Stationary cell size distributions and mean protein chain length distributions of Archaea, Bacteria and Eukaryotes described with an increment model in terms of irreversible thermodynamics.

In terms of an increment model irreversible thermodynamics allows to formulate general relations of stationary cell size distributions observed in growing colonies. The treatment is based on the following key postulates: i) The growth dynamics covers a broad spectrum of fast and slow processes. ii) Slow processes are considered to install structural patterns that operate in short periods as temporary stationary states of reference in the sense of irreversible thermodynamics. iii) Distortion during growth is balanced out via the many fast processes until an optimized stationary state is achieved. The relation deduced identifies the numerous different stationary patterns as equivalents, predicting that they should fall on one master curve. Stationary cell size distributions of different cell types, like Hyperphilic archaea, E. coli (Prokaryotes) and S. cerevisiae (Eukaryotes), altogether taken from the literature, are in fact consistently described. As demanded by the model they agree together with the same master curve. Considering the "protein factories" as subsystems of cells the mean protein chain length distributions deduced from completely sequenced genomes should be optimized. In fact, the mean course can be described with analogous relations as used above. Moreover, the master curve fits well to the patterns of different species of Archaea, Bacteria and Eukaryotes. General consequences are discussed.

Enzyme activity of the cytochrome P-450 monooxygenase system in the presence of single chain lipid molecules.

The influence of single chain lipids on the 7-ethoxycoumarin O-deethyase activity of the reconstituted binary protein complex of isolated cytochrome P450 and NADPH-cytochrome P450 reductase has been examined. The enzyme activity of this binary enzyme complex has been shown to be influenced by (i) altering the complexation process of both proteins, (ii) by altering the catalytic cycle time of the active binary protein complex and (iii) by altering the fraction of substrate molecules at the catalytic center of the enzyme. Competitive inhibition was measured for all single chain molecules. The following dissociation coefficients of substrate and lipids used for the catalytic center of the protein were obtained: 110 microM 7-ethoxycoumarin (substrate), 1.1 microM MOG (1-monooleoyl-rac-glycerol), 0.3 microM SPH (D-sphingosine), 1.5 microM OA (oleic acid), 3.0 microM LPC (L-alpha-lysophosphatidyl-choline), 15.5 microM MSG (1-monostearoyl-rac-glycerol), 9.5 microM AA (arachidonic acid), 9.0 microM PaCar (palmitoyl-L-carnitine), 3.5 microM MPG (2-monopalmitoyl-glycerol), 1.5 microM LPI (L-alpha-lysophosphatidyl-inositol), 50 microM LA (lauric acid), 60 microM MA (myristic acid), 85 microM PA (palmitic acid), >100 microM SA (stearic acid). Only competitive inhibition with the substrate molecule 7-ethoxycoumarin was observed for the single chain lipids LA, MA, PA, SPH, SA, and OA. Non-competitive effects were observed for MPG (-0.03 microM(-1)), PaCar (-0.02 microM(-1)), MSG (-0.023 microM(-1)), LPC (-0.03 microM(-1)), AA (-0.03 microM(-1)), and MOG (+0.04 microM(-1)). The negative sign indicates that the cycle time of the working binary complex is enlarged. The positive sign indicates that the formation of the binary complex is enhanced by MOG.

Complexation of membrane-bound enzyme systems.

The effect of changes in the N-terminal membrane-binding domain of cytochrome P450 forms and NADPH-cytochrome P450 reductase types on the cytochrome P450-dependent monooxygenase activities, has been examined. The nifedipine oxidase activity of two human P450 forms (CYP3A4, CYP3A4NF14) which differ only in their primary structure by ten amino acid residues in the N-terminal membrane-binding domain, yields nearly the same catalytic cycle time tau =2.65 +/- 0.15 s, due to their identical cytosolic catalytic protein structure. In contrast, the complex formation process ([P450]+[reductase] <--> [complex]) described by the dissociation constant KD, at high substrate concentration ([S]>>KS) and low product concentration ([P]<

The galvanotaxis response mechanism of keratinocytes can be modeled as a proportional controller.

Human keratinocytes actively crawl in vitro when plated onto a collagen-coated glass substrate, and their direction of migration is totally random. In response to an imposed DC electric field, they migrate asymmetrically, moving mostly toward the negative pole of the field. The authors have analyzed experimental data reported by others to determine the basic characteristics of the cellular response machinery in these keratinocytes. This movement can be completely described mathematically using two independent variables: the speed, V, and the angle of migration, phi. The authors propose a model in which a steerer (controller without feedback) is responsible for determining the speed, and an automatic controller (controller with feedback) is responsible for determining the angle of migration. The torque to rotate is induced by a deterministic cellular signal and a stochastic cellular signal. The cellular machine characteristics are determined as follows: The angular dependence of the detection unit is sin phi; the detection unit detects the guiding field in a linear fashion; the cellular reaction unit can be described by a constant; the chemical amplifier, as well as the cellular motor work, is linear; the cellular characteristic time, which quantifies the cellular stochastic signal, is 50 min.

