Journal of Physics A-mathematical and General, 2004
We study bond percolation of $N$ non-interacting Gaussian polymers of $\ell$ segments on a 2D squ... more We study bond percolation of $N$ non-interacting Gaussian polymers of $\ell$ segments on a 2D square lattice of size $L$ with reflecting boundaries. Through simulations, we find the fraction of configurations displaying {\em no} connected cluster which span from one edge to the opposite edge. From this fraction, we define a critical segment density $\rho_{c}^L(\ell)$ and the associated critical fraction of occupied bonds $p_{c}^L(\ell)$, so that they can be identified as the percolation threshold in the $L \to \infty$ limit. Whereas $p_{c}^L(\ell)$ is found to decrease monotonically with $\ell$ for a wide range of polymer lengths, $\rho_{c}^L(\ell)$ is non-monotonic. We give physical arguments for this intriguing behavior in terms of the competing effects of multiple bond occupancies and polymerization.
We study the diffusion of gas molecules through a two-dimensional network of polymers with the he... more We study the diffusion of gas molecules through a two-dimensional network of polymers with the help of Monte Carlo simulations. The polymers are modeled as non-interacting random walks on the bonds of a two-dimensional square lattice, while the gas particles occupy the lattice cells. When a particle attempts to jump to a nearest-neighbor empty cell, it has to overcome an energy barrier which is determined by the number of polymer segments on the bond separating the two cells. We investigate the gas current $J$ as a function of the mean segment density $\rho$, the polymer length $\ell$ and the probability $q^{m}$ for hopping across $m$ segments. Whereas $J$ decreases monotonically with $\rho$ for fixed $\ell$, its behavior for fixed $\rho$ and increasing $\ell$ depends strongly on $q$. For small, non-zero $q$, $J$ appears to increase slowly with $\ell$. In contrast, for $q=0$, it is dominated by the underlying percolation problem and can be non-monotonic. We provide heuristic arguments to put these interesting phenomena into context.
We study the diffusion of gas molecules through a polymer film via two-dimensional Monte Carlo si... more We study the diffusion of gas molecules through a polymer film via two-dimensional Monte Carlo simulations, with emphasis on the amount of free volume in the system and its spatial distribution. Using bond-traversal properties of two-dimensional lattice random walks in the limit of large polymer length l, we argue that the polymer system shows a percolation transition as the amount of free volume is increased. We map this transition in the k-l phase diagram, k being the mean polymer density. Numerical simulations support this prediction, but the transition is smeared out, presumably due to spatial correlations in the free volume. This is verified by studying a random energy barrier model, which has the same free volume content as the original system, but is devoid of any correlations. For this model, the percolation transition is sharp, and the particle current is higher. These observations are compared with recent experimental studies.
European Biophysics Journal With Biophysics Letters, 2005
Rebinding of dissociated ligands from cell surface proteins can confound quantitative measurement... more Rebinding of dissociated ligands from cell surface proteins can confound quantitative measurements of dissociation rates important for characterizing the affinity of binding interactions. This can be true also for in vitro techniques such as surface plasmon resonance (SPR). We present experimental results using SPR for the interaction of insulin-like growth factor-I (IGF-I) with one of its binding proteins, IGF binding protein-3 (IGFBP-3), and show that the dissociation, even with the addition of soluble heparin in the dissociation phase, does not exhibit the expected exponential decay characteristic of a 1:1 binding reaction. We thus consider the effect of (multiple) rebinding events and, within a self-consistent mean-field approximation, we derive the complete mathematical form for the fraction of bound ligands as a function of time. We show that, except for very low association rate and surface coverage, this function is nonexponential at all times, indicating that multiple rebinding events strongly influence dissociation even at early times. We compare the mean-field results with numerical simulations and find good agreement, although deviations are measurable in certain cases. Our analysis of the IGF-I–IGFBP-3 data indicates that rebinding is prominent for this system and that the theoretical predictions fit the experimental data well. Our results provide a means for analyzing SPR biosensor data where rebinding is problematic and a methodology to do so is presented.
