Coupled Protein Diffusion and Folding in the Cell

When a protein unfolds in the cell, its diffusion coefficient is affected by its increased hydrodynamic radius and by interactions of exposed hydrophobic residues with the cytoplasmic matrix, including chaperones. We characterize protein diffusion by photobleaching whole cells at a single point, and imaging the concentration change of fluorescent-labeled protein throughout the cell as a function of time. As a folded reference protein we use green fluorescent protein. The resulting region-dependent anomalous diffusion is well characterized by 2-D or 3-D diffusion equations coupled to a clustering algorithm that accounts for position-dependent diffusion. Then we study diffusion of a destabilized mutant of the enzyme phosphoglycerate kinase (PGK) and of its stable control inside the cell. Unlike the green fluorescent protein control''s diffusion coefficient, PGK''s diffusion coefficient is a non-monotonic function of temperature, signaling ‘sticking’ of the protein in the cytosol as it begins to unfold. The temperature-dependent increase and subsequent decrease of the PGK diffusion coefficient in the cytosol is greater than a simple size-scaling model suggests. Chaperone binding of the unfolding protein inside the cell is one plausible candidate for even slower diffusion of PGK, and we test the plausibility of this hypothesis experimentally, although we do not rule out other candidates.     

Exact solutions to a spatially extended model of kinase-receptor interaction

B and Mast cells are activated by the aggregation of the immune receptors. Motivated by this phenomena we consider a simple spatially extended model of mutual interaction of kinases and membrane receptors. It is assumed that kinase activates membrane receptors and in turn the kinase molecules bound to the active receptors are activated by transphosphorylation. Such a type of interaction implies positive feedback and may lead to bistability. In this study we apply the Steklov eigenproblem theory to analyze the linearized model and find exact solutions in the case of non-uniformly distributed membrane receptors. This approach allows us to determine the critical value of receptor dephosphorylation rate at which cell activation (by arbitrary small perturbation of the inactive state) is possible. We found that cell sensitivity grows with decreasing kinase diffusion and increasing anisotropy of the receptor distribution. Moreover, these two effects are cooperating. We showed that the cell activity can be abruptly triggered by the formation of the receptor aggregate. Since the considered activation mechanism is not based on receptor crosslinking by polyvalent antigens, the proposed model can also explain B cell activation due to receptor aggregation following binding of monovalent antigens presented on the antigen presenting cell.     

Diffusion in immobilized-cell gels

Summary The relationship between the diffusion coefficient, the effective diffusion coefficient and the partition coefficient for a solute in a cell-containing gel is discussed. The use of correlation equations that are based on some kind of physical model is recommended when the effect of cell concentration on diffusion is interpreted.     

Diffusion of phenol through a biofilm grown on activated carbon particles in a draft-tube three-phase fluidized-bed bioreactor

Diffusion of phenol through a biofilm attached to activated carbon particles was investigated. The biofilm was grown on activated carbon particles in a draft-tube three-phase fluidized-bed bioreactor operating in a fed-batch mode. It was found that phenol did not adsorb on the biofilm and that the diffusion coefficient of phenol within the biofilm varied from 13 to 39% of its corresponding value in water. The diffusion coefficient of phenol within the biofilm was reduced by increasing the biofilm density. An extensive literature review of diffusion of substrates through biofilms indicated that this conclusion could be extended to biofilms grown on flat surfaces, rotating cylinders, and even bioflocs.     

Improving parameter estimation for cell surface FRAP data

Fluorescence Recovery After Photobleaching (FRAP) using the confocal laser scanning microscope has become a standard method used to determine the diffusion coefficient and mobile fraction of cell surface proteins. A common experimental approach is to bleach a stripe on the cell surface and fit the ensuing FRAP curve to a 1D diffusion model. This model is derived from the time course of recovery to an infinitely long stripe bleached on an infinite flat plane. This choice of model dictates the use of a long bleach stripe. We demonstrate that, in the case of a long bleach stripe, the finite extent of the cell leads to significant errors in parameter estimation. We further show that these errors are reduced when a relatively small stripe is bleached. Unfortunately, diffusion to such a region is fundamentally two dimensional and therefore applying the 1D model of diffusion leads to significant errors. We derive an equation suitable for fitting to FRAP data acquired from small bleach regions and analyze its accuracy using simulated data. We propose that the use of a small bleach region along with a two dimensional diffusion model is the ideal protocol for cell surface FRAP.     

