Intracellular transport of cargo, including macromolecules, vesicles and organelles, through the ... more Intracellular transport of cargo, including macromolecules, vesicles and organelles, through the attachment to microtubules via molecular motors, such as kinesin and dynein, is a complex process that plays a significant role in neuronal function. Disruption of this transport has been linked to neurodegenerative diseases, such as Alzheimer's and Parkinson's diseases. Thus, studying the interactions among different types of cargo and molecular motors can lead to a better understanding of the complicated processes involved during intracellular transport. Here, we present a mathematical model based on traffic-like partial differential equations to describe coupled cargo transport within the squid giant. The model is informed using direct microscopic measurements of nano-bead transport within the squid giant axon which allows for meaningful validation of the model framework. An analytical solution of the model equations is obtained under conditions characterized by an excess of m...
Bulletin of the American Physical Society, Feb 28, 2012
Differential equation models have recently drawn increasing attentions as a useful tool to help a... more Differential equation models have recently drawn increasing attentions as a useful tool to help advance the knowledge in cancer research. However, challenges remain for applying such models to clinical practices on a patient-specific basis to assist surgical decisions. Clinical diagnoses essentially at a single time point are often insufficient to fully constrain the time-dependent differential equations. Here we present a novel mathematical pathology approach, identifying robust indicators for time-invariant predictions of the model that can be used for surgical planning. We ...
Despite major advances in the study of glioma, the quantitative links between intra-tumor molecul... more Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) t...
Clinical outcome prognostication in oncology is a guiding principle in therapeutic choice. A weal... more Clinical outcome prognostication in oncology is a guiding principle in therapeutic choice. A wealth of qualitative empirical evidence links disease progression with tumor morphology, histopathology, invasion, and associated molecular phenomena. However, the quantitative contribution of each of the known parameters in this progression remains elusive. Mathematical modeling can provide the capability to quantify the connection between variables governing growth, prognosis,
Empirical evidence and theoretical studies suggest that the phenotype, i.e., cellular- and molecu... more Empirical evidence and theoretical studies suggest that the phenotype, i.e., cellular- and molecular-scale dynamics, including proliferation rate and adhesiveness due to microenvironmental factors and gene expression that govern tumor growth and invasiveness, also determine gross tumor-scale morphology. It has been difficult to quantify the relative effect of these links on disease progression and prognosis using conventional clinical and experimental methods and observables. As a result, successful individualized treatment of highly malignant and invasive cancers, such as glioblastoma, via surgical resection and chemotherapy cannot be offered and outcomes are generally poor. What is needed is a deterministic, quantifiable method to enable understanding of the connections between phenotype and tumor morphology. Here, we critically assess advantages and disadvantages of recent computational modeling efforts (e.g., continuum, discrete, and cellular automata models) that have pursued t...
The kinesins have long been known to drive microtubule-based transport of sub-cellular components... more The kinesins have long been known to drive microtubule-based transport of sub-cellular components, yet the mechanisms of their attachment to cargo remain a mystery. Several different cargo-receptors have been proposed based on their in vitro binding affinities to kinesin-1. Only two of these-phosphatidyl inositol, a negatively charged lipid, and the carboxyl terminus of the amyloid precursor protein (APP-C), a trans-membrane protein-have been reported to mediate motility in living systems. A major question is how these many different cargo, receptors and motors interact to produce the complex choreography of vesicular transport within living cells. Here we describe an experimental assay that identifies cargo-motor receptors by their ability to recruit active motors and drive transport of exogenous cargo towards the synapse in living axons. Cargo is engineered by derivatizing the surface of polystyrene fluorescent nanospheres (100 nm diameter) with charged residues or with synthetic peptides derived from candidate motor receptor proteins, all designed to display a terminal COOH group. After injection into the squid giant axon, particle movements are imaged by laser-scanning confocal time-lapse microscopy. In this report we compare the motility of negatively charged beads with APP-C beads in the presence of glycine-conjugated non-motile beads using new strategies to measure bead movements. The ensuing quantitative analysis of time-lapse digital sequences reveals detailed information about bead movements: instantaneous and maximum velocities, run lengths, pause frequencies and pause durations. These measurements provide parameters for a mathematical model that predicts the spatiotemporal evolution of distribution of the two different types of bead cargo in the axon. The results reveal that negatively charged beads differ from APP-C beads in velocity and dispersion, and predict that at long time points APP-C will achieve greater progress towards the presynaptic terminal. The significance of this data and accompanying model pertains to the role transport plays in neuronal function, connectivity, and survival, and has implications in the pathogenesis of neurological disorders, such as Alzheimer's, Huntington and Parkinson's diseases.