We use lattice Monte-Carlo simulations to probe the kinetics of ligand-receptor association and d... more We use lattice Monte-Carlo simulations to probe the kinetics of ligand-receptor association and dissociation. Simulations were run under conditions approximating the geometric configuration of surface plasmon resonance devices. These conditions include viscous flow of ligands over a surface of receptors which is achieved by using a spatially varying biased random walk. Our simulations allow for the occurrence of multiple rebinding events which result in strong deviations from the standard mean-field rate equation approximation. Our simulations also allow us to test improved theoretical predictions for the binding dynamics and to determine their range of applicability.
Rebinding of dissociated ligands from cell surface proteins can confound quantitative measurement... more Rebinding of dissociated ligands from cell surface proteins can confound quantitative measurements of dissociation rates important for characterizing the affinity of binding interactions. This can be true also for in vitro techniques such as surface plasmon resonance (SPR). We present experimental results using SPR for the interaction of insulin-like growth factor-I (IGF-I) with one of its binding proteins, IGF binding protein-3 (IGFBP-3), and show that rebinding, even with the addition of soluble heparin in the dissociation phase, does not exhibit the expected exponential decay characteristic of a 1:1 binding reaction. We thus consider the effect of (multiple) rebinding events and, within a self-consistent mean-field approximation, we derive the complete mathematical form for the fraction of bound ligand as a function of time. We show that, except for very low surface coverage/association rate, this function is non-exponential at all times, indicating that multiple rebinding events strongly influence dissociation even at early times. We compare the mean-field results with numerical simulations and find good agreement, although deviations are measurable in certain cases. Our analysis of the IGF-I-IGFBP-3 data indicates that rebinding is prominent for this system and that the theoretical predictions fit the experimental data well. Our results provide a means for analyzing SPR biosensor data where rebinding is problematic and a methodology to do so is presented.
Receptor-ligand binding is a critical first step in signal transduction and the duration of the i... more Receptor-ligand binding is a critical first step in signal transduction and the duration of the interaction can impact signal generation. In mammalian cells, clustering of receptors may be facilitated by heterogeneous zones of lipids, known as lipid rafts. In vitro experiments show that disruption of rafts significantly alters the dissociation of fibroblast growth factor-2 (FGF-2) from heparan sulfate proteoglycans, co-receptors for FGF-2. In this paper, we develop a continuum stochastic formalism in order to (i) study how rebinding affects the dissociation of ligands from a planar substrate, and (ii) address the question of how receptor clustering influences ligand rebinding. We find that clusters reduce the effective dissociation rate dramatically when the clusters are dense and the overall surface density of receptors is low. The effect is much less pronounced in the case of high receptor density and shows non-monotonic behavior with time. These predictions are verified via lattice Monte Carlo simulations. Comparison with experimental results suggests that the theory does not capture the complete biological system. We speculate that additional co-operative mechanisms might be present in order to increase ligand retention, and present one possible ``internal diffusion'' model.
The binding of basic fibroblast growth factor (FGF-2) to its cell surface receptor (CSR) and subs... more The binding of basic fibroblast growth factor (FGF-2) to its cell surface receptor (CSR) and subsequent signal transduction is known to be enhanced by Heparan Sulfate Proteoglycans (HSPGs). HSPGs bind FGF-2 with low affinity and likely impact CSR-mediated signaling via stabilization of FGF-2-CSR complexes via association with both the ligand and the receptor. What is unknown is whether HSPG associates with CSR in the absence of FGF-2. In this paper, we determine conditions by which pre-association would impact CSR-FGF-2-HSPG triad formation assuming diffusion-limited surface reactions. Using mean-field rate equations, we show that (i) when [HSPG] is much higher than [CSR], the presence of pre-formed complexes does not affect the steady state of FGF-2 binding, and (ii) when the concentrations are comparable, the presence of pre-formed complexes substantially increases the steady state concentration of FGF-2 bound to CSR. These findings are supported by explicit cellular automaton simulations, which justify the mean-field treatment. We discuss the advantages of such a two-receptor system compared to a single receptor model, when the parameters are comparable. Further, we speculate that the observed high concentration of HSPG in intact cells ([HSPG] ~ 100[CSR]) provides a way to ensure that the binding levels of FGF-2 to its signaling receptor remains high, irrespective of the presence of pre-formed CSR-HSPG complexes on the cell surface, while allowing the cell to finely tune the response to FGF-2 via down-regulation of the signaling receptor.
