During development of the brain, morphogenesis of neurons is dynamically organized from a simple rounded shape to a highly polarized morphology consisting of soma, one axon, and dendrites, which is a basis for establishing the unidirectional transfer of electric signals between neurons. The mechanism of such polarization is thought to be "local activation-global inhibition"; however, globally diffusing inhibitor molecules have not been identified. In this chapter, we present a theoretical modeling approach of such neuronal development. We first summarize biological research on neuronal polarization and then develop a biophysical model. Through mathematical analysis, principles of local activation-global inhibition are illustrated based on active transport, protein degradation, and neurite growth, but not on globally diffusing inhibitor.
Phenotypic heterogeneity of cancer cells is caused not only by genetic and epigenetic alterations but also by stochastic variation of intracellular signaling molecules. Using cells that stably express Förster resonance energy transfer (FRET) biosensors, we show here a correlation between a temporal fluctuation in the activity of Rac1 and the invasive properties of C6 glioma cells. By using long-term time-lapse imaging, we found that Rac1 activity in C6 glioma cells fluctuated over a timescale that was substantially longer than that of the replication cycle. Because the relative level of Rac1 activity in each cell was unaffected by a suspension-adhesion procedure, we were able to sort C6 glioma cells according to the levels of Rac1 activity, yielding Rac1(high) and Rac1(low) cells. The Rac1(high) cells invaded more efficiently than did Rac1(low) cells in a Matrigel invasion assay. We assessed the transcriptional profiles of Rac1(high) and Rac1(low) cells and performed gene ontology analysis. Among the 14 genes that were most associated with the term 'membrane' (membrane-related genes) in Rac1(high) cells, we identified four genes that were associated with glioma invasion and Rac1 activity by using siRNA knockdown experiments. Among the transcription factors upregulated in Rac1(high) cells, Egr2 was found to positively regulate expression of the four membrane-related invasion-associated genes. The identified signaling network might cause the fluctuations in Rac1 activity and the heterogeneity in the invasive capacity of glioma cells.
ONO-5334, a selective inhibitor of cathepsin K, is a potential new treatment for osteoporosis. The objectives of this study were to (1) develop population pharmacokinetic-pharmacodynamic (PK-PD) models for ONO-5334 using dose-ascending data from healthy postmenopausal females, (2) examine comparability of PK and/or PD profile between Caucasian and Japanese, and (3) compare PK-PD profile between immediate release tablet (IRT) and sustained release tablet (SRT). The population PK-PD models were developed for each formulation for post-dose levels of bone resorption markers (serum CTX and NTX). The data were provided from 4 phase 1 studies with total of 201 Caucasian and 94 Japanese subjects. Plasma concentrations of ONO-5334 and bone resorption markers were thoroughly evaluated in those studies. An indirect response model described relationships between bone resorption markers and plasma concentrations of ONO-5334. There was no significant difference in PK and pharmacodynamic potency (IC50 ) between Caucasian and Japanese. Based on the developed model, serum CTX and NTX after administration of ONO-5334 IRT or SRT were simulated, and the results showed that ONO-5334 SRT would provide comparable PD effect on bone resorption markers with lower dose relative to IRT.
The purpose of the study was clarify the effect of the cathepsin K inhibitor ONO-5334 on bone resortion markers using sustained release (SR) formulations with different pharmacokinetic (PK) patterns, and identify the optimal SR formulation. The PK profiles and pharmacodynamic effect on bone resorption markers of 4 SR candidates formulations were evaluated in healthy postmenopausal women within a randomized, 2-part, open-label crossover study. In Part A, subject received a single dose of each formulation orally in the fed state. In Part B, two selected formulations were evaluated in the fasted state. From the results from Part A, C max was reduced and plasma concentrations of ONO-5334 were sustained with all SR formulations compared with an immediate release tablet. In pharmacodynamics, the level of C-terminal telopeptide of type I collagen (CTX) in serum and urine were inhibited with SR tablets rather than with granules. C max and area under the concentration-time curve from time 0 to the last measurable time point (AUC0-t ) of SR tablets were higher than those of granules. From Part B, C max in the fasted condition was lower than that in the fed condition with two SR tablets. In contrast, C 24 h in the fasted condition was slightly higher than that in the fed condition, but AUC0-t was similar. The inhibitory effect on CTX in serum and urine may depend on the PK pattern of ONO-5334. The SR tablets was well tolerated in postmenopausal women and has the optimal SR profiles on pharmacodynamics effect on bone resortion markers and PK profile. These results suggest that SR tablets of ONO-5334 are an excellent drug candidate for osteoporosis.
