Propagators and time-dependent diffusion coefficients for anomalous diffusion

Complex diffusive dynamics are often observed when one is investigating the mobility of macromolecules in living cells and other complex environments, yet the underlying physical or chemical causes of anomalous diffusion are often not fully understood and are thus a topic of ongoing research interest. Theoretical models capturing anomalous dynamics are widely used to analyze mobility data from fluorescence correlation spectroscopy and other experimental measurements, yet there is significant confusion regarding these models because published versions are not entirely consistent and in some cases do not appear to satisfy the diffusion equation. Further confusion is introduced through variations in how fitting parameters are reported. A clear definition of fitting parameters and their physical significance is essential for accurate interpretation of experimental data and comparison of results from different studies acquired under varied experimental conditions. This article aims to clarify the physical meaning of the time-dependent diffusion coefficients associated with commonly used fitting models to facilitate their use for investigating the underlying causes of anomalous diffusion. We discuss a propagator for anomalous diffusion that captures the power law dependence of the mean-square displacement and can be shown to rigorously satisfy the extended diffusion equation provided one correctly defines the time-dependent diffusion coefficient. We also clarify explicitly the relation between the time-dependent diffusion coefficient and fitting parameters in fluorescence correlation spectroscopy.     

A general diffusion model for analyzing the efficacy of synaptic input to threshold neurons

We describe a general diffusion model for analyzing the efficacy of individual synaptic inputs to threshold neurons. A formal expression is obtained for the system propagator which, when given an arbitrary initial state for the cell, yields the conditional probability distribution for the state at all later times. The propagator for a cell with a finite threshold is written as a series expansion, such that each term in the series depends only on the infinite threshold propagator, which in the diffusion limit reduces to a Gaussian form. This procedure admits a graphical representation in terms of an infinite sequence of diagrams. To connect the theory to experiment, we construct an analytical expression for the primary correlation kernel (PCK) which profiles the change in the instantaneous firing rate produced by a single postsynaptic potential (PSP). Explicit solutions are obtained in the diffusion limit to first order in perturbation theory. Our approximate expression resembles the PCK obtained by computer simulation, with the accuracy depending strongly on the mode of firing. The theory is most accurate when the synaptic input drives the membrane potential to a mean level more than one standard deviation below the firing threshold, making such cells highly sensitive to synchronous synaptic input.     

Binding of double-stranded DNA by Escherichia coli RecA protein monitored by a fluorescent dye displacement assay.

We have developed a new assay to characterize the double-stranded DNA (dsDNA) binding properties of RecA protein. This assay is based on measurement of changes in the fluorescence of a 4',6-diamidino-2-phenylindole (DAPI)-dsDNA complex upon RecA protein binding. The binding of RecA protein to a complex of DAPI and dsDNA results in displacement of the bound DAPI, producing a decrease in the observed fluorescence. DAPI displacement is dependent on both RecA protein and ATP; dATP and, to a lesser extent, UTP and dCTP also support the DAPI displacement reaction, but dGTP, GTP, dITP and TTP do not. Binding stoichiometry for the RecA protein-dsDNA complex measured by DAPI displacement is 3 bp per RecA protein monomer in the presence of ATP. These results, taken together with data for mutant RecA proteins, suggest that this DAPI displacement assay monitors formation of the high affinity DNA binding state of RecA protein. Since this state of RecA protein defines the form of the nucleoprotein filament that is active in DNA strand exchange, these findings raise the possibility that the RecA protein-dsDNA filament may possess a homologous pairing capacity.     

Micromanipulation of statoliths in gravity-sensing Chara rhizoids by optical tweezers