Intracellular transport of cargo, including macromolecules, vesicles and organelles, through the ... more Intracellular transport of cargo, including macromolecules, vesicles and organelles, through the attachment to microtubules via molecular motors, such as kinesin and dynein, is a complex process that plays a significant role in neuronal function. Disruption of this transport has been linked to neurodegenerative diseases, such as Alzheimer's and Parkinson's diseases. Thus, studying the interactions among different types of cargo and molecular motors can lead to a better understanding of the complicated processes involved during intracellular transport. Here, we present a mathematical model based on traffic-like partial differential equations to describe coupled cargo transport within the squid giant. The model is informed using direct microscopic measurements of nano-bead transport within the squid giant axon which allows for meaningful validation of the model framework. An analytical solution of the model equations is obtained under conditions characterized by an excess of m...
The dynamics of viscous drops in linear creeping flows are investigated near the critical flow st... more The dynamics of viscous drops in linear creeping flows are investigated near the critical flow strength at which stationary drop shapes cease to exist. According to our theory the near-critical behavior of drops is dominated by a single slow mode evolving on a time scale that diverges at the critical point with exponent 1/2. The theory is based on the
We report a study on the deformation and breakup of viscous drops in an impulsively-started shear... more We report a study on the deformation and breakup of viscous drops in an impulsively-started shear flow. We used adaptive boundary-integral simulations and video-microscopy experiments. We find that the size of droplets produced by breakup events scales with the maximum stable drop size in the flow, and the parent drop volume determines the number, but not the size, of droplets
Three dimensional and axisymmetric boundary integral calculations have been developed that descri... more Three dimensional and axisymmetric boundary integral calculations have been developed that describe the entire process of drop breakup including the evolution of the resulting drop fragments. At the final stages of breakup, the neck of the drop thins with constant velocity and acquires a universal axisymmetric form that is independent of conditions away from the neck. In the neck, distinct
Intracellular transport of cargo, including macromolecules, vesicles and organelles, through the ... more Intracellular transport of cargo, including macromolecules, vesicles and organelles, through the attachment to microtubules via molecular motors, such as kinesin and dynein, is a complex process that plays a significant role in neuronal function. Disruption of this transport has been linked to neurodegenerative diseases, such as Alzheimer's and Parkinson's diseases. Thus, studying the interactions among different types of cargo and molecular motors can lead to a better understanding of the complicated processes involved during intracellular transport. Here, we present a mathematical model based on traffic-like partial differential equations to describe coupled cargo transport within the squid giant. The model is informed using direct microscopic measurements of nano-bead transport within the squid giant axon which allows for meaningful validation of the model framework. An analytical solution of the model equations is obtained under conditions characterized by an excess of m...
