T. Kaper - Academia.edu (original) (raw)

Papers by T. Kaper

Research paper thumbnail of Structural studies of a glycoside hydrolase family 3 β-glucosidase from the model fungusNeurospora crassa

Acta Crystallographica Section F Structural Biology Communications, 2018

The glycoside hydrolase family 3 (GH3) β-glucosidases are a structurally diverse family of enzyme... more The glycoside hydrolase family 3 (GH3) β-glucosidases are a structurally diverse family of enzymes. Cel3A fromNeurospora crassa(NcCel3A) belongs to a subfamily of key enzymes that are crucial for industrial biomass degradation. β-Glucosidases hydrolyse the β-1,4 bond at the nonreducing end of cellodextrins. The hydrolysis of cellobiose is of special importance as its accumulation inhibits other cellulases acting on crystalline cellulose. Here, the crystal structure of the biologically relevant dimeric form ofNcCel3A is reported. The structure has been refined to 2.25 Å resolution, with anRcrystandRfreeof 0.18 and 0.22, respectively.NcCel3A is an extensively N-glycosylated glycoprotein that shares 46% sequence identity withHypocrea jecorinaCel3A, the structure of which has recently been published, and 61% sequence identity with the thermophilic β-glucosidase fromRasamsonia emersonii.NcCel3A is a three-domain protein with a number of extended loops that deepen the active-site cleft of...

Research paper thumbnail of Reduction for Michaelis-Menten-Henri kinetics in the presence of diffusion

The Michaelis-Menten-Henri (MMH) mechanism is one of the paradigm reaction mechanisms in biology ... more The Michaelis-Menten-Henri (MMH) mechanism is one of the paradigm reaction mechanisms in biology and chemistry. In its simplest form, it involves a substrate that reacts (reversibly) with an enzyme, forming a complex which is transformed (irreversibly) into a product and the enzyme. Given these basic kinetics, a dimension reduction has traditionally been achieved in two steps, by using conservation relations to reduce the number of species and by exploiting the inherent fast-slow structure of the resulting equations. In the present article, we investigate how the dynamics change if the species are additionally allowed to diffuse. We study the two extreme regimes of large diffusivities and of small diffusivities, as well as an intermediate regime in which the time scale of diffusion is comparable to that of the fast reaction kinetics. We show that reduction is possible in each of these regimes, with the nature of the reduction being regime dependent. Our analysis relies on the classical method of matched asymptotic expansions to derive approximations for the solutions that are uniformly valid in space and time.

Research paper thumbnail of Modelling, Analysis and Simulation Nonlinear asymptotic stability of the semi-strong pulse dynamics in a regularized Gierer-Meinhardt model

We use renormalization group (RG) techniques to prove the nonlinear asymptotic stability for the ... more We use renormalization group (RG) techniques to prove the nonlinear asymptotic stability for the semi-strong regime of two-pulse interactions in a regularized Gierer-Meinhardt system. In the semi-strong limit the strongly localized activator pulses interact through the weakly localized inhibitor, the interaction is not tail-tail as in the weak interaction limit, and the pulses change amplitude and even stability as their separation distance evolves on algebraically slow time scales. The RG approach employed here validates the interaction laws of quasi-steady pulse patterns obtained formally in the literature, and establishes that the pulse dynamics reduce to a closed system of ordinary differential equations for the activator pulse locations. Moreover, we fully justify the reduction to the nonlocal eigenvalue problem (NLEP) showing the large difference between the quasi-steady NLEP operator and the operator arising from linearization about the pulse is controlled by the resolvent. 2...