Infrared laser traps (optical tweezers) were used to micromanipulate statoliths in gravity-sensing rhizoids of the green alga Chara vulgaris Vail. We were able to hold and move statoliths with high accuracy and to observe directly the effects of statolith position on cell growth in horizontally positioned rhizoids. The first step in gravitropism, namely the physical action of gravity on statoliths, can be simulated by optical tweezers. The direct laser microirradiation of the rhizoid apex did not cause any visible damage to the cells. Through lateral positioning of statoliths a differential growth of the opposite flank of the cell wall could be induced, corresponding to bending growth in gravitropism. The acropetal displacement of the statolith complex into the extreme apex of the rhizoid caused a temporary decrease in cell growth rate. The rhizoids regained normal growth after remigration of the statoliths to their initial position 10–30 m basal to the rhizoid apex. During basipetal displacement of statoliths, cell growth continued and the statoliths remigrated towards the rhizoid tip after release from the optical trap. The resistance to statolith displacement increased towards the nucleus. The basipetal displacement of the whole complex of statoliths for a long distance (>100 m) caused an increase in cell diameter and a subsequent regaining of normal growth after the statoliths reappeared in the rhizoid apex. We conclude that the statolith displacement interferes with the mechanism of tip growth, i.e. with the transport of Golgi vesicles, either directly by mechanically blocking their flow and/or, indirectly, by disturbing the actomyosin system. In the presence of the actin inhibitor cytochalasin B the optical forces required for acropetal and basipetal displacement of statoliths were significantly reduced to a similar level. The lateral displacement of statoliths was not changed by cytochalasin B. The results indicate: (i) the viscous resistance to optical displacement of statoliths depends mainly on actin, (ii) the lateral displacement of statoliths is not impeded by actin filaments, (iii) the axially directed actin-mediated forces against optical displacement of statoliths (for a distance of 10 m) are stronger in the basipetal than in the acropetal direction, (iv) the forces acting on single statoliths by axially oriented actin filaments are estimated to be in the range of 11–110 pN for acropetal and of 18–180 pN for basipetal statolith displacements.Abbreviation CB cytochalasin B This work was supported by the Bundesminister für Forschung und Technologie, and by Fonds der Chemischen Industrie. We thank Professor Dr. A. Sievers (Botanisches Institut, Universität Bonn, Germany) for helpful discussions.     

The recombination-deficient mutant RPA (rfa1-t11) is displaced slowly from single-stranded DNA by Rad51 protein

Replication protein-A (RPA) is involved in many processes of DNA metabolism, including DNA replication, repair, and recombination. Cells carrying a mutation in the largest subunit of RPA (rfa1-t11: K45E) have defects in meiotic recombination, mating-type switching, and survival after DNA damage caused by UV and methyl methanesulfonate, as well as increased genome instability; however, this mutant has no significant defect in DNA replication. We purified the RPA heterotrimer containing the rfa1-t11 substitution (RPA(rfa1-t11)). This mutant RPA binds single-stranded DNA (ssDNA) with the same site size, and the RPA(rfa1-t11).ssDNA complex shows a similar sensitivity to disruption by salt as the wild-type RPA.ssDNA complex. RPA(rfa1-t11) stimulates DNA strand exchange, provided that the Rad51 protein.ssDNA nucleoprotein complex is assembled prior to introduction of the mutant RPA. However, RPA(rfa1-t11) is displaced from ssDNA by Rad51 protein more slowly than wild-type RPA and, as a consequence, Rad51 protein-mediated DNA strand exchange is inhibited when the ssDNA is in a complex with RPA(rfa1-t11). Rad52 protein can stimulate displacement of RPA(rfa1-t11) from ssDNA by Rad51 protein, but the rate of displacement remains slow compared with wild-type RPA. These in vitro results suggest that, in vivo, RPA is bound to ssDNA prior to Rad51 protein and that RPA displacement by Rad51 protein is a critical step in homologous recombination, which is impaired in the rfa1-t11 mutation.     

Mechanism of ubiquinol oxidation by the bc(1) complex: role of the iron sulfur protein and its mobility

Native structures of ubihydroquinone:cytochrome c oxidoreductase (bc(1) complex) from different sources, and structures with inhibitors in place, show a 16-22 A displacement of the [2Fe-2S] cluster and the position of the C-terminal extrinsic domain of the iron sulfur protein. None of the structures shows a static configuration that would allow catalysis of all partial reactions of quinol oxidation. We have suggested that the different conformations reflect a movement of the subunit necessary for catalysis. The displacement from an interface with cytochrome c(1) in native crystals to an interface with cytochrome b is induced by stigmatellin or 5-n-undecyl-6-hydroxy-4,7-dioxobenzothiazole (UHDBT) and involves ligand formation between His-161 of the [2Fe-2S] binding cluster and the inhibitor. The movement is a rotational displacement, so that the same conserved docking surface on the iron sulfur protein interacts with cytochrome c(1) and with cytochrome b. The mobile extrinsic domain retains essentially the same tertiary structure, and the anchoring N-terminal tail remains in the same position. The movement occurs through an extension of a helical segment in the short linking span. We report details of the protein structure for the two main configurations in the chicken heart mitochondrial complex and discuss insights into mechanism provided by the structures and by mutant strains in which the docking at the cytochrome b interface is impaired. The movement of the iron sulfur protein represents a novel mechanism of electron transfer, in which a tethered mobile head allows electron transfer through a distance without the entropic loss from free diffusion.     

