authors already constructed a dynamical system and investigated asymptotic behaviour of trajectories of the dynamical system. This paper is then devoted to studying not only the structure (including stability and instability) of homogeneous stationary solutions but also the existence of inhomogeneous stationary solutions. Especially it shall be shown that in some cases, one can construct an infinite number of discontinuous stationary solutions.

Average conditions for permanence and extinction in nonautonomous single-species Kolmogorov systems

2017 ◽  
Vol 10 (02) ◽  
pp. 1750028
Author(s):  
Jiandong Zhao ◽  
Zhenzhen Chen
Keyword(s):  
Global Attractivity ◽  
Single Species ◽  
Logistic Equation ◽  
Math Biol ◽  
Kolmogorov System ◽  
Generalized Logistic Equation

The nonautonomous single-species Kolmogorov system is studied in this paper. Average conditions are obtained for permanence, global attractivity and extinction in the system. Applications of our main results to logistic equation and generalized logistic equation are given. It is shown that our average conditions are improvement of those in Vance and Coddington [J. Math. Biol. 27 (1989) 491–506] and some published literature on the system.

scholarly journals Amendment to: populations in environments with a soft carrying capacity are eventually extinct

2021 ◽  
Vol 83 (1) ◽  
Author(s):  
Peter Jagers ◽  
Sergei Zuyev
Keyword(s):  
Population Size ◽  
Conditional Probability ◽  
Carrying Capacity ◽  
Population History ◽  
Random Time ◽  
Time Points ◽  
The Past ◽  
Population Decrease ◽  
Math Biol ◽  
Past Population

AbstractThis sharpens the result in the paper Jagers and Zuyev (J Math Biol 81:845–851, 2020): consider a population changing at discrete (but arbitrary and possibly random) time points, the conditional expected change, given the complete past population history being negative, whenever population size exceeds a carrying capacity. Further assume that there is an $$\epsilon > 0$$ ϵ > 0 such that the conditional probability of a population decrease at the next step, given the past, always exceeds $$\epsilon $$ ϵ if the population is not extinct but smaller than the carrying capacity. Then the population must die out.

Decay bounds in a model for aggregation of microglia: application to Alzheimer's disease senile plaques

2005 ◽  
Vol 461 (2061) ◽  
pp. 2887-2897 ◽  
Author(s):  
R.A Quinlan ◽  
B Straughan
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Senile Plaques ◽  
Three Dimensional ◽  
Amyloid Plaques ◽  
Cell System ◽  
Biological Parameters ◽  
Math Biol ◽  
Decay Bounds ◽  
Spatial Domains

We present a model for chemotaxis, as applied to the aggregation of microglia in Alzheimer's disease. Using biological parameters found in the literature, testable thresholds are derived such that amyloid plaques are predicted not to form if conditions fall below a threshold. The model we use was developed by Luca et al . (Luca et al . 2003 Bull. Math. Biol. 65 , 693–730) and incorporates terms for both attractant and repellent signals. Our analysis can be applied to both two and three-dimensional spatial domains with application to any cell system involving chemotaxis.

scholarly journals Equivalence classes of circular codes induced by permutation groups

2021 ◽  
Vol 140 (1) ◽  
pp. 107-121
Author(s):  
Fariba Fayazi ◽  
Elena Fimmel ◽  
Lutz Strüngmann
Keyword(s):  
Protein A ◽  
Algebraic Approach ◽  
Equivalence Classes ◽  
Finite Alphabet ◽  
Reading Frame ◽  
Biological Reality ◽  
Math Biol ◽  
Circular Codes ◽  
Circular Code ◽  
Translational Process