Fibroblast growth factors (FGF) stimulates proliferation of many cell types, and are crucial in s... more Fibroblast growth factors (FGF) stimulates proliferation of many cell types, and are crucial in such processes as eg. wound healing. Cells have specific receptor (R) protein molecules on their surface which bind FGF for this purpose. FGF is also bound by Heparan Sulfate Proteoglycan (HSPG) molecules which are present on the cell surface. In isolation, both these complexes are unstable, with half-life of the order of 10-20 minutes, wheras in intact cells, the half-life of FGF-R complex is nearly 5 hours! To account for this increased stability, it has been proposed that R-FGF complex combines with HSPG via surface diffusion and forms the triad R-FGF-HSPG. We examine the feasibility of this reaction using the well-known Smoluchowski theory and Monte Carlo simulations. Our results support the triad formation theory, and are in qualitative agreement with experimental results. We also discuss the effects of slowing down of surface diffusion of these molecules by such factors as eg. the cytosekeletal network and anchored proteins.
In this article, we study the kinetics of reversible ligand binding to receptors on a spherical c... more In this article, we study the kinetics of reversible ligand binding to receptors on a spherical cell surface using a self-consistent stochastic theory. Binding, dissociation, diffusion and rebinding of ligands are incorporated into the theory in a systematic manner. We derive explicitly the time evolution of the ligand-bound receptor fraction p(t) in various regimes . Contrary to the commonly accepted view, we find that the well-known Berg-Purcell scaling for the association rate is modified as a function of time. Specifically, the effective on-rate changes non-monotonically as a function of time and equals the intrinsic rate at very early as well as late times, while being approximately equal to the Berg-Purcell value at intermediate times. The effective dissociation rate, as it appears in the binding curve or measured in a dissociation experiment, is strongly modified by rebinding events and assumes the Berg-Purcell value except at very late times, where the decay is algebraic and not exponential. In equilibrium, the ligand concentration everywhere in the solution is the same and equals its spatial mean, thus ensuring that there is no depletion in the vicinity of the cell. Implications of our results for binding experiments and numerical simulations of ligand-receptor systems are also discussed.
The mitotic spindle is an important intermediate structure in eukaryotic cell division, in which ... more The mitotic spindle is an important intermediate structure in eukaryotic cell division, in which each of a pair of duplicated chromosomes is attached through microtubules to centrosomal bodies located close to the two poles of the dividing cell. Several mechanisms are at work toward the formation of the spindle, one of which is the ‘capture’ of chromosome pairs, held together by kinetochores, by randomly searching microtubules. Although the entire cell cycle can be up to 24 hours long, the mitotic phase typically takes only less than an hour. How does the cell keep the duration of mitosis within this limit? Previous theoretical studies have suggested that the chromosome search and capture is optimized by tuning the microtubule dynamic parameters to minimize the search time. In this paper, we examine this conjecture. We compute the mean search time for a single target by microtubules from a single nucleating site, using a systematic and rigorous theoretical approach, for arbitrary kinetic parameters. The result is extended to multiple targets and nucleating sites by physical arguments. Estimates of mitotic time scales are then obtained for different cells using experimental data. In yeast and mammalian cells, the observed changes in microtubule kinetics between interphase and mitosis are beneficial in reducing the search time. In Xenopus extracts, by contrast, the opposite effect is observed, in agreement with the current understanding that large cells use additional mechanisms to regulate the duration of the mitotic phase.
In many intracellular processes, the length distribution of microtubules is controlled by depolym... more In many intracellular processes, the length distribution of microtubules is controlled by depolymerizing motor proteins. Experiments have shown that, following non-specific binding to the surface of a microtubule, depolymerizers are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there. We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution of microtubules. We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the length distribution is, in general, non-monotonic with a single peak. However, for highly processive motors and large motor densities, this distribution effectively becomes an exponential decay. Our findings suggest that such motor proteins may be selectively used by the cell to ensure precise control of MT lengths. The model is also used to analyze experimental observations of motor-induced depolymerization.