Cell orientation induced by extracellular signals.

Cells like fibroblasts and osteoblasts are oriented by different extracellular guiding signals like an electric field, a bent surface, and a periodically stretched surface. An automatic controller is responsible for the cell alignment. The controller contains both a deterministic and a stochastic signal. The following machine properties were determined: (1) The angle dependence of the cellular signal transformer is cos 2(psi 0 - psi). (2) The set point of the automatic controller is psi 0 = +/- 90 degrees. The cells like to orient their long axis perpendicular to the direction of the applied guiding signal. (3) The signal transformer measures the extracellular signal in a quadratic fashion. The cells cannot register the sign of the guiding field. (4) The stochastic signal in the automatic controller can be quantified by a characteristic time (approximately 130 min for fibroblasts). (5) The extracellular signal is registered in cell-made standards (ratio of the deterministic and stochastic signal equals one): 0.3 +/- 0.05 V/mm for human fibroblasts (electric field) and 85 +/- 3 microns for human fibroblasts and osteoblasts (cyclindrically bent surface). (6) The lag-time in the signal transduction system of fibroblasts is approximately 4 min.

New insights into directed cell migration: characteristics and mechanisms.

The present article describes how it is possible to elucidate the essential cellular machines controlling directed migration. Investigations are performed with cells like granulocytes, fibroblasts or neural crest cells and these cells are found to contain two independent types of machines, a steerer (controller without feedback) for the speed and an automatic controller (controller with feedback) for the angle of migration. The first intracellular signal is the distribution of membrane bound receptors occupied by kinesis stimulating molecules from the extracellular space. Motile force is produced by a linear motor supplied by the chemically amplified first intracellular signal (total number of occupied receptors). When properties of the cellular steering device are investigated, results show the angle of migration to be corrected by an automatic controller and an asymmetric distribution of occupied receptors to be the first intracellular signal for directed migration. Properties of the goal-seeking device are also investigated. As in many different types of technical machines, the cellular machinery operates in a cyclic manner which in the case of granulocytes a measuring cycle of 8 s and a response cycle of approximately 60 s. These cellular machines may be understood in terms of a self-ignition mechanism where the renewal of membrane bound receptors is the essential step.

Directed cell movement in pulsed electric fields.

Human granulocytes exposed to pulsed electric guiding fields were investigated. The trajectories were determined from digitized pictures (phase contrast). The basic results are: (i) No directed response was induced by pulsed electric guiding fields having a zero averaged field. (ii) A directed response was induced by pulsed electric guiding fields having a non-zero averaged field. (iii) The directed response was enhanced for pulse sequences having a repetition time of 8 s. (iv) The lag-time between signal recognition and cellular response was 8-10 s. The results are discussed in the framework of a self-ignition model.

Langevin equation, Fokker-Planck equation and cell migration.

Cell migration can be characterized by two independent variables: the speed, v, and the migration angle, phi. Each variable can be described by a stochastic differential equation--a Langevin equation. The migration behaviour of an ensemble of cells can be predicted due to the stochastic processes involved in the signal transduction/response system of each cell. Distribution functions, correlation functions, etc. are determined by using the corresponding Fokker-Planck equation. The model assumptions are verified by experimental results. The theoretical predictions are mainly compared with the galvanotactic response of human granulocytes. The coefficient characterizing the mean effect of the signal transduction/response system of the cell is experimentally determined to 0.08 mm/V sec (galvanotaxis) or 0.7 mm/sec (chemotaxis) and the characteristic time characterizing stochastic effects in the signal transduction/response system is experimentally determined as 30 sec. The temporal directed response induced by electric field pulses is investigated: the experimental cells react slower but are more sensitive than predicted by theory.

Directed cell movement: a biophysical analysis.

The directed movement or directed growth of a cell in a polar guiding field (such as an electric field, a concentration gradient of chemotactic active molecules, a necrotactic gradient induced by a lysed cell, etc.) can be characterized by two independent variables: the speed, nu, of the cell and its migration angle, phi. Here it is shown that the direction of migration is controlled by a cellular automatic controller. The automatic controller can be regarded as the framework for the directed movement or growth and it can be applied even when the physicochemical signals to which the cell is responding are unknown.

Directed cell movement with steric exclusion.

The space-dependent density of cells is evaluated for the following situation: (i) The cells are forced to make a directed movement (ii) the space for the cellular migration is restricted. The steady state distribution density is obtained when the drift current density equals the diffusion current density. The analogy to the Boltzmann statistics is shown. In a further step the cellular volume is introduced. For this case the density distribution is described in analogy to the Fermi statistics. The necrotactic response of granulocytes is used to verify the model.