B cell activation triggered by the formation of the small receptor cluster: a computational study

We proposed a spatially extended model of early events of B cell receptors (BCR) activation, which is based on mutual kinase-receptor interactions that are characteristic for the immune receptors and the Src family kinases. These interactions lead to the positive feedback which, together with two nonlinearities resulting from the double phosphorylation of receptors and Michaelis-Menten dephosphorylation kinetics, are responsible for the system bistability. We demonstrated that B cell can be activated by a formation of a tiny cluster of receptors or displacement of the nucleus. The receptors and Src kinases are activated, first locally, in the locus of the receptor cluster or the region where the cytoplasm is the thinnest. Then the traveling wave of activation propagates until activity spreads over the whole cell membrane. In the models in which we assume that the kinases are free to diffuse in the cytoplasm, we found that the fraction of aggregated receptors, capable to initiate B cell activation decreases with the decreasing thickness of cytoplasm and decreasing kinase diffusion. When kinases are restricted to the cell membrane - which is the case for most of the Src family kinases - even a cluster consisting of a tiny fraction of total receptors becomes activatory. Interestingly, the system remains insensitive to the modest changes of total receptor level. The model provides a plausible mechanism of B cells activation due to the formation of small receptors clusters collocalized by binding of polyvalent antigens or arising during the immune synapse formation.     

Spatial distribution and dose-response relationship for different operation modes in a reaction-diffusion model of the MAPK cascade

The mitogen-activated protein kinase (MAPK) cascade plays a critical role in the control of cell growth. Deregulation of this pathway contributes to the development of many cancers. To better understand its signal transduction, we constructed a reaction-diffusion model for the MAPK pathway. We modeled the three layers of phosphorylation-dephosphorylation reactions and diffusion processes from the cell membrane to the nucleus. Based on different types of feedback in the MAPK cascade, four operation modes are introduced. For each of the four modes, spatial distributions and dose-response curves of active kinases (i.e. ppMAPK) are explored by numerical simulation. The effects of propagation length, diffusion coefficient and feedback strength on the pathway dynamics are investigated. We found that intrinsic bistability in the MAPK cascade can generate a traveling wave of ppMAPK with constant amplitude when the propagation length is short. ppMAPK in this mode of intrinsic bistability decays more slowly than it does in all other modes as the propagation length increases. Moreover, we examined the global and local responses to Ras-GTP of these four modes, and demonstrated how the shapes of these dose-response curves change as the propagation length increases. Also, we found that larger diffusion constant gives a higher response level on the zero-order regime and makes the ppMAPK profiles flatter under strong Ras-GTP stimulus. Furthermore, we observed that spatial responses of ppMAPK are more sensitive to negative feedback than to positive feedback in the broader signal range. Finally, we showed how oscillatory signals pass through the kinase cascade, and found that high frequency signals are damped faster than low frequency ones.     

A diffusion model and optimal cell loading for immobilized cell biocatalysts

A diffusion model based on the random pore model is derived for immobilized cell biocatalysts and verified with 19 sets of experimental diffusion data. The predicted effective diffusivity relative to that for the support matrix reflects a quadratic dependence on the cell loading and contains a single parameter that depends on the intracellular diffusivity and the chemical partitioning coefficient. The model is used to predict optimal cell loadings that maximize the total reaction rate in an immobilized cell biocatalyst. A rule of thumb based on the diffusion model is obtained to the effect that the cell loading should be at least (1/3) for single reactions regardless of the kinetics and diffusional resistances. A means of calculating improved lower bounds is provided for cases where the cellular diffusional resistance is known but the kinetics are not. The optimal cell loadings for reversible first-order and for Michaelis-Menten kinetics are presented and demonstrated to be within the range of conditions of practical interest.     