Magnetic resonance microscopy analysis of advective transport in a biofilm reactor

In this article we present magnetic resonance microscopy (MRM) characterization of the advective transport in a biofilm capillary reactor. The biofilm generates non-axial flows that are up to 20% of the maximum axial velocity. The presence of secondary velocities of this magnitude alters the mass transport in the bioreactor relative to non-biofilm fouled reactors and questions the applicability of empirical mass transfer coefficient approaches. The data are discussed in the context of simulations and models of biofilm transport and conceptual aspects of transport modeling in complex flows are also discussed. The variation in the residence time distribution due to biofilm growth is calculated from the measured propagator of the motion. Dynamical systems methods applied to model fluid mixing in complex flows are indicated as a template for extending mass transport theory to quantitatively incorporate microscale data on the advection field into macroscale mass transfer models.     

Alcohol redirects CCK-mediated apical exocytosis to the acinar basolateral membrane in alcoholic pancreatitis

The molecular mechanism of clinical alcohol-induced pancreatitis remains vague. We had reported that experimental high-dose cholecystokinin (CCK)-induced pancreatitis is in part because of excessive aberrant basolateral exocytosis. High-dose CCK caused Munc18c on basolateral plasma membrane (BPM) to dissociate from syntaxin (Syn)-4, activating Syn-4 to complex with plasma membrane (PM)-SNAP-23 and granule-VAMP to mediate basolateral exocytosis. We now hypothesize that alcohol could render the acinar cell BPM conducive to exocytosis by a similar mechanism. Weakly stimulating postprandial doses of alcohol (20-50 mM) inhibited postprandial low-dose CCK-stimulated secretion by blocking physiologic apical exocytosis and redirecting exocytosis to less-efficient basal PM (visualized by FM1-43 fluorescence imaging) and lateral PM sites (electron microscopy). Alcohol or low-dose CCK had no effect on PM-Munc18c, but alcohol preincubation enabled low-dose CCK to displace Munc18c from BPM, leading to SNARE complex assembly in the BPM. Similarly, alcohol diet-fed rats did not exhibit morphologic defects in the pancreas nor affected PM-Munc18c behavior, but subsequent intraperitoneal injections of low-dose CCK analog cerulein caused Munc18c displacement from BPM and cytosolic degradation, which contributed to pancreatitis. We conclude that alcohol induces BPM-Munc18c to become receptive to postprandial CCK-induced displacement into the cytosol, a process which facilitates SNARE complex assembly that in turn activates restricted BPM sites to become available for aberrant exocytosis into the interstitial space, where zymogen activation would take place and cause pancreatitis.     

Modulation of the neuronal binding of the beta subunit of nerve growth factor (NGF) by the alpha-NGF subunit

The effect of the alpha subunit of the 7S-NGF on the binding of beta-NGF to its two classes of sites on target cells has been studied. The presence of microM concentrations of alpha-NGF causes the displacement of 125I-beta-NGF from one class of sites on dissociated dorsal root ganglia neurons from stage E9 chicken embryos. At 0.1 nM 125I-beta-NGF, increasing alpha-NGF concentrations produce a monotonic displacement curve with half-maximal displacement occurring at 10 microM alpha-NGF. The affinity and number of sites of the 125I-beta-NGF displaced by alpha-NGF are similar to those of beta-NGF that binds to the higher affinity (site I) receptors. The binding to the lower affinity class of sites (site II) is not affected by concentrations of alpha-NGF up to 30 microM. This modulation of 125I-beta-NGF binding does not occur with equivalent concentrations of serum albumin. No detectable neuronal binding of 125I-alpha-NGF was found, suggesting that the mechanism does not involve direct competition for receptor sites. The dissociation constant for the alpha-beta complex is in the microM range, and formation of this complex in solution can thus compete with the process of 125I-beta-NGF binding to neurons. A model accounting for these observations includes binding of the alpha-beta complex to the lower affinity but not to the higher affinity sites. We conclude that there are differences in the specificity of the two classes of receptors.     