Research paper thumbnail of Spatially periodic and aperiodic multi-pulse patterns in the one-dimensional Gierer–Meinhardt equation

Methods and Applications of Analysis

Research paper thumbnail of Stationary periodic patterns in the 1D Gray–Scott model

Methods and Applications of Analysis, 2000

Research paper thumbnail of The stability of large pulse solutions in the generalized Gierer-Meinhardt equation

Research paper thumbnail of A note on two pulse solutions in the 1-D Gray-Scott model

Research paper thumbnail of New Developments in Dynamical Systems Arising from the Biosciences Preface

Research paper thumbnail of Global dynamics of a rapidly forced cart and pendulum

In this paper, we study emergent behaviors elicited by applying open-loop, high-frequency oscilla... more In this paper, we study emergent behaviors elicited by applying open-loop, high-frequency oscillatory forcing to nonlinear control systems. First, we study hovering motions, which are periodic orbits associated with stable fixed points of the averaged system which are not fixed points of the forced system. We use the method of successive approximations to establish the existence of hovering motions, as well as compute analytical approximations of their locations, for the cart and pendulum on an inclined plane. Moreover, when small-amplitude dissipation is added, we show that the hovering motions are asymptotically stable. We compare the results for all of the local analysis with results of simulating Poincaré maps. Second, we perform a complete global analysis on this cart and pendulum system. Toward this end, the same iteration scheme we use to establish the existence of the hovering periodic orbits also yields the existence of periodic orbits near saddle equilibria of the averaged system. These latter periodic orbits are shown to be saddle periodic orbits, and in turn they have stable and unstable manifolds that form homoclinic tangles. A quantitative global analysis of these tangles is carried out. Three distinguished limiting cases are analyzed. Melnikov theory is applied in one case, and an extension of a recent result about exponentially small splitting of separatrices is developed and applied in another case. Finally, the influence of small damping is studied. This global analysis is useful in the design of open-loop control laws.

Research paper thumbnail of Stationary periodic patterns in the 1D Gray-Scott model

Research paper thumbnail of Spatially periodic and aperiodic multi-pulse patterns in the one-dimensional Gierer-Meinhardt equation

Research paper thumbnail of Nonlinear Asymptotic Stability of the Semistrong Pulse Dynamics in a Regularized Gierer–Meinhardt Model

SIAM Journal on Mathematical Analysis, 2007

Research paper thumbnail of Canards of mixed type in a neural burster

Physical Review E, 2012

Canards are solutions of slow-fast systems that spend long times near branches of repelling equil... more Canards are solutions of slow-fast systems that spend long times near branches of repelling equilibria, periodic orbits, or higher-dimensional invariant sets. Here, we report on the observation of a new type of canard orbit, labeled a canard of mixed type. This canard orbit is a hybrid of the classical limit cycle canards, which spend long times near attracting and repelling branches of equilibria, and torus canards, which spend long times near attracting and repelling branches of periodic orbits. The canards of mixed type arise in a model of neural bursting activity of fold-fold cycle type, and, as other canard phenomena, separate different dynamic states.

Research paper thumbnail of Lobe area in adiabatic Hamiltonian systems

Physica D: Nonlinear Phenomena, 1991

Information Center is to provide broadest dissemination possiof information contained in DOE's Re... more Information Center is to provide broadest dissemination possiof information contained in DOE's Research and Development Reports to business, industry, the academic community, and federal, state and local governments. Although a small portion of this report is not reproducible, it is being made available to expedite the availability of information on the research discussed herein.

Research paper thumbnail of Pattern formation in the one-dimensional Gray - Scott model

Research paper thumbnail of Pulse Dynamics in a Three-Component System: Existence Analysis

Journal of Dynamics and Differential Equations, 2009

Research paper thumbnail of Analysis of the accuracy and convergence of equation-free projection to a slow manifold

ESAIM: Mathematical Modelling and Numerical Analysis, 2009

Research paper thumbnail of Stability and stabilization of the constrained runs schemes for equation-free projection to a slow manifold

Discrete and Continuous Dynamical Systems, 2012

Research paper thumbnail of Stability and stabilization of the constrained runs schemes for equation-free projection to a slow manifold

Research paper thumbnail of Analysis of the accuracy and convergence of equation-free projection to a slow manifold