Role of phosphocreatine in energy transport in skeletal muscle of bullfrog studied by 31P-NMR

To evaluate the energy-shuttle hypothesis of the phosphocreatine/creatine kinase system, diffusion rates for ATP, phosphocreatine and flux through the creatine kinase reaction were determined by 31P-NMR in resting bullfrog biceps muscle. The diffusion coefficient of phosphocreatine measured by 31P-pulsed gradient NMR was 1.4-times larger than ATP in the muscle, indicating the advantage of phosphocreatine molecules for the intracellular energy transport. The flux of the creatine kinase reaction measured by 31P-saturation transfer NMR was 3.6 mmol/kg wet wt. per s in the resting muscle. The flux is equal to the turnover rate of ATP, ADP, phosphocreatine and creatine molecules, therefore, the life-times of these substrates and the average distance traversed after the life-times by the diffusing molecules were calculated using the diffusion coefficients obtained by 31P-NMR. The mean square length of one-dimensional diffusion was 22 microns in ATP molecules and the minimum diffusion length was 1.8 microns in ADP molecules. The latter was calculated using free ADP concentration, 30 mumol/kg wet wt., obtained from the equilibrium constant of the creatine kinase reaction and the diffusion coefficient assumed to be the same of ATP in muscle. Similar diffusion lengths of ADP were calculated using the reported values for the flux of the creatine kinase reaction in heart and smooth-muscle. The diffusion lengths of all substrates involved in the creatine kinase reaction were larger than the radii of myofibrils. Therefore, in the muscles with an alternating arrangement of mitochondria and myofibrils, such as heart and certain skeletal muscles, ATP and ADP molecules can move freely between myofibrils and mitochondria without the aid of the creatine kinase reaction; thus, we conclude that the energy-shuttle hypothesis is not obligatory for energy transport between the mitochondria and the myofibrils.     

A Highlights from MBoC Selection: Diffusion of GPI-anchored proteins is influenced by the activity of dynamic cortical actin

Molecular diffusion at the surface of living cells is believed to be predominantly driven by thermal kicks. However, there is growing evidence that certain cell surface molecules are driven by the fluctuating dynamics of cortical cytoskeleton. Using fluorescence correlation spectroscopy, we measure the diffusion coefficient of a variety of cell surface molecules over a temperature range of 24–37°C. Exogenously incorporated fluorescent lipids with short acyl chains exhibit the expected increase of diffusion coefficient over this temperature range. In contrast, we find that GPI-anchored proteins exhibit temperature-independent diffusion over this range and revert to temperature-dependent diffusion on cell membrane blebs, in cells depleted of cholesterol, and upon acute perturbation of actin dynamics and myosin activity. A model transmembrane protein with a cytosolic actin-binding domain also exhibits the temperature-independent behavior, directly implicating the role of cortical actin. We show that diffusion of GPI-anchored proteins also becomes temperature dependent when the filamentous dynamic actin nucleator formin is inhibited. However, changes in cortical actin mesh size or perturbation of branched actin nucleator Arp2/3 do not affect this behavior. Thus cell surface diffusion of GPI-anchored proteins and transmembrane proteins that associate with actin is driven by active fluctuations of dynamic cortical actin filaments in addition to thermal fluctuations, consistent with expectations from an “active actin-membrane composite” cell surface.     

