The still-open problem of the variety of asymptotic solutions to one-variable, one-dimensional in... more The still-open problem of the variety of asymptotic solutions to one-variable, one-dimensional infinite multistable reaction-diffusion systems is solved. We show that in such systems, besides monotonic traveling fronts, nonmonotonic traveling fronts can exist for appropriate initial conditions. The dependence of numbers of various types of traveling fronts on the number of stable stationary states also is given. Examples of traveling fronts for the chemical model describing two enzymatic (catalytic) reactions inhibited by an excess of their reactant is presented.
Periodic spatiotemporal two-dimensional (2D) asymptotic patterns in an excitable two-variable the... more Periodic spatiotemporal two-dimensional (2D) asymptotic patterns in an excitable two-variable thermochemical (reaction-diffusion) system are shown. In a one-dimensional system the traveling impulse which reflects from impermeable boundaries is a stable asymptotic solution if the diffusion coefficient of the reactant is greater than the thermal diffusivity of the system. Periodic patterns of two symmetries are presented in the 2D system: the impulse of excitation propagating along the diagonal of a square spatial domain and a structure consisting of curved impulses which propagate in the direction perpendicular to one side of a rectangular domain.
To initiate directed movement, cells must become polarized, establishing a protrusive leading edg... more To initiate directed movement, cells must become polarized, establishing a protrusive leading edge and a contractile trailing edge. This symmetry-breaking process involves reorganization of cytoskeleton and asymmetric distribution of regulatory molecules. However, what triggers and maintains this asymmetry during cell migration remains largely elusive. Here, we established a micropatterning-based 1D motility assay to investigate the molecular basis of symmetry breaking required for directed cell migration. We show that microtubule (MT) detyrosination drives cell polarization by directing kinesin-1-based transport of the adenomatous polyposis coli (APC) protein to cortical sites. This is essential for the formation of cell's leading edge during 1D and 3D cell migration. These data, combined with biophysical modeling, unveil a key role for MT detyrosination in the generation of a positive feedback loop linking MT dynamics and kinesin-1-based transport. Thus, symmetry breaking during cell polarization relies on a feedback loop driven by MT detyrosination that supports directed cell migration.
Many cells can generate complementary traveling waves of actin filaments (F-actin) and cytoskelet... more Many cells can generate complementary traveling waves of actin filaments (F-actin) and cytoskeletal regulators. This phenomenon, termed cortical excitability, results from coupled positive and negative feedback loops of cytoskeletal regulators. The nature of these feedback loops, however, remains poorly understood. We assessed the role of the Rho GAP RGA-3/4 in the cortical excitability that accompanies cytokinesis in both frog and starfish. RGA-3/4 localizes to the cytokinetic apparatus, “chases” Rho waves in an F-actin–dependent manner, and when coexpressed with the Rho GEF Ect2, is sufficient to convert the normally quiescent, immature Xenopus oocyte cortex into a dramatically excited state. Experiments and modeling show that changing the ratio of RGA-3/4 to Ect2 produces cortical behaviors ranging from pulses to complex waves of Rho activity. We conclude that RGA-3/4, Ect2, Rho, and F-actin form the core of a versatile circuit that drives a diverse range of cortical behaviors, a...
Matlab codes used in the publication: J. Landino, M. Leda, ... A. Goryachev, and A. Miller, "... more Matlab codes used in the publication: J. Landino, M. Leda, ... A. Goryachev, and A. Miller, "Rho and F-actin self-organize within an artificial cell cortex" Current Biology, 2021 All Matlab .m files are in the single windows .zip file and are arranged into a directory tree according to the type of dynamics studied.
Interest in cortical excitability – the ability of the cell cortex to generate traveling waves of... more Interest in cortical excitability – the ability of the cell cortex to generate traveling waves of protein activity – has grown considerably over the past twenty years. Attributing biological functions to cortical excitability requires an understanding of the natural behavior of excitable waves and the ability to accurately quantify wave properties. Here we have investigated and quantified the onset of cortical excitability in X. laevis eggs and embryos, and the changes in cortical excitability throughout early development. We found that cortical excitability begins to manifest shortly after egg activation. Further, we identified a close relationship between wave properties – such as wave frequency and amplitude – and cell cycle progression as well as cell size. Finally, we identified quantitative differences between cortical excitability in the cleavage furrow relative to non-furrow cortical excitability and showed that these wave regimes are mutually exclusive.