Research paper thumbnail of Structural studies of a glycoside hydrolase family 3 β-glucosidase from the model fungusNeurospora crassa

Acta Crystallographica Section F Structural Biology Communications, 2018

The glycoside hydrolase family 3 (GH3) β-glucosidases are a structurally diverse family of enzyme... more The glycoside hydrolase family 3 (GH3) β-glucosidases are a structurally diverse family of enzymes. Cel3A fromNeurospora crassa(NcCel3A) belongs to a subfamily of key enzymes that are crucial for industrial biomass degradation. β-Glucosidases hydrolyse the β-1,4 bond at the nonreducing end of cellodextrins. The hydrolysis of cellobiose is of special importance as its accumulation inhibits other cellulases acting on crystalline cellulose. Here, the crystal structure of the biologically relevant dimeric form ofNcCel3A is reported. The structure has been refined to 2.25 Å resolution, with anRcrystandRfreeof 0.18 and 0.22, respectively.NcCel3A is an extensively N-glycosylated glycoprotein that shares 46% sequence identity withHypocrea jecorinaCel3A, the structure of which has recently been published, and 61% sequence identity with the thermophilic β-glucosidase fromRasamsonia emersonii.NcCel3A is a three-domain protein with a number of extended loops that deepen the active-site cleft of...

Research paper thumbnail of Reduction for Michaelis-Menten-Henri kinetics in the presence of diffusion

The Michaelis-Menten-Henri (MMH) mechanism is one of the paradigm reaction mechanisms in biology ... more The Michaelis-Menten-Henri (MMH) mechanism is one of the paradigm reaction mechanisms in biology and chemistry. In its simplest form, it involves a substrate that reacts (reversibly) with an enzyme, forming a complex which is transformed (irreversibly) into a product and the enzyme. Given these basic kinetics, a dimension reduction has traditionally been achieved in two steps, by using conservation relations to reduce the number of species and by exploiting the inherent fast-slow structure of the resulting equations. In the present article, we investigate how the dynamics change if the species are additionally allowed to diffuse. We study the two extreme regimes of large diffusivities and of small diffusivities, as well as an intermediate regime in which the time scale of diffusion is comparable to that of the fast reaction kinetics. We show that reduction is possible in each of these regimes, with the nature of the reduction being regime dependent. Our analysis relies on the classical method of matched asymptotic expansions to derive approximations for the solutions that are uniformly valid in space and time.

Research paper thumbnail of Modelling, Analysis and Simulation Nonlinear asymptotic stability of the semi-strong pulse dynamics in a regularized Gierer-Meinhardt model

We use renormalization group (RG) techniques to prove the nonlinear asymptotic stability for the ... more We use renormalization group (RG) techniques to prove the nonlinear asymptotic stability for the semi-strong regime of two-pulse interactions in a regularized Gierer-Meinhardt system. In the semi-strong limit the strongly localized activator pulses interact through the weakly localized inhibitor, the interaction is not tail-tail as in the weak interaction limit, and the pulses change amplitude and even stability as their separation distance evolves on algebraically slow time scales. The RG approach employed here validates the interaction laws of quasi-steady pulse patterns obtained formally in the literature, and establishes that the pulse dynamics reduce to a closed system of ordinary differential equations for the activator pulse locations. Moreover, we fully justify the reduction to the nonlocal eigenvalue problem (NLEP) showing the large difference between the quasi-steady NLEP operator and the operator arising from linearization about the pulse is controlled by the resolvent. 2...