Activation of the Cdc42-associated tyrosine kinase-2 (ACK-2) by cell adhesion via integrin beta1

Activated Cdc42-associated kinase-2 (ACK-2) is a non-receptor tyrosine kinase that appears to be a highly specific target for the Rho-related GTP-binding protein Cdc42. In order to understand better how ACK-2 activity is regulated in cells, we have expressed epitope-tagged forms of this tyrosine kinase in COS-7 and NIH3T3 cells. We find that ACK-2 can be activated by cell adhesion in a Cdc42-dependent manner. However, unlike the focal adhesion kinase, which also is activated by cell adhesion, the activation of ACK-2 is F-actin-independent and does not require cell spreading. In addition, overexpression of ACK-2 in COS-7 cells did not result in the stimulation of extracellular signal-regulated kinase activity but rather activated the c-Jun kinase. Both anti-integrin beta1 antibody and RGD peptides inhibited the activation of ACK-2 by cell adhesion. In addition, ACK-2 was co-immunoprecipitated with integrin beta1. Overall, these findings suggest that ACK-2 interacts with integrin complexes and mediates cell adhesion signals in a Cdc42-dependent manner.     

Diffusion of methylene blue organic cation in the polymeric matrix of cell walls of the crustose lichen Cladonia rangiferina (L.) F. H. Wigg.

The diffusion within the polymeric matrix of the cell wall is a process that determines the possibility and the rate of ion penetration into cell. In this work, we quantitatively determined the diffusion of Methylene Blue cation within the cell walls isolated from the crustose lichen Cladonia rangiferina (L.) F. H. Wigg. and its possible contribution to the processes of absorption into the lichen thalli. The swelling coefficient of the cell wall matrix and the diffusion coefficient of the organic cation within the cell walls were determined. Our results show that lichen cell walls are characterized by a higher crosslinking degree and a smaller diffusion coefficient than plants.     

A novel function of p38-regulated/activated kinase in endothelial cell migration and tumor angiogenesis

The p38 mitogen-activated protein kinase (MAPK) pathway has been implicated in both suppression and promotion of tumorigenesis. It remains unclear how these 2 opposite functions of p38 operate in vivo to impact cancer development. We previously reported that a p38 downstream kinase, p38-regulated/activated kinase (PRAK), suppresses tumor initiation and promotion by mediating oncogene-induced senescence in a murine skin carcinogenesis model. Here, using the same model, we show that once the tumors are formed, PRAK promotes the growth and progression of skin tumors. Further studies identify PRAK as a novel host factor essential for tumor angiogenesis. In response to tumor-secreted proangiogenic factors, PRAK is activated by p38 via a vascular endothelial growth factor receptor 2 (VEGFR2)-dependent mechanism in host endothelial cells, where it mediates cell migration toward tumors and incorporation of these cells into tumor vasculature, at least partly by regulating the phosphorylation and activation of focal adhesion kinase (FAK) and cytoskeletal reorganization. These findings have uncovered a novel signaling circuit essential for endothelial cell motility and tumor angiogenesis. Moreover, we demonstrate that the tumor-suppressing and tumor-promoting functions of the p38-PRAK pathway are temporally and spatially separated during cancer development in vivo, relying on the stimulus, and the tissue type and the stage of cancer development in which it is activated.     

Kin1 is a plasma membrane‐associated kinase that regulates the cell surface in fission yeast

Cell morphogenesis is a complex process that depends on cytoskeleton and membrane organization, intracellular signalling and vesicular trafficking. The rod shape of the fission yeast Schizosaccharomyces pombe and the availability of powerful genetic tools make this species an excellent model to study cell morphology. Here we have investigated the function of the conserved Kin1 kinase. Kin1‐GFP associates dynamically with the plasma membrane at sites of active cell surface remodelling and is present in the membrane fraction. Kin1Δ null cells show severe defects in cell wall structure and are unable to maintain a rod shape. To explore Kin1 primary function, we constructed an ATP analogue‐sensitive allele kin1‐as1. Kin1 inhibition primarily promotes delocalization of plasma membrane‐associated markers of actively growing cell surface regions. Kin1 itself is depolarized and its mobility is strongly reduced. Subsequently, amorphous cell wall material accumulates at the cell surface, a phenotype that is dependent on vesicular trafficking, and the cell wall integrity mitogen‐activated protein kinase pathway is activated. Deletion of cell wall integrity mitogen‐activated protein kinase components reduces kin1Δ hypersensitivity to stresses such as those induced by Calcofluor white and SDS. We propose that Kin1 is required for a tight link between the plasma membrane and the cell wall.     