During development, the formation of biological networks (such as organs and neuronal networks) is controlled by multicellular transportation phenomena based on cell migration. In multi-cellular systems, cellular locomotion is restricted by physical interactions with other cells in a crowded space, similar to passengers pushing others out of their way on a packed train. The motion of individual cells is intrinsically stochastic and may be viewed as a type of random walk. However, this walk takes place in a noisy environment because the cell interacts with its randomly moving neighbors. Despite this randomness and complexity, development is highly orchestrated and precisely regulated, following genetic (and even epigenetic) blueprints. Although individual cell migration has long been studied, the manner in which stochasticity affects multi-cellular transportation within the precisely controlled process of development remains largely unknown. To explore the general principles underlying multicellular migration, we focus on the migration of neural crest cells, which migrate collectively and form streams. We introduce a mechanical model of multi-cellular migration. Simulations based on the model show that the migration mode depends on the relative strengths of the noise from migratory and non-migratory cells. Strong noise from migratory cells and weak noise from surrounding cells causes "collective migration," whereas strong noise from non-migratory cells causes "dispersive migration." Moreover, our theoretical analyses reveal that migratory cells attract each other over long distances, even without direct mechanical contacts. This effective interaction depends on the stochasticity of the migratory and non-migratory cells. On the basis of these findings, we propose that stochastic behavior at the single-cell level works effectively and precisely to achieve collective migration in multi-cellular systems.
Polarization, a disruption of symmetry in cellular morphology, occurs spontaneously, even in symmetrical extracellular conditions. This process is regulated by intracellular chemical reactions and the active transport of proteins and it is accompanied by cellular morphological changes. To elucidate the general principles underlying polarization, we focused on developing neurons. Neuronal polarity is stably established; a neuron initially has several neurites of similar length, but only one elongates and is selected to develop into an axon. Polarization is flexibly controlled; when multiple neurites are selected, the selection is eventually reduced to yield a single axon. What is the system by which morphological information is decoded differently based on the presence of a single or multiple axons? How are stability and flexibility achieved? To answer these questions, we constructed a biophysical model with the active transport of proteins that regulate neurite growth. Our mathematical analysis and computer simulation revealed that, as neurites elongate, transported factors accumulate in the growth cone but are degraded during retrograde diffusion to the soma. Such a system effectively works as local activation-global inhibition mechanism, resulting in both stability and flexibility. Our model shows good accordance with a number of experimental observations.
Cellular motility is a complicated phenomenon that involves multiphysics, including the cytoskeleton, the plasma membrane and intracellular signal transduction. In this study, a hybrid computational model was developed for the simulation of whole-cell migration behaviors. The model integrates sub-models of reaction-diffusion, actin filaments (F-actin) and the plasma membrane. Reaction-diffusion was calculated as if enclosed by a moving membrane. Individual F-actins were reorganized on the basis of stochastic kinetic events, such as polymerization, capping, branching and severing. Membrane dynamics were modeled using an optimization of energy function that depends on cell volume, surface area, smoothness and the elasticity of F-actin against the membrane. Simulations of this model demonstrated self-organization of F-actin networks, as in lamellipodia, and chemotactic migration. Furthermore, this method was extended to address external obstacles to simulate the dynamic cellular morphological changes seen during invasive migration.
The pharmacokinetic (PK) and pharmacodynamic (PD) parameters of ONO-4641 in humans were estimated using preclinical data in order to provide essential information to better design future clinical studies. The characterization of PK/PD was measured in terms of decreased lymphocyte counts in blood after administration of ONO-4641, a sphingosine 1-phosphate receptor modulator. Using a two-compartment model, human PK parameters were estimated from preclinical PK data of cynomolgus monkey and in vitro human metabolism data. To estimate human PD parameters, the relationship between lymphocyte counts and plasma concentrations of ONO-4641 in cynomolgus monkeys was determined. The relationship between lymphocyte counts and plasma concentrations of ONO-4641 was described by an indirect-response model. The indirect-response model had an I(max) value of 0.828 and an IC(50) value of 1.29?ng/ml based on the cynomolgus monkey data. These parameters were used to represent human PD parameters for the simulation of lymphocyte counts. Other human PD parameters such as input and output rate constants for lymphocytes were obtained from the literature. Based on these estimated human PK and PD parameters, human lymphocyte counts after administration of ONO-4641 were simulated. In conclusion, the simulation of human lymphocyte counts based on preclinical data led to the acquisition of useful information for designing future clinical studies.
Myosin light chain (MLC) phosphorylation plays important roles in various cellular functions such as cellular morphogenesis, motility, and smooth muscle contraction. MLC phosphorylation is determined by the balance between activities of Rho-associated kinase (Rho-kinase) and myosin phosphatase. An impaired balance between Rho-kinase and myosin phosphatase activities induces the abnormal sustained phosphorylation of MLC, which contributes to the pathogenesis of certain vascular diseases, such as vasospasm and hypertension. However, the dynamic principle of the system underlying the regulation of MLC phosphorylation remains to be clarified. Here, to elucidate this dynamic principle whereby Rho-kinase regulates MLC phosphorylation, we developed a mathematical model based on the behavior of thrombin-dependent MLC phosphorylation, which is regulated by the Rho-kinase signaling network. Through analyzing our mathematical model, we predict that MLC phosphorylation and myosin phosphatase activity exhibit bistability, and that a novel signaling pathway leading to the auto-activation of myosin phosphatase is required for the regulatory system of MLC phosphorylation. In addition, on the basis of experimental data, we propose that the auto-activation pathway of myosin phosphatase occurs in vivo. These results indicate that bistability of myosin phosphatase activity is responsible for the bistability of MLC phosphorylation, and the sustained phosphorylation of MLC is attributed to this feature of bistability.
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