AbstractIn the 1950s, Crick proposed the concept of so-called comma-free codes as an answer to the frame-shift problem that biologists have encountered when studying the process of translating a sequence of nucleotide bases into a protein. A little later it turned out that this proposal unfortunately does not correspond to biological reality. However, in the mid-90s, a weaker version of comma-free codes, so-called circular codes, was discovered in nature in J Theor Biol 182:45–58, 1996. Circular codes allow to retrieve the reading frame during the translational process in the ribosome and surprisingly the circular code discovered in nature is even circular in all three possible reading-frames ($$C^3$$ C 3 -property). Moreover, it is maximal in the sense that it contains 20 codons and is self-complementary which means that it consists of pairs of codons and corresponding anticodons. In further investigations, it was found that there are exactly 216 codes that have the same strong properties as the originally found code from J Theor Biol 182:45–58. Using an algebraic approach, it was shown in J Math Biol, 2004 that the class of 216 maximal self-complementary $$C^3$$ C 3 -codes can be partitioned into 27 equally sized equivalence classes by the action of a transformation group $$L \subseteq S_4$$ L ⊆ S 4 which is isomorphic to the dihedral group. Here, we extend the above findings to circular codes over a finite alphabet of even cardinality $$|\Sigma |=2n$$ | Σ | = 2 n for $$n \in {\mathbb {N}}$$ n ∈ N . We describe the corresponding group $$L_n$$ L n using matrices and we investigate what classes of circular codes are split into equally sized equivalence classes under the natural equivalence relation induced by $$L_n$$ L n . Surprisingly, this is not always the case. All results and constructions are illustrated by examples.

Inner medullary lactate production and accumulation: a vasa recta model

2000 ◽  
Vol 279 (3) ◽  
pp. F468-F481 ◽  
Author(s):  
S. Randall Thomas
Keyword(s):  
Lactate Production ◽  
Experimental Tests ◽  
Anaerobic Glycolysis ◽  
Axial Distribution ◽  
Tissue Mass ◽  
Glucose Depletion ◽  
Vasa Recta ◽  
Math Biol ◽  
Plausible Values ◽  
Single Effect

Since anaerobic glycolysis yields two lactates for each glucose consumed and since it is reported to be a major source of ATP for inner medullary (IM) cell maintenance, it is a likely source of “external” IM osmoles. It has long been known that such an osmole source could theoretically contribute to the “single-effect” of the urine concentrating mechanism, but there was previously no suggestion of a plausible source. I used numerical simulation to estimate axial gradients of lactate and glucose that might be accumulated by countercurrent recycling in IM vasa recta (IMVR). Based on measurements in other tissues, anaerobic glycolysis (assumed to be independent of diuretic state) was estimated to consume ∼20% of the glucose delivered to the IM. IM tissue mass and axial distribution of loops and vasa recta were according to reported values for rat and other rodents. Lactate ( P LAC) and glucose ( P GLU) permeabilities were varied over a range of plausible values. The model results suggest that P LAC of 100 × 10−5 cm/s (similar to measured permeabilities for other small solutes) is sufficiently high to ensure efficient lactate recycling. By contrast, it was necessary in the model to reduce P GLU to a small fraction of this value (1/25th) to avoid papillary glucose depletion by countercurrent shunting. The results predict that IM lactate production could suffice to build a significant steady-state axial lactate gradient in the IM interstitium. Other modeling studies (Jen JF and Stephenson JL. Bull Math Biol 56: 491–514, 1994; and Thomas SR and Wexler AS. Am J Physiol Renal Fluid Electrolyte Physiol 269: F159–F171, 1995) have shown that 20–100 mosmol/kgH2O of unspecified external, interstitial, osmolytes could greatly improve IM concentrating ability. The present study gives several plausible scenarios consistent with accumulation of metabolically produced lactate osmoles, although only to the lower end of this range. For example, if 20% of entering glucose is consumed, the model predicts that papillary lactate would attain about 15 mM assuming vasa recta outflow is increased 30% by fluid absorbed from the nephrons and collecting ducts and that this lactate gradient would double if IM blood flow were reduced by one-half, as may occur in antidiuresis. Several experimental tests of the hypothesis are indicated.

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