High-energy phosphate transfer in human muscle: diffusion of phosphocreatine

The creatine kinase (CK) reaction is central to muscle energetics, buffering ATP levels during periods of intense activity via consumption of phosphocreatine (PCr). PCr is believed to serve as a spatial shuttle of high-energy phosphate between sites of energy production in the mitochondria and sites of energy utilization in the myofibrils via diffusion. Knowledge of the diffusion coefficient of PCr (D(PCr)) is thus critical for modeling and understanding energy transport in the myocyte, but D(PCr) has not been measured in humans. Using localized phosphorus magnetic resonance spectroscopy, we measured D(PCr) in the calf muscle of 11 adults as a function of direction and diffusion time. The results show that the diffusion of PCr is anisotropic, with significantly higher diffusion along the muscle fibers, and that the diffusion of PCr is restricted to a ～28-μm pathlength assuming a cylindrical model, with an unbounded diffusion coefficient of ～0.69 × 10(-3) mm(2)/s. This distance is comparable in size to the myofiber radius. On the basis of prior measures of CK reaction kinetics in human muscle, the expected diffusion distance of PCr during its half-life in the CK reaction is ～66 μm. This distance is much greater than the average distances between mitochondria and myofibrils. Thus these first measurements of PCr diffusion in human muscle in vivo support the view that PCr diffusion is not a factor limiting high-energy phosphate transport between the mitochondria and the myofibrils in healthy resting myocytes.     

Turing instabilities in a mathematical model for signaling networks

GTPase molecules are important regulators in cells that continuously run through an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated GTPase is able to localize in parts of the membranes and to induce cell polarity. As feedback loops contribute to the GTPase cycle and as the coupling between membrane-bound and cytoplasmic processes introduces different diffusion coefficients a Turing mechanism is a natural candidate for this symmetry breaking. We formulate a mathematical model that couples a reaction–diffusion system in the inner volume to a reaction–diffusion system on the membrane via a flux condition and an attachment/detachment law at the membrane. We present a reduction to a simpler non-local reaction–diffusion model and perform a stability analysis and numerical simulations for this reduction. Our model in principle does support Turing instabilities but only if the lateral diffusion of inactivated GTPase is much faster than the diffusion of activated GTPase.     

Compartmentalized energy transfer in cardiomyocytes: use of mathematical modeling for analysis of in vivo regulation of respiration.

The mathematical model of the compartmentalized energy transfer system in cardiac myocytes presented includes mitochondrial synthesis of ATP by ATP synthase, phosphocreatine production in the coupled mitochondrial creatine kinase reaction, the myofibrillar and cytoplasmic creatine kinase reactions, ATP utilization by actomyosin ATPase during the contraction cycle, and diffusional exchange of metabolites between different compartments. The model was used to calculate the changes in metabolite profiles during the cardiac cycle, metabolite and energy fluxes in different cellular compartments at high workload (corresponding to the rate of oxygen consumption of 46 mu atoms of O.(g wet mass)-1.min-1) under varying conditions of restricted ADP diffusion across mitochondrial outer membrane and creatine kinase isoenzyme "switchoff." In the complete system, restricted diffusion of ADP across the outer mitochondrial membrane stabilizes phosphocreatine production in cardiac mitochondria and increases the role of the phosphocreatine shuttle in energy transport and respiration regulation. Selective inhibition of myoplasmic or mitochondrial creatine kinase (modeling the experiments with transgenic animals) results in "takeover" of their function by another, active creatine kinase isoenzyme. This mathematical modeling also shows that assumption of the creatine kinase equilibrium in the cell may only be a very rough approximation to the reality at increased workload. The mathematical model developed can be used as a basis for further quantitative analyses of energy fluxes in the cell and their regulation, particularly by adding modules for adenylate kinase, the glycolytic system, and other reactions of energy metabolism of the cell.     