In earlier studies, we showed that certain low-molecular-weight carboxylic acids (profens, amino ... more In earlier studies, we showed that certain low-molecular-weight carboxylic acids (profens, amino acids, hydroxy acids) can undergo spontaneous in vitro chiral conversion accompanied by condensation to from oligomers, and we proposed two simple models to describe these processes. Here, we present the results of investigations using non-chiral high-performance liquid chromatography with diode array detector (HPLC-DAD) and mass spectrometry (MS) on the dynamics of peptidization of S-, R-, and rac-phenylglycine dissolved in 70 % aqueous ethanol and stored for times up to one year. The experimental results demonstrate that peptidization of phenylglycine can occur in an oscillatory fashion. We also describe, and carry out simulations with, three models that capture key aspects of the oscillatory condensation and chiral conversion processes. Background The remarkable phenomenon of spontaneous in vitro oscillatory chiral conversion of selected profens, amino acids, and hydroxy acids has bee...
Animal cell cytokinesis results from patterned activation of the small GTPase Rho, which directs ... more Animal cell cytokinesis results from patterned activation of the small GTPase Rho, which directs assembly of actomyosin in the equatorial cortex. Cytokinesis is restricted to a portion of the cell cycle following anaphase onset in which the cortex is responsive to signals from the spindle. We show that shortly after anaphase onset oocytes and embryonic cells of frogs and echinoderms exhibit cortical waves of Rho activity and F-actin polymerization. The waves are modulated by cyclin-dependent kinase 1 (Cdk1) activity and require the Rho GEF (guanine nucleotide exchange factor), Ect2. Surprisingly, during wave propagation, although Rho activity elicits F-actin assembly, F-actin subsequently inactivates Rho. Experimental and modelling results show that waves represent excitable dynamics of a reaction–diffusion system with Rho as the activator and F-actin the inhibitor. We propose that cortical excitability explains fundamental features of cytokinesis including its cell cycle regulation.
As the interface between the cell and its environment, the cell cortex must be able to respond to... more As the interface between the cell and its environment, the cell cortex must be able to respond to a variety of external stimuli. This is made possible in part by cortical excitability, a behavior driven by coupled positive and negative feedback loops that generate propagating waves of actin assembly in the cell cortex. Cortical excitability is best known for promoting cell protrusion and allowing the interpretation of and response to chemoattractant gradients in migrating cells. It has recently become apparent, however, that cortical excitability is involved in the response of the cortex to internal signals from the cell-cycle regulatory machinery and the spindle during cell division. Two overlapping functions have been ascribed to cortical excitability in cell division: control of cell division plane placement, and amplification of the activity of the small GTPase Rho at the equatorial cortex during cytokinesis. Here, we propose that cortical excitability explains several important yet poorly understood features of signaling during cell division. We also consider the potential advantages that arise from the use of cortical excitability as a signaling mechanism to regulate cortical dynamics in cell division.
Cellular morphogenesis is governed by the prepattern based on the symmetry-breaking emergence of ... more Cellular morphogenesis is governed by the prepattern based on the symmetry-breaking emergence of dense protein clusters. Thus, a cluster of active GTPase Cdc42 marks the site of nascent bud in the baker’s yeast. An important biological question is which mechanisms control the number of pattern maxima (spots) and, thus, the number of nascent cellular structures. Distinct flavors of theoretical models seem to suggest different predictions. While the classical Turing scenario leads to an array of stably coexisting multiple structures, mass-conserved models predict formation of a single spot that emerges via the greedy competition between the pattern maxima for the common molecular resources. Both the outcome and the kinetics of this competition are of significant biological importance but remained poorly explored. Recent theoretical analyses largely addressed these questions, but their results have not yet been fully appreciated by the broad biological community. Keeping mathematical a...