The crystal structure analysis of group B Streptococcus sortase C1: a model for the "lid" movement upon substrate binding

A unique feature of the class-C-type sortases, enzymes essential for Gram-positive pilus biogenesis, is the presence of a flexible “lid” anchored in the active site. However, the mechanistic details of the “lid” displacement, suggested to be a critical prelude for enzyme catalysis, are not yet known. This is partly due to the absence of enzyme-substrate and enzyme-inhibitor complex crystal structures. We have recently described the crystal structures of the Streptococcus agalactiae SAG2603 V/R sortase SrtC1 in two space groups (type II and type III) and that of its “lid” mutant and proposed a role of the “lid” as a protector of the active-site hydrophobic environment. Here, we report the crystal structures of SAG2603 V/R sortase C1 in a different space group (type I) and that of its complex with a small-molecule cysteine protease inhibitor. We observe that the catalytic Cys residue is covalently linked to the small-molecule inhibitor without lid displacement. However, the type I structure provides a view of the sortase SrtC1 lid displacement while having structural elements similar to a substrate sorting motif suitably positioned in the active site. We propose that these major conformational changes seen in the presence of a substrate mimic in the active site may represent universal features of class C sortase substrate recognition and enzyme activation.     

Phase transition in tensionless surfaces

We study the critical behavior of the Laplacian roughening model, which describes the growth of tensionless surfaces. This type of growth phenomena is very important, for instance, in biological membranes and in molecular beam epitaxy. We summarize previous analytical and numerical results and point out their contradictions and differences, thus making clear the context of our work. Our contribution, achieved through large-scale numerical simulations, is the confirmation that the model exhibits a single continuous phase transition: the transition takes place between a continuum massless (i.e., with infinite correlation length) bilaplacian behavior and a massive propagator (finite correlation length).     

Estimation of the deformations induced by articulated bodies: Registration of the spinal column

We present a new non-rigid registration algorithm estimating the displacement field generated by articulated bodies. Indeed the bony structures between different patient images may rigidly move while other tissues may deform in a more complex way. Our algorithm tracks the displacement induced in the column by a movement of the patient between two acquisitions. The volumetric deformation field in the whole body is then inferred from those displacements using a linear elastic biomechanical finite element model. We demonstrate in this paper that this method provides accurate results on 3D sets of computed tomography (CT), MR and positron emission tomography (PET) images and that the results of the registration algorithm show significant decreases in the mean, min and max errors.     

Computational analysis of the transient movement of helices in sensory rhodopsin II

MD simulation of sensory rhodopsin II was executed for three intermediates (ground-state, K-state, M-state) appearing in its photocycle. We observed a large displacement of the cytoplasmic side of helixF only in M-state among the three intermediates. This displacement was transmitted to TM2, and the cytoplasmic side of TM2 rotated clockwise. These transient movements are in agreement with the results of an EPR experiment. That is, the early stage of signal transduction in a sRII-HtrII complex was successfully reproduced by the in silico MD simulation. By analyzing the structure of the sRII-HtrII complex, the following findings about the photocycle of sRII were obtained: (1) The hydrogen bonds between helixF and other helices determine the direction of the movement of helixF; (2) three amino acids (Arg162, Thr189, Tyr199) are essential for sRII-HtrII binding and contribute to the motion transfer from sRII to HtrII; (3) after the isomerization of retinal, a major conformational change of retinal was caused by proton transfer from Schiff base to Asp75, which, in turn, triggers the steric collision of retinal with Trp171. This is the main reason for the movement of the cytoplasmic side of helixF.     

Roles of DNA ligase III and XRCC1 in regulating the switch between short patch and long patch BER

Damaged DNA bases are repaired by base excision repair (BER), which can proceed via two pathways: short patch and long patch BER. During the latter, a stretch of several nucleotides is replaced by strand displacement DNA synthesis. We recently demonstrated that the ATP concentration may govern the decision between these BER sub-pathways. Employing a reconstituted BER complex containing among others DNA polymerase beta (Pol beta), DNA ligase III (Lig III) and XRCC1, here we show that Lig III and XRCC1 are essential mediators of this regulation. XRCC1 stimulates Pol beta strand displacement activity and releases inhibition of Pol beta by DNA-bound Lig III if ligation is prevented. XRCC1 is thus able to strongly promote strand displacement and long patch BER under conditions of ATP shortage. If sufficient ATP is available, ligation by Lig III prevents strand displacement, leading to short patch BER. Ligation-inactive mutants of Lig III do not prevent strand displacement by Pol beta under the same conditions. Consequently, the preferred use of short patch BER depends on the ligation competence of Lig III. Accordingly, lowering the levels of the XRCC1/Lig III complex in HeLa cells using siRNA decreases ligation capacity but enhances Pol beta-dependent DNA synthesis.     