Slaving the cytochrome P-450 dependent monooxygenase system by periodically applied light pulses.

The light-induced enhancement of 7-ethoxycoumarin-O-deethylase activity was measured in a reconstituted system consisting of the enzyme P-450 II B1 (P-450PB-B) and the NADPH-cytochrome P-450 reductase. The phases of the catalytic cycle of 2 x 10(12) protein complexes were locked by periodic application of light pulses (0.1 s duration, 1.2-2.5 s repetition time, and 390-470 nm 0.27 Joule/nmol P-450). More than 80% of the active reconstituted enzyme complexes worked in phase if the repetition time (1.32 s) was slightly smaller than the catalytic cycle time of the free running enzyme (1.54 s). The percentage of synchronized enzyme complexes as a function of the repetition time is shown. It is shown that the lifetime of the product-enzyme complex is shortened by the light.

Neural crest cell galvanotaxis: new data and a novel approach to the analysis of both galvanotaxis and chemotaxis.

The galvanotaxis response of neural crest cells that had migrated out of the neural tube of a 56-hr-old quail embryo onto glass coverslips was observed using time-lapse video microscopy. These cells exhibit a track velocity of about 7 microns/min and actively translocate toward the negative pole of an imposed DC electric field. This nonrandom migration could be detected for fields as low as 7 mV/mm (0.4 mV/cell length). We find that this directional migration is independent of the speed of migration and have generated a rather simple mathematical equation that fits these data. We find that the number of cells that translocate at a given angle, phi, with respect to the field is given by the equation N(phi) = exp(a0 + a1cos phi), where a1 is linearly proportional to the electric field strength for fields less than 390 mV/mm with a constant of proportionality equal to KG, the galvanotaxis constant. We show that KG = (150 mV/mm)-1, and at this field strength the cellular response is approximately half maximal. This approach to cellular translocation data analysis is generalizable to other directed movements such as chemotaxis and allows the direct comparison of different types of directed movements This analysis requires that the response of every cell, rather than averages of cellular responses, is reported. Once an equation for N(phi) is derived, several characteristics of the cellular response can be determined. Specifically, we describe 1) the critical field strength (390 mV/mm) below which the cellular response exhibits a simple, linear dependence on field strength (for larger field strengths, an inhibitory constant can be used to fit the data, suggesting that larger field strengths influence a second cellular target that inhibits the first); and 2) the amount of information the cell must obtain in order to generate the observed asymmetry in the translocation distribution (for a field strength of 100 mV/mm, 0.3 bits of information is required).

Automatic control and directed cell movement. Novel approach for understanding chemotaxis, galvanotaxis, galvanotropism.

It is shown that chemotaxis, galvanotaxis, galvanotropism, etc. are functions of cells having a goal-seeking system. Even when the involved physicochemical signals are unknown, the cellular system can be treated phenomenologically like an automatic controller having a closed-loop feedback system. The model is verified by means of galvanotaxis and chemotaxis data of human granulocytes. The galvanotaxis and chemotaxis coefficient quantifying the cellular sensibility can be predicted from the coefficient which characterizes the deterministic part of the signal transduction/response system of the cell divided by the coefficient which characterizes the noise strength in the cellular signal transduction/response system. The model is not restricted to directed movement of granulocytes. It is very general and can be applied to any cell type for directed phenomena like chemotaxis, galvanotaxis, phototaxis, magnetotaxis, directed growth, etc. The virus-disturbed directed migration of granulocytes is discussed and it is shown that the virus alters the deterministic part of the cellular controller.

Light-induced activation and synchronization of the cytochrome P-450 dependent monooxygenase system.

The light-induced enhancement of the 7-ethoxycoumarin-O-deethylase activity was measured in a reconstituted system, consisting of the enzyme P-450PB-B and the NADPH-cytochrome P-450 reductase. The relative increase of the activity was about 15%. It is shown that the product release process is accelerated by light. The phases of the catalytic cycle of 2 x 10(12) protein complexes were locked by periodic application of light pulses (0.1 s duration, 1.32 s repetition time, and 390-470 nm, 0.27 joule/nmol P-450). More than 80% of the active reconstituted enzyme complexes (= "molecular machines") worked in phase after a few light pulses. The phase relation continued even after switching off the light pulses. The catalytic cycle time was 1.54 s, giving a turnover number of 39 min-1. The turnover number, as determined from the enzyme activity under optimum conditions, was 39 min-1. Due to the dissociation constant of the P-450PB-B:NADPH-P-450 reductase complexes [3] only 24% of the proteins were in the active (= working) state under the conditions used. The lifetime of this complexes is larger than 6 s since more than 4 cycles of the free running enzyme can be observed. This is the first report, that all catalytic active complexes in the test tube can be synchronized by an external light source, if the right repetition time of the pulses is chosen, so that all these "molecular machines" work in phase.