We present a tumor-level di use interface model of cancer growth. This work ex-pands the capabili... more We present a tumor-level di use interface model of cancer growth. This work ex-pands the capability to simulate non-symmetric, multispecies tumor growth at the continuum level in three spatial dimensions, enabling more detailed description of disease progression and treatment. Specifically, we use a Cahn-Hilliard-type equa-tion with added advection and reaction terms to describe tumor growth and to capture the complicated
Intracellular transport of cargo, including macromolecules, vesicles and organelles, through the ... more Intracellular transport of cargo, including macromolecules, vesicles and organelles, through the attachment to microtubules via molecular motors, such as kinesin and dynein, is a complex process that plays a significant role in neuronal function. Disruption of this transport has been linked to neurodegenerative diseases, such as Alzheimer's and Parkinson's diseases. Thus, studying the interactions among different types of cargo and molecular motors can lead to a better understanding of the complicated processes involved during intracellular transport. Here, we present a mathematical model based on traffic-like partial differential equations to describe coupled cargo transport within the squid giant. The model is informed using direct microscopic measurements of nano-bead transport within the squid giant axon which allows for meaningful validation of the model framework. An analytical solution of the model equations is obtained under conditions characterized by an excess of m...
Bulletin of the American Physical Society, Feb 28, 2012
Differential equation models have recently drawn increasing attentions as a useful tool to help a... more Differential equation models have recently drawn increasing attentions as a useful tool to help advance the knowledge in cancer research. However, challenges remain for applying such models to clinical practices on a patient-specific basis to assist surgical decisions. Clinical diagnoses essentially at a single time point are often insufficient to fully constrain the time-dependent differential equations. Here we present a novel mathematical pathology approach, identifying robust indicators for time-invariant predictions of the model that can be used for surgical planning. We ...
Despite major advances in the study of glioma, the quantitative links between intra-tumor molecul... more Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) t...
Clinical outcome prognostication in oncology is a guiding principle in therapeutic choice. A weal... more Clinical outcome prognostication in oncology is a guiding principle in therapeutic choice. A wealth of qualitative empirical evidence links disease progression with tumor morphology, histopathology, invasion, and associated molecular phenomena. However, the quantitative contribution of each of the known parameters in this progression remains elusive. Mathematical modeling can provide the capability to quantify the connection between variables governing growth, prognosis,
Empirical evidence and theoretical studies suggest that the phenotype, i.e., cellular- and molecu... more Empirical evidence and theoretical studies suggest that the phenotype, i.e., cellular- and molecular-scale dynamics, including proliferation rate and adhesiveness due to microenvironmental factors and gene expression that govern tumor growth and invasiveness, also determine gross tumor-scale morphology. It has been difficult to quantify the relative effect of these links on disease progression and prognosis using conventional clinical and experimental methods and observables. As a result, successful individualized treatment of highly malignant and invasive cancers, such as glioblastoma, via surgical resection and chemotherapy cannot be offered and outcomes are generally poor. What is needed is a deterministic, quantifiable method to enable understanding of the connections between phenotype and tumor morphology. Here, we critically assess advantages and disadvantages of recent computational modeling efforts (e.g., continuum, discrete, and cellular automata models) that have pursued t...
The kinesins have long been known to drive microtubule-based transport of sub-cellular components... more The kinesins have long been known to drive microtubule-based transport of sub-cellular components, yet the mechanisms of their attachment to cargo remain a mystery. Several different cargo-receptors have been proposed based on their in vitro binding affinities to kinesin-1. Only two of these-phosphatidyl inositol, a negatively charged lipid, and the carboxyl terminus of the amyloid precursor protein (APP-C), a trans-membrane protein-have been reported to mediate motility in living systems. A major question is how these many different cargo, receptors and motors interact to produce the complex choreography of vesicular transport within living cells. Here we describe an experimental assay that identifies cargo-motor receptors by their ability to recruit active motors and drive transport of exogenous cargo towards the synapse in living axons. Cargo is engineered by derivatizing the surface of polystyrene fluorescent nanospheres (100 nm diameter) with charged residues or with synthetic peptides derived from candidate motor receptor proteins, all designed to display a terminal COOH group. After injection into the squid giant axon, particle movements are imaged by laser-scanning confocal time-lapse microscopy. In this report we compare the motility of negatively charged beads with APP-C beads in the presence of glycine-conjugated non-motile beads using new strategies to measure bead movements. The ensuing quantitative analysis of time-lapse digital sequences reveals detailed information about bead movements: instantaneous and maximum velocities, run lengths, pause frequencies and pause durations. These measurements provide parameters for a mathematical model that predicts the spatiotemporal evolution of distribution of the two different types of bead cargo in the axon. The results reveal that negatively charged beads differ from APP-C beads in velocity and dispersion, and predict that at long time points APP-C will achieve greater progress towards the presynaptic terminal. The significance of this data and accompanying model pertains to the role transport plays in neuronal function, connectivity, and survival, and has implications in the pathogenesis of neurological disorders, such as Alzheimer's, Huntington and Parkinson's diseases.