The mitotic spindle is an important intermediate structure in eukaryotic cell division, in which ... more The mitotic spindle is an important intermediate structure in eukaryotic cell division, in which each of a pair of duplicated chromosomes is attached through microtubules to centrosomal bodies located close to the two poles of the dividing cell. Several mechanisms are at work toward the formation of the spindle, one of which is the ‘capture’ of chromosome pairs, held together by kinetochores, by randomly searching microtubules. Although the entire cell cycle can be up to 24 hours long, the mitotic phase typically takes only less than an hour. How does the cell keep the duration of mitosis within this limit? Previous theoretical studies have suggested that the chromosome search and capture is optimized by tuning the microtubule dynamic parameters to minimize the search time. In this paper, we examine this conjecture. We compute the mean search time for a single target by microtubules from a single nucleating site, using a systematic and rigorous theoretical approach, for arbitrary kinetic parameters. The result is extended to multiple targets and nucleating sites by physical arguments. Estimates of mitotic time scales are then obtained for different cells using experimental data. In yeast and mammalian cells, the observed changes in microtubule kinetics between interphase and mitosis are beneficial in reducing the search time. In Xenopus extracts, by contrast, the opposite effect is observed, in agreement with the current understanding that large cells use additional mechanisms to regulate the duration of the mitotic phase.
In many intracellular processes, the length distribution of microtubules is controlled by depolym... more In many intracellular processes, the length distribution of microtubules is controlled by depolymerizing motor proteins. Experiments have shown that, following non-specific binding to the surface of a microtubule, depolymerizers are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there. We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution of microtubules. We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the length distribution is, in general, non-monotonic with a single peak. However, for highly processive motors and large motor densities, this distribution effectively becomes an exponential decay. Our findings suggest that such motor proteins may be selectively used by the cell to ensure precise control of MT lengths. The model is also used to analyze experimental observations of motor-induced depolymerization.
Journal of Physics A-mathematical and General, 2004
We study bond percolation of $N$ non-interacting Gaussian polymers of $\ell$ segments on a 2D squ... more We study bond percolation of $N$ non-interacting Gaussian polymers of $\ell$ segments on a 2D square lattice of size $L$ with reflecting boundaries. Through simulations, we find the fraction of configurations displaying {\em no} connected cluster which span from one edge to the opposite edge. From this fraction, we define a critical segment density $\rho_{c}^L(\ell)$ and the associated critical fraction of occupied bonds $p_{c}^L(\ell)$, so that they can be identified as the percolation threshold in the $L \to \infty$ limit. Whereas $p_{c}^L(\ell)$ is found to decrease monotonically with $\ell$ for a wide range of polymer lengths, $\rho_{c}^L(\ell)$ is non-monotonic. We give physical arguments for this intriguing behavior in terms of the competing effects of multiple bond occupancies and polymerization.
We study the diffusion of gas molecules through a two-dimensional network of polymers with the he... more We study the diffusion of gas molecules through a two-dimensional network of polymers with the help of Monte Carlo simulations. The polymers are modeled as non-interacting random walks on the bonds of a two-dimensional square lattice, while the gas particles occupy the lattice cells. When a particle attempts to jump to a nearest-neighbor empty cell, it has to overcome an energy barrier which is determined by the number of polymer segments on the bond separating the two cells. We investigate the gas current $J$ as a function of the mean segment density $\rho$, the polymer length $\ell$ and the probability $q^{m}$ for hopping across $m$ segments. Whereas $J$ decreases monotonically with $\rho$ for fixed $\ell$, its behavior for fixed $\rho$ and increasing $\ell$ depends strongly on $q$. For small, non-zero $q$, $J$ appears to increase slowly with $\ell$. In contrast, for $q=0$, it is dominated by the underlying percolation problem and can be non-monotonic. We provide heuristic arguments to put these interesting phenomena into context.