The process of displacing the single-stranded DNA-binding protein from single-stranded DNA by RecO and RecR proteins

The regions of single-stranded (ss) DNA that result from DNA damage are immediately coated by the ssDNA-binding protein (SSB). RecF pathway proteins facilitate the displacement of SSB from ssDNA, allowing the RecA protein to form protein filaments on the ssDNA region, which facilitates the process of recombinational DNA repair. In this study, we examined the mechanism of SSB displacement from ssDNA using purified Thermus thermophilus RecF pathway proteins. To date, RecO and RecR are thought to act as the RecOR complex. However, our results indicate that RecO and RecR have distinct functions. We found that RecR binds both RecF and RecO, and that RecO binds RecR, SSB and ssDNA. The electron microscopic studies indicated that SSB is displaced from ssDNA by RecO. In addition, pull-down assays indicated that the displaced SSB still remains indirectly attached to ssDNA through its interaction with RecO in the RecO-ssDNA complex. In the presence of both SSB and RecO, the ssDNA-dependent ATPase activity of RecA was inhibited, but was restored by the addition of RecR. Interestingly, the interaction of RecR with RecO affected the ssDNA-binding properties of RecO. These results suggest a model of SSB displacement from the ssDNA by RecF pathway proteins.     

Evaluation of anchorage-dependent cell propagation systems for production of human acetylcholinesterase by recombinant 293 cells

Production of recombinant human acetylcholinesterase (AChE) by a high producer human embryonic kidney cell line (293) was evaluated by three main cell propagation systems; surface propagator, fixed-bed reactor and stirred microcarrier cultures. The recombinant cell line expresses AChE levels as high as 10–20 mg/l/day. System productivities in either the surface propagator (multitray system), or in the fixed-bed reactor (polyurethane macroporous sponges) were 4–8 mg AChE/l/day during a production period of 8 days. Similar productive rates, yet longer production periods (up to 22 days), were obtained in microcarrier (MC) cultures using either polystyrene beads (Biosilon); collagen-coated dextran beads (Cytodex-3); or gelatin macroporous beads (Cultispher-G). Best results were obtained in an aggregate cculture using cellulose beads charged with diethylaminoethyl (DEAE) groups, (Servacel), as carriers. In this culture, a system productivity of 6–10 mg/l/day was maintained for 28 days.     

Kinetic evidence for a two-step mechanism for the binding of chymotrypsin to alpha 1-proteinase inhibitor.

We have used the proflavin displacement method and a stopped-flow apparatus to measure the rate constant for the binding of 2 microM-chymotrypsin to 20-125 microM-alpha 1-proteinase inhibitor. The observed pseudo-first-order constant showed a hyperbolic dependence on alpha 1-proteinase inhibitor concentration, suggesting a reaction mechanism in which a fast pre-equilibrium (K = 0.19 mM) is followed by a first-order formation of the final complex (k = 252 s-1).     

The serpin inhibitory mechanism is critically dependent on the length of the reactive center loop

The recent crystallographic structure of a serpin-protease complex revealed that protease inactivation results from a disruption of the catalytic site architecture caused by the displacement of the catalytic serine. We hypothesize that inhibition depends on the length of the N-terminal portion of the reactive center loop, to which the active serine is covalently attached. To test this, alpha(1)-antitrypsin Pittsburgh variants were prepared with lengthened and shortened reactive center loops. The rates of inhibition of factor Xa and of complex dissociation were measured. The addition of one residue reduced the stability of the complex more than 200,000-fold, and the addition of two residues reduced it by more than 1,000,000-fold, whereas the deletion of one or two residues lowered the efficiency of inhibition and increased the stability of the complex (2-fold). The deletion of more than two residues completely converted the serpin into a substrate. Similar results were obtained for the alpha(1)-antitrypsin variants with thrombin and for PAI-1 and PAI-2 with their common target tissue plasminogen activator. We conclude that the length of the serpin reactive center loop is critical for its mechanism of inhibition and is precisely regulated to balance the efficiency of inhibition and stability of the final complex.