Glycolipid storage material in Fabry's disease: a study by electron microscopy, freeze-fracture, and digital image analysis.

The glycolipid storage material in Fabry's disease was studied by electron microscopy of thin-sectioned (TS) and freeze-fractured (FF) specimens. In the kidney all deposits were found to be located in lysosomes, arranged as lamellar stacks. Deposits in the heart consisted of intracytoplasmic concentric whirls or folded lamellar structures. High resolution TS micrographs disclosed various defects in the lamellar structure. For stabilization, such defects require additional amphiphilic, surface-active molecules. These molecules could interact with other cellular constituents. The lamellar periodicity of the deposits in FF specimens was determined by reconstruction of the three-dimensional fracture face by digital image analysis. Homogeneous multilamellar deposits exhibited a periodicity of 14-15 nm, contrasting with the conventional estimates of 4-5 nm on TS micrographs. This difference is explained by better preservation of the physiologic hydrated state in FF specimens, with 1 vol of lipids binding 2 vol of water. Inhomogeneous structures with an even higher state of hydration included water lenses between the sheets. The strong hydration obviously contributes to the enlargement of the intracellular glycolipid deposits.

Galvanotaxis of human granulocytes: electric field jump studies.

The static and dynamic responses of human granulocytes to an electric field were investigated. The trajectories of the cells were determined from digitized pictures (phase contrast). The basic results are: (i) The track velocity is a constant as shown by means of the velocity autocorrelation function. (ii) The chemokinetic signal transduction/response mechanism is described in analogy to enzyme kinetics. The model predicts a single gaussian for the track velocity distribution density as measured. (iii) The mean drift velocity induced by an electric field, is the product of the mean track velocity and the polar order parameter. (iv) The galvanotactic dose-response curve was determined and described by using a generating function. This function is linear in E for E less than EO = 0.78 V/mm with a galvanotaxis coefficient KG of (-0.22 V/mm)-1 at 2.5 mM Ca++. For E greater than EO the galvanotactic response is diminished. This inhibition is described by a second term in the generating function (-KG.KI(E-EO)) with an inhibition coefficient KI of 3.5 (v) The characteristic time involved in directed movement is a function of the applied electric field strength: about 30 s at low field strengths and below 10 s at high field strengths. The characteristic time is 32.4 s if the cells have to make a large change in direction of movement even at large field strength (E-jump). (vi) The lag-time between signal recognition and cellular response was 8.3 s. (vii) The galvanotactic response is Ca++ dependent. The granulocytes move towards the anode at 2.5 mM Ca++ towards the cathode at 0.1 mM Ca++. (viii) The directed movement of granulocytes can be described by a proportional-integral controller.

Locomotion of white blood cells: a biophysical analysis.

We determined some biophysical properties of human granulocytes, monocytes, and lymphocytes in respect to their locomotion. Granulocytes were exposed to plasma and were allowed to crawl on uncoated or glycol methacrylate coated glass plates. Monocytes did not migrate on uncoated glass, but did so on glycol methacrylated glass. Lymphocytes did not move on glass or glycol methacrylated glass, but moved on plexiglas coverslips. Granulocytes and monocytes showed a pronounced, directed movement towards a lysed erythrocyte (necrotaxis), lymphocytes showed no necrotactic response. The information collected by the granulocytes and monocytes in the necrotactic gradient was between 1 and 2 bits. This small amount of information indicated that the cellular decision in favor of a new direction of migration is based on a mechanism involving instability. We showed that the necrotactic response of granulocytes and monocytes is the product of the chemokinetic activity and the polar order parameter (= McCutcheon index) indicating that the cellular decision for a new direction of migration is independent of the speed of the cell movement. The movement of monocytes can be characterized in a similar way to that of granulocytes: the angle of deviation from a straight line path is nearly a fixed value (+/- 35 degrees). Lymphocytes stay in a restricted area after straight line movement. Particular attention was focused on cellular properties involved in locomotion. The characteristic time of the internal clock controlling the locomotion was 0.9 minutes for granulocytes and 2 minutes for monocytes. We were not able to determine the characteristic time of lymphocytes. We were able to determine the internal program responsible for the change in direction of movement. The directional memory time for granulocytes was 0.9 minutes. Monocytes had two directional memory times, short (2 minutes) and long (greater than 18 minutes). Lymphocytes had a very short directional memory time of 40 seconds. The distribution of the track velocities of migrating granulocytes and monocytes was described by bell shaped curves indicating homogeneous populations of cells. The distribution for lymphocytes had two maxima.