We study the diffusion of gas molecules through a polymer film via two-dimensional Monte Carlo si... more We study the diffusion of gas molecules through a polymer film via two-dimensional Monte Carlo simulations, with emphasis on the amount of free volume in the system and its spatial distribution. Using bond-traversal properties of two-dimensional lattice random walks in the limit of large polymer length l, we argue that the polymer system shows a percolation transition as the amount of free volume is increased. We map this transition in the k-l phase diagram, k being the mean polymer density. Numerical simulations support this prediction, but the transition is smeared out, presumably due to spatial correlations in the free volume. This is verified by studying a random energy barrier model, which has the same free volume content as the original system, but is devoid of any correlations. For this model, the percolation transition is sharp, and the particle current is higher. These observations are compared with recent experimental studies.
European Biophysics Journal With Biophysics Letters, 2005
Rebinding of dissociated ligands from cell surface proteins can confound quantitative measurement... more Rebinding of dissociated ligands from cell surface proteins can confound quantitative measurements of dissociation rates important for characterizing the affinity of binding interactions. This can be true also for in vitro techniques such as surface plasmon resonance (SPR). We present experimental results using SPR for the interaction of insulin-like growth factor-I (IGF-I) with one of its binding proteins, IGF binding protein-3 (IGFBP-3), and show that the dissociation, even with the addition of soluble heparin in the dissociation phase, does not exhibit the expected exponential decay characteristic of a 1:1 binding reaction. We thus consider the effect of (multiple) rebinding events and, within a self-consistent mean-field approximation, we derive the complete mathematical form for the fraction of bound ligands as a function of time. We show that, except for very low association rate and surface coverage, this function is nonexponential at all times, indicating that multiple rebinding events strongly influence dissociation even at early times. We compare the mean-field results with numerical simulations and find good agreement, although deviations are measurable in certain cases. Our analysis of the IGF-I–IGFBP-3 data indicates that rebinding is prominent for this system and that the theoretical predictions fit the experimental data well. Our results provide a means for analyzing SPR biosensor data where rebinding is problematic and a methodology to do so is presented.
We use lattice Monte-Carlo simulations to probe the kinetics of ligand-receptor association and d... more We use lattice Monte-Carlo simulations to probe the kinetics of ligand-receptor association and dissociation. Simulations were run under conditions approximating the geometric configuration of surface plasmon resonance devices. These conditions include viscous flow of ligands over a surface of receptors which is achieved by using a spatially varying biased random walk. Our simulations allow for the occurrence of multiple rebinding events which result in strong deviations from the standard mean-field rate equation approximation. Our simulations also allow us to test improved theoretical predictions for the binding dynamics and to determine their range of applicability.
Rebinding of dissociated ligands from cell surface proteins can confound quantitative measurement... more Rebinding of dissociated ligands from cell surface proteins can confound quantitative measurements of dissociation rates important for characterizing the affinity of binding interactions. This can be true also for in vitro techniques such as surface plasmon resonance (SPR). We present experimental results using SPR for the interaction of insulin-like growth factor-I (IGF-I) with one of its binding proteins, IGF binding protein-3 (IGFBP-3), and show that rebinding, even with the addition of soluble heparin in the dissociation phase, does not exhibit the expected exponential decay characteristic of a 1:1 binding reaction. We thus consider the effect of (multiple) rebinding events and, within a self-consistent mean-field approximation, we derive the complete mathematical form for the fraction of bound ligand as a function of time. We show that, except for very low surface coverage/association rate, this function is non-exponential at all times, indicating that multiple rebinding events strongly influence dissociation even at early times. We compare the mean-field results with numerical simulations and find good agreement, although deviations are measurable in certain cases. Our analysis of the IGF-I-IGFBP-3 data indicates that rebinding is prominent for this system and that the theoretical predictions fit the experimental data well. Our results provide a means for analyzing SPR biosensor data where rebinding is problematic and a methodology to do so is presented.