The still-open problem of the variety of asymptotic solutions to one-variable, one-dimensional in... more The still-open problem of the variety of asymptotic solutions to one-variable, one-dimensional infinite multistable reaction-diffusion systems is solved. We show that in such systems, besides monotonic traveling fronts, nonmonotonic traveling fronts can exist for appropriate initial conditions. The dependence of numbers of various types of traveling fronts on the number of stable stationary states also is given. Examples of traveling fronts for the chemical model describing two enzymatic (catalytic) reactions inhibited by an excess of their reactant is presented.
Periodic spatiotemporal two-dimensional (2D) asymptotic patterns in an excitable two-variable the... more Periodic spatiotemporal two-dimensional (2D) asymptotic patterns in an excitable two-variable thermochemical (reaction-diffusion) system are shown. In a one-dimensional system the traveling impulse which reflects from impermeable boundaries is a stable asymptotic solution if the diffusion coefficient of the reactant is greater than the thermal diffusivity of the system. Periodic patterns of two symmetries are presented in the 2D system: the impulse of excitation propagating along the diagonal of a square spatial domain and a structure consisting of curved impulses which propagate in the direction perpendicular to one side of a rectangular domain.
To initiate directed movement, cells must become polarized, establishing a protrusive leading edg... more To initiate directed movement, cells must become polarized, establishing a protrusive leading edge and a contractile trailing edge. This symmetry-breaking process involves reorganization of cytoskeleton and asymmetric distribution of regulatory molecules. However, what triggers and maintains this asymmetry during cell migration remains largely elusive. Here, we established a micropatterning-based 1D motility assay to investigate the molecular basis of symmetry breaking required for directed cell migration. We show that microtubule (MT) detyrosination drives cell polarization by directing kinesin-1-based transport of the adenomatous polyposis coli (APC) protein to cortical sites. This is essential for the formation of cell's leading edge during 1D and 3D cell migration. These data, combined with biophysical modeling, unveil a key role for MT detyrosination in the generation of a positive feedback loop linking MT dynamics and kinesin-1-based transport. Thus, symmetry breaking during cell polarization relies on a feedback loop driven by MT detyrosination that supports directed cell migration.
Many cells can generate complementary traveling waves of actin filaments (F-actin) and cytoskelet... more Many cells can generate complementary traveling waves of actin filaments (F-actin) and cytoskeletal regulators. This phenomenon, termed cortical excitability, results from coupled positive and negative feedback loops of cytoskeletal regulators. The nature of these feedback loops, however, remains poorly understood. We assessed the role of the Rho GAP RGA-3/4 in the cortical excitability that accompanies cytokinesis in both frog and starfish. RGA-3/4 localizes to the cytokinetic apparatus, “chases” Rho waves in an F-actin–dependent manner, and when coexpressed with the Rho GEF Ect2, is sufficient to convert the normally quiescent, immature Xenopus oocyte cortex into a dramatically excited state. Experiments and modeling show that changing the ratio of RGA-3/4 to Ect2 produces cortical behaviors ranging from pulses to complex waves of Rho activity. We conclude that RGA-3/4, Ect2, Rho, and F-actin form the core of a versatile circuit that drives a diverse range of cortical behaviors, a...
Matlab codes used in the publication: J. Landino, M. Leda, ... A. Goryachev, and A. Miller, "... more Matlab codes used in the publication: J. Landino, M. Leda, ... A. Goryachev, and A. Miller, "Rho and F-actin self-organize within an artificial cell cortex" Current Biology, 2021 All Matlab .m files are in the single windows .zip file and are arranged into a directory tree according to the type of dynamics studied.
Interest in cortical excitability – the ability of the cell cortex to generate traveling waves of... more Interest in cortical excitability – the ability of the cell cortex to generate traveling waves of protein activity – has grown considerably over the past twenty years. Attributing biological functions to cortical excitability requires an understanding of the natural behavior of excitable waves and the ability to accurately quantify wave properties. Here we have investigated and quantified the onset of cortical excitability in X. laevis eggs and embryos, and the changes in cortical excitability throughout early development. We found that cortical excitability begins to manifest shortly after egg activation. Further, we identified a close relationship between wave properties – such as wave frequency and amplitude – and cell cycle progression as well as cell size. Finally, we identified quantitative differences between cortical excitability in the cleavage furrow relative to non-furrow cortical excitability and showed that these wave regimes are mutually exclusive.