Intracellular transport of cargo, including macromolecules, vesicles and organelles, through the ... more Intracellular transport of cargo, including macromolecules, vesicles and organelles, through the attachment to microtubules via molecular motors, such as kinesin and dynein, is a complex process that plays a significant role in neuronal function. Disruption of this transport has been linked to neurodegenerative diseases, such as Alzheimer's and Parkinson's diseases. Thus, studying the interactions among different types of cargo and molecular motors can lead to a better understanding of the complicated processes involved during intracellular transport. Here, we present a mathematical model based on traffic-like partial differential equations to describe coupled cargo transport within the squid giant. The model is informed using direct microscopic measurements of nano-bead transport within the squid giant axon which allows for meaningful validation of the model framework. An analytical solution of the model equations is obtained under conditions characterized by an excess of m...
The dynamics of viscous drops in linear creeping flows are investigated near the critical flow st... more The dynamics of viscous drops in linear creeping flows are investigated near the critical flow strength at which stationary drop shapes cease to exist. According to our theory the near-critical behavior of drops is dominated by a single slow mode evolving on a time scale that diverges at the critical point with exponent 1/2. The theory is based on the
We report a study on the deformation and breakup of viscous drops in an impulsively-started shear... more We report a study on the deformation and breakup of viscous drops in an impulsively-started shear flow. We used adaptive boundary-integral simulations and video-microscopy experiments. We find that the size of droplets produced by breakup events scales with the maximum stable drop size in the flow, and the parent drop volume determines the number, but not the size, of droplets
Three dimensional and axisymmetric boundary integral calculations have been developed that descri... more Three dimensional and axisymmetric boundary integral calculations have been developed that describe the entire process of drop breakup including the evolution of the resulting drop fragments. At the final stages of breakup, the neck of the drop thins with constant velocity and acquires a universal axisymmetric form that is independent of conditions away from the neck. In the neck, distinct
Intracellular transport of cargo, including macromolecules, vesicles and organelles, through the ... more Intracellular transport of cargo, including macromolecules, vesicles and organelles, through the attachment to microtubules via molecular motors, such as kinesin and dynein, is a complex process that plays a significant role in neuronal function. Disruption of this transport has been linked to neurodegenerative diseases, such as Alzheimer's and Parkinson's diseases. Thus, studying the interactions among different types of cargo and molecular motors can lead to a better understanding of the complicated processes involved during intracellular transport. Here, we present a mathematical model based on traffic-like partial differential equations to describe coupled cargo transport within the squid giant. The model is informed using direct microscopic measurements of nano-bead transport within the squid giant axon which allows for meaningful validation of the model framework. An analytical solution of the model equations is obtained under conditions characterized by an excess of m...
We present a tumor-level di use interface model of cancer growth. This work ex-pands the capabili... more We present a tumor-level di use interface model of cancer growth. This work ex-pands the capability to simulate non-symmetric, multispecies tumor growth at the continuum level in three spatial dimensions, enabling more detailed description of disease progression and treatment. Specifically, we use a Cahn-Hilliard-type equa-tion with added advection and reaction terms to describe tumor growth and to capture the complicated
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Papers by Vittorio Cristini