Receptor-ligand binding is a critical first step in signal transduction and the duration of the i... more Receptor-ligand binding is a critical first step in signal transduction and the duration of the interaction can impact signal generation. In mammalian cells, clustering of receptors may be facilitated by heterogeneous zones of lipids, known as lipid rafts. In vitro experiments show that disruption of rafts significantly alters the dissociation of fibroblast growth factor-2 (FGF-2) from heparan sulfate proteoglycans, co-receptors for FGF-2. In this paper, we develop a continuum stochastic formalism in order to (i) study how rebinding affects the dissociation of ligands from a planar substrate, and (ii) address the question of how receptor clustering influences ligand rebinding. We find that clusters reduce the effective dissociation rate dramatically when the clusters are dense and the overall surface density of receptors is low. The effect is much less pronounced in the case of high receptor density and shows non-monotonic behavior with time. These predictions are verified via lattice Monte Carlo simulations. Comparison with experimental results suggests that the theory does not capture the complete biological system. We speculate that additional co-operative mechanisms might be present in order to increase ligand retention, and present one possible ``internal diffusion'' model.
The binding of basic fibroblast growth factor (FGF-2) to its cell surface receptor (CSR) and subs... more The binding of basic fibroblast growth factor (FGF-2) to its cell surface receptor (CSR) and subsequent signal transduction is known to be enhanced by Heparan Sulfate Proteoglycans (HSPGs). HSPGs bind FGF-2 with low affinity and likely impact CSR-mediated signaling via stabilization of FGF-2-CSR complexes via association with both the ligand and the receptor. What is unknown is whether HSPG associates with CSR in the absence of FGF-2. In this paper, we determine conditions by which pre-association would impact CSR-FGF-2-HSPG triad formation assuming diffusion-limited surface reactions. Using mean-field rate equations, we show that (i) when [HSPG] is much higher than [CSR], the presence of pre-formed complexes does not affect the steady state of FGF-2 binding, and (ii) when the concentrations are comparable, the presence of pre-formed complexes substantially increases the steady state concentration of FGF-2 bound to CSR. These findings are supported by explicit cellular automaton simulations, which justify the mean-field treatment. We discuss the advantages of such a two-receptor system compared to a single receptor model, when the parameters are comparable. Further, we speculate that the observed high concentration of HSPG in intact cells ([HSPG] ~ 100[CSR]) provides a way to ensure that the binding levels of FGF-2 to its signaling receptor remains high, irrespective of the presence of pre-formed CSR-HSPG complexes on the cell surface, while allowing the cell to finely tune the response to FGF-2 via down-regulation of the signaling receptor.
Fibroblast growth factors (FGF) stimulates proliferation of many cell types, and are crucial in s... more Fibroblast growth factors (FGF) stimulates proliferation of many cell types, and are crucial in such processes as eg. wound healing. Cells have specific receptor (R) protein molecules on their surface which bind FGF for this purpose. FGF is also bound by Heparan Sulfate Proteoglycan (HSPG) molecules which are present on the cell surface. In isolation, both these complexes are unstable, with half-life of the order of 10-20 minutes, wheras in intact cells, the half-life of FGF-R complex is nearly 5 hours! To account for this increased stability, it has been proposed that R-FGF complex combines with HSPG via surface diffusion and forms the triad R-FGF-HSPG. We examine the feasibility of this reaction using the well-known Smoluchowski theory and Monte Carlo simulations. Our results support the triad formation theory, and are in qualitative agreement with experimental results. We also discuss the effects of slowing down of surface diffusion of these molecules by such factors as eg. the cytosekeletal network and anchored proteins.
In this article, we study the kinetics of reversible ligand binding to receptors on a spherical c... more In this article, we study the kinetics of reversible ligand binding to receptors on a spherical cell surface using a self-consistent stochastic theory. Binding, dissociation, diffusion and rebinding of ligands are incorporated into the theory in a systematic manner. We derive explicitly the time evolution of the ligand-bound receptor fraction p(t) in various regimes . Contrary to the commonly accepted view, we find that the well-known Berg-Purcell scaling for the association rate is modified as a function of time. Specifically, the effective on-rate changes non-monotonically as a function of time and equals the intrinsic rate at very early as well as late times, while being approximately equal to the Berg-Purcell value at intermediate times. The effective dissociation rate, as it appears in the binding curve or measured in a dissociation experiment, is strongly modified by rebinding events and assumes the Berg-Purcell value except at very late times, where the decay is algebraic and not exponential. In equilibrium, the ligand concentration everywhere in the solution is the same and equals its spatial mean, thus ensuring that there is no depletion in the vicinity of the cell. Implications of our results for binding experiments and numerical simulations of ligand-receptor systems are also discussed.