Research paper thumbnail of Spatially periodic and aperiodic multi-pulse patterns in the one-dimensional Gierer–Meinhardt equation

Methods and Applications of Analysis

Research paper thumbnail of Stationary periodic patterns in the 1D Gray–Scott model

Methods and Applications of Analysis, 2000

Research paper thumbnail of The stability of large pulse solutions in the generalized Gierer-Meinhardt equation

Research paper thumbnail of A note on two pulse solutions in the 1-D Gray-Scott model

Research paper thumbnail of New Developments in Dynamical Systems Arising from the Biosciences Preface

Research paper thumbnail of Global dynamics of a rapidly forced cart and pendulum

In this paper, we study emergent behaviors elicited by applying open-loop, high-frequency oscilla... more In this paper, we study emergent behaviors elicited by applying open-loop, high-frequency oscillatory forcing to nonlinear control systems. First, we study hovering motions, which are periodic orbits associated with stable fixed points of the averaged system which are not fixed points of the forced system. We use the method of successive approximations to establish the existence of hovering motions, as well as compute analytical approximations of their locations, for the cart and pendulum on an inclined plane. Moreover, when small-amplitude dissipation is added, we show that the hovering motions are asymptotically stable. We compare the results for all of the local analysis with results of simulating Poincaré maps. Second, we perform a complete global analysis on this cart and pendulum system. Toward this end, the same iteration scheme we use to establish the existence of the hovering periodic orbits also yields the existence of periodic orbits near saddle equilibria of the averaged system. These latter periodic orbits are shown to be saddle periodic orbits, and in turn they have stable and unstable manifolds that form homoclinic tangles. A quantitative global analysis of these tangles is carried out. Three distinguished limiting cases are analyzed. Melnikov theory is applied in one case, and an extension of a recent result about exponentially small splitting of separatrices is developed and applied in another case. Finally, the influence of small damping is studied. This global analysis is useful in the design of open-loop control laws.

Research paper thumbnail of Stationary periodic patterns in the 1D Gray-Scott model

Research paper thumbnail of Spatially periodic and aperiodic multi-pulse patterns in the one-dimensional Gierer-Meinhardt equation

Research paper thumbnail of Nonlinear Asymptotic Stability of the Semistrong Pulse Dynamics in a Regularized Gierer–Meinhardt Model

SIAM Journal on Mathematical Analysis, 2007

Research paper thumbnail of Canards of mixed type in a neural burster

Physical Review E, 2012

Canards are solutions of slow-fast systems that spend long times near branches of repelling equil... more Canards are solutions of slow-fast systems that spend long times near branches of repelling equilibria, periodic orbits, or higher-dimensional invariant sets. Here, we report on the observation of a new type of canard orbit, labeled a canard of mixed type. This canard orbit is a hybrid of the classical limit cycle canards, which spend long times near attracting and repelling branches of equilibria, and torus canards, which spend long times near attracting and repelling branches of periodic orbits. The canards of mixed type arise in a model of neural bursting activity of fold-fold cycle type, and, as other canard phenomena, separate different dynamic states.

Research paper thumbnail of Lobe area in adiabatic Hamiltonian systems

Physica D: Nonlinear Phenomena, 1991

Information Center is to provide broadest dissemination possiof information contained in DOE's Re... more Information Center is to provide broadest dissemination possiof information contained in DOE's Research and Development Reports to business, industry, the academic community, and federal, state and local governments. Although a small portion of this report is not reproducible, it is being made available to expedite the availability of information on the research discussed herein.

Research paper thumbnail of Pattern formation in the one-dimensional Gray - Scott model

Research paper thumbnail of Pulse Dynamics in a Three-Component System: Existence Analysis

Journal of Dynamics and Differential Equations, 2009

Research paper thumbnail of Analysis of the accuracy and convergence of equation-free projection to a slow manifold

ESAIM: Mathematical Modelling and Numerical Analysis, 2009

Research paper thumbnail of Stability and stabilization of the constrained runs schemes for equation-free projection to a slow manifold

Discrete and Continuous Dynamical Systems, 2012

Research paper thumbnail of Stability and stabilization of the constrained runs schemes for equation-free projection to a slow manifold

Research paper thumbnail of Analysis of the accuracy and convergence of equation-free projection to a slow manifold