In earlier studies, we showed that certain low-molecular-weight carboxylic acids (profens, amino ... more In earlier studies, we showed that certain low-molecular-weight carboxylic acids (profens, amino acids, hydroxy acids) can undergo spontaneous in vitro chiral conversion accompanied by condensation to from oligomers, and we proposed two simple models to describe these processes. Here, we present the results of investigations using non-chiral high-performance liquid chromatography with diode array detector (HPLC-DAD) and mass spectrometry (MS) on the dynamics of peptidization of S-, R-, and rac-phenylglycine dissolved in 70 % aqueous ethanol and stored for times up to one year. The experimental results demonstrate that peptidization of phenylglycine can occur in an oscillatory fashion. We also describe, and carry out simulations with, three models that capture key aspects of the oscillatory condensation and chiral conversion processes. Background The remarkable phenomenon of spontaneous in vitro oscillatory chiral conversion of selected profens, amino acids, and hydroxy acids has bee...
Animal cell cytokinesis results from patterned activation of the small GTPase Rho, which directs ... more Animal cell cytokinesis results from patterned activation of the small GTPase Rho, which directs assembly of actomyosin in the equatorial cortex. Cytokinesis is restricted to a portion of the cell cycle following anaphase onset in which the cortex is responsive to signals from the spindle. We show that shortly after anaphase onset oocytes and embryonic cells of frogs and echinoderms exhibit cortical waves of Rho activity and F-actin polymerization. The waves are modulated by cyclin-dependent kinase 1 (Cdk1) activity and require the Rho GEF (guanine nucleotide exchange factor), Ect2. Surprisingly, during wave propagation, although Rho activity elicits F-actin assembly, F-actin subsequently inactivates Rho. Experimental and modelling results show that waves represent excitable dynamics of a reaction–diffusion system with Rho as the activator and F-actin the inhibitor. We propose that cortical excitability explains fundamental features of cytokinesis including its cell cycle regulation.
As the interface between the cell and its environment, the cell cortex must be able to respond to... more As the interface between the cell and its environment, the cell cortex must be able to respond to a variety of external stimuli. This is made possible in part by cortical excitability, a behavior driven by coupled positive and negative feedback loops that generate propagating waves of actin assembly in the cell cortex. Cortical excitability is best known for promoting cell protrusion and allowing the interpretation of and response to chemoattractant gradients in migrating cells. It has recently become apparent, however, that cortical excitability is involved in the response of the cortex to internal signals from the cell-cycle regulatory machinery and the spindle during cell division. Two overlapping functions have been ascribed to cortical excitability in cell division: control of cell division plane placement, and amplification of the activity of the small GTPase Rho at the equatorial cortex during cytokinesis. Here, we propose that cortical excitability explains several important yet poorly understood features of signaling during cell division. We also consider the potential advantages that arise from the use of cortical excitability as a signaling mechanism to regulate cortical dynamics in cell division.
Cellular morphogenesis is governed by the prepattern based on the symmetry-breaking emergence of ... more Cellular morphogenesis is governed by the prepattern based on the symmetry-breaking emergence of dense protein clusters. Thus, a cluster of active GTPase Cdc42 marks the site of nascent bud in the baker’s yeast. An important biological question is which mechanisms control the number of pattern maxima (spots) and, thus, the number of nascent cellular structures. Distinct flavors of theoretical models seem to suggest different predictions. While the classical Turing scenario leads to an array of stably coexisting multiple structures, mass-conserved models predict formation of a single spot that emerges via the greedy competition between the pattern maxima for the common molecular resources. Both the outcome and the kinetics of this competition are of significant biological importance but remained poorly explored. Recent theoretical analyses largely addressed these questions, but their results have not yet been fully appreciated by the broad biological community. Keeping mathematical a...
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