The mitotic spindle is an important intermediate structure in eukaryotic cell division, in which ... more The mitotic spindle is an important intermediate structure in eukaryotic cell division, in which each of a pair of duplicated chromosomes is attached through microtubules to centrosomal bodies located close to the two poles of the dividing cell. Several mechanisms are at work toward the formation of the spindle, one of which is the ‘capture’ of chromosome pairs, held together by kinetochores, by randomly searching microtubules. Although the entire cell cycle can be up to 24 hours long, the mitotic phase typically takes only less than an hour. How does the cell keep the duration of mitosis within this limit? Previous theoretical studies have suggested that the chromosome search and capture is optimized by tuning the microtubule dynamic parameters to minimize the search time. In this paper, we examine this conjecture. We compute the mean search time for a single target by microtubules from a single nucleating site, using a systematic and rigorous theoretical approach, for arbitrary kinetic parameters. The result is extended to multiple targets and nucleating sites by physical arguments. Estimates of mitotic time scales are then obtained for different cells using experimental data. In yeast and mammalian cells, the observed changes in microtubule kinetics between interphase and mitosis are beneficial in reducing the search time. In Xenopus extracts, by contrast, the opposite effect is observed, in agreement with the current understanding that large cells use additional mechanisms to regulate the duration of the mitotic phase.
In many intracellular processes, the length distribution of microtubules is controlled by depolym... more In many intracellular processes, the length distribution of microtubules is controlled by depolymerizing motor proteins. Experiments have shown that, following non-specific binding to the surface of a microtubule, depolymerizers are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there. We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution of microtubules. We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the length distribution is, in general, non-monotonic with a single peak. However, for highly processive motors and large motor densities, this distribution effectively becomes an exponential decay. Our findings suggest that such motor proteins may be selectively used by the cell to ensure precise control of MT lengths. The model is also used to analyze experimental observations of motor-induced depolymerization.
The mitotic spindle is an important intermediate structure in eukaryotic cell division, in which ... more The mitotic spindle is an important intermediate structure in eukaryotic cell division, in which each of a pair of duplicated chromosomes is attached through microtubules to centrosomal bodies located close to the two poles of the dividing cell. Several mechanisms are at work toward the formation of the spindle, one of which is the ‘capture’ of chromosome pairs, held together by kinetochores, by randomly searching microtubules. Although the entire cell cycle can be up to 24 hours long, the mitotic phase typically takes only less than an hour. How does the cell keep the duration of mitosis within this limit? Previous theoretical studies have suggested that the chromosome search and capture is optimized by tuning the microtubule dynamic parameters to minimize the search time. In this paper, we examine this conjecture. We compute the mean search time for a single target by microtubules from a single nucleating site, using a systematic and rigorous theoretical approach, for arbitrary kinetic parameters. The result is extended to multiple targets and nucleating sites by physical arguments. Estimates of mitotic time scales are then obtained for different cells using experimental data. In yeast and mammalian cells, the observed changes in microtubule kinetics between interphase and mitosis are beneficial in reducing the search time. In Xenopus extracts, by contrast, the opposite effect is observed, in agreement with the current understanding that large cells use additional mechanisms to regulate the duration of the mitotic phase.
In many intracellular processes, the length distribution of microtubules is controlled by depolym... more In many intracellular processes, the length distribution of microtubules is controlled by depolymerizing motor proteins. Experiments have shown that, following non-specific binding to the surface of a microtubule, depolymerizers are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there. We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution of microtubules. We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the length distribution is, in general, non-monotonic with a single peak. However, for highly processive motors and large motor densities, this distribution effectively becomes an exponential decay. Our findings suggest that such motor proteins may be selectively used by the cell to ensure precise control of MT lengths. The model is also used to analyze experimental observations of motor-induced depolymerization.
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Papers by Manoj Gopalakrishnan