Isotherm,Kinetic, and Thermodynamic Characteristics for Adsorption of 2,5-Xylenol onto Activated Carbon

The adsorption of the major tar compound, 2,5-xylenol, derived from the plant cell cultures of Taxus chinensis, onto activated carbon was examined at different initial 2,5-xylenol concentrations, durations, and temperatures. From the analysis of adsorption isotherms, the Langmuir isotherm model showed good fit to the equilibrium adsorption data. It was found that adsorption capacity decreased with increasing temperature, and the adsorption of 2,5-xylenol onto activated carbon was favorable. The obtained kinetic data for 2,5-xylenol adsorption with activated carbon agreed well with the pseudo-second-order kinetic model. By using intraparticle diffusion model, intraparticle diffusion and boundary layer diffusion did not play a dominant role in 2,5-xylenol adsorption. Thermodynamic parameters were calculated, which indicated that the adsorption was non-spontaneous, irreversible and exothermic nature. The isosteric heat of adsorption decreased with increase in surface loading, indicating a heterogeneous surface.     

ATR-dependent activation of p38 MAP kinase is responsible for apoptotic cell death in cells depleted of Cdc7

Cdc7 is a serine/threonine kinase that plays essential roles in the initiation of eukaryotic DNA replication and checkpoint response. In previous studies, depletion of Cdc7 by small interfering RNA was shown to induce an abortive S phase that led to the cell cycle arrest in normal human fibroblasts and apoptotic cell death in various cancer cells. Here we report that stress-activated p38 MAP kinase was activated and responsible for apoptotic cell death in Cdc7-depleted HeLa cells. The activation of p38 MAP kinase in the Cdc7-depleted cells was shown to depend on ATR, a major sensor kinase for checkpoint or DNA damage responses. Only the p38 MAP kinase, and not the other stress-activated kinases such as JNK or ERK, was activated, and both caspase 8 and caspase 9 were activated for the induction of apoptosis. Activation of apoptosis in Cdc7-depleted cells was completely abolished in cells treated with small interfering RNA or an inhibitor of the p38 MAP kinase, suggesting that p38 MAP kinase activation was responsible for apoptotic cell death. Taken together, we suggest that the ATR-dependent activation of the p38 MAP kinase is a major signaling pathway that induces apoptotic cell death after depletion of Cdc7 in cancer cells.     

The survival kinase Mirk/dyrk1B is activated through Rac1-MKK3 signaling

The serine/threonine kinase Mirk/dyrk1B is activated in several solid tumors where it mediates cell survival, but the mechanism by which Mirk is activated in tumors is unknown. We now demonstrate that Mirk is activated as a kinase by signaling from Rac1 to the mitogen-activated protein kinase kinase MKK3. Rac is a Ras superfamily GTPase that, when activated, functions downstream of Ras oncoproteins to promote cell survival, transformation, and membrane ruffling. The constitutively active mutant Rac1QL activated Mirk in several cell types through MKK3, which in turn activated Mirk by phosphorylation. Dominant negative Rac1, dominant negative MKK3, and knockdown of MKK3 by RNA interference inhibited the kinase activity of co-expressed Mirk. E-cadherin ligation in confluent Madin-Darby canine kidney (MDCK) epithelial cells is known to transiently activate Rac1. Mirk was activated by endogenous Rac1 following E-cadherin ligation in confluent MDCK epithelial cells, whereas treatment of confluent MDCK cells with an Rac1 inhibitor decreased Mirk activity. Disruption of cadherin ligation by EGTA or prevention of cadherin ligation by maintenance of cells at subconfluent density blocked activation of Mirk. Engagement of cadherin molecules on subconfluent cells by an E-cadherin/Fc chimeric molecule transiently activated both Rac1 and Mirk with a similar time course. Rac activity is up-regulated in many human tumors and mediates survival signals, which enable tumor cells to evade apoptosis. This study characterizes a new anti-apoptotic signaling pathway that connects Rac1 with a novel downstream effector, Mirk kinase, which has recently been demonstrated to mediate survival in human tumors.