On the progenitor cell migration velocity

An attempt is presented to extract cell kinetic information from histomorphological features. It is applicable to rapidly proliferating tissues like the intestinal epithelium. Each replicating tissue has an origin where cells are formed and a periphery toward which cells migrate. The migration path along which they move is denominated as tissue radius on which all cell positions are mapped. Cell migration on the radius is associated with cell proliferation at tissue origin. Each mitosis there is associated with the displacement of all cells distal to it by one cell position. The more mitoses positioned between a cell and tissue origin, the greater its migration velocity. It is possible therefore to derive the cell migration velocity v(x) from the cumulative mitotic distribution on the radius, N(x). v(x) = N(x)/tm (tm = mitotic time). In this form v(x) represents also cell production at any point on the radius and may serve for the computation of other cell kinetic parameters like generation time. These arguments are illustrated on the rat incisor tooth inner enamel epithelium which has been studied in the normal and rapidly erupting tooth.     

ON THE DERIVATION OF CELL KINETICS FROM HISTOMORPHOLOGY, OBSERVED IN THE RAT INCISOR ODONTOBLAST

A method to extract cell kinetic information from histomorphology is presented. Each replicating tissue is essentially an ordered structure with an origin where cells are formed and a periphery toward which they are displaced. the displacement path is called the tissue radius. the tissue variables may be studied in two domains, space and time. the first embraces all the states a cell may assume while the second specifies the cell transition rates. During steady state both domains are related linearly. These ideas are illustrated in the rat incisor odontoblast population whose life expectation is determined by the tooth wall shape. the odontoblast cell population paves the interior of the tooth wall delimiting a cone-shaped pulp. Near the root apex the dentine wall is barely visible. As one proceeds distally, the wall thickens while the pulp narrows. Pulp narrowing is associated with odontoblast cell loss whose magnitude may be deduced from the change of the pulp circumference CI(x) (x is the distance from tooth origin). the odontoblast force of mortality μ(x) may be calculated from the instantaneous perimeter change: μ(x) = -CI' (x)/CI(x); where CI'(x) stands for the derivative of CI(x). This equation serves for the construction of the odontoblast life table which may be studied in space and time.     

THE KINETICS OF CELL PROLIFERATION IN THE TRACHEOBRONCHIAL EPITHELIA OF RATS WITH AND WITHOUT CHRONIC RESPIRATORY DISEASE

Labelling indices of the tracheobronchial epithelia of conventionally-derived rats with chronic respiratory disease (CRD) and minimal-disease rats without CRD have been determined. The duration of the DNA synthesis phase (t_s) computed from the percentage of mitoses labelled at various intervals of time after injection of tritiated thymidine was 7 hr: t_G2 was 3.5 hr. Using the measured value of t_s and the labelling indices, the mean turnover times of the tracheobronchial epithelia in three groups of six 5-week-old conventionally-derived rats were calculated to be 11.2, 14.6 and 22.4 days, while in similar groups of 5-week-old minimal-disease rats the turnover times were found to be 24.3, 36.5 and 41.6 days. The majority of cell divisions in the tracheobronchial epithelium of these minimal disease rats were probably required for growth rather than renewal. The mean turnover time of this tissue in 5-week-old Syrian hamsters was 73 days. The cells of the rat tracheobronchial epithelium have been classed as basal or superficial, depending on their shape and proximity to the basement membrane. The mean turnover time of the basal cells in 5-week-old minimal-disease rats was 11.7 days calculated from labelling indices. The migration method of Brown & Oliver (1968) gave a similar value for the basal cells in minimal-disease rats, and a value of 9.5 days for the basal cells in a group of conventionally-derived rats. The mean turnover time in the latter was only 5.4 days if two rats with tracheobronchitis were included. Consideration of the slow rate of fall in mean grain count over labelled cells at intervals of time after labelling and the calculated turnover times suggests that the proliferative fraction of the basal cell population is close to unity. Well-labelled cells were still present in both basal and superficial populations in the minimal-disease rats at 10 days after labelling. The marked effects of CRD on cell proliferation in this epithelium are emphasized and the significance of this in relation to published work is discussed.     

Cellular and shunt conductances of toad bladder epithelium

Summary Toad urinary bladders were mounted in Ussing-type chambers and voltage-clamped. At nonzero voltages only, small fluctuations in current, I, and therefore in tissue conductance, G _t, were detected. These fluctuations were caused by the smooth muscle of the underlying tissue which could be monitored continuously and simultaneously with the current,I. Inhibition of the smooth muscle contraction with verapamil (2×10^–5 m) abolished the fluctuations inI andG _t. Amiloride (10^–4 m) had no significant effect on the magnitude of G _t, oxytocin increasedG _t without affecting G _t, and mucosal hypertonicity produced by mannitol increased G _t. These results are consistent with the hypothesis that two parallel pathways exist for passive current flow across the toad urinary bladder: one, the cellular pathway, was not affected by smooth muscle activity; the other, the paracellular pathway, was the route whose conductance was altered by the action of the smooth muscle.Thus the relationship between the cellular and shunt conductances of the epithelium of the toad urinary bladder, under a variety of conditions, can be investigated by utilizing the effects of the movement of the smooth muscle.     

Experimental evidence for negative turgor pressure in small leaf cells of Robinia pseudoacacia L versus large cells of Metasequoia glyptostroboides Hu et W.C. Cheng. 2. Höfler diagrams below the volume of zero turgor and the theoretical implication for pressure‐volume curves of living cells

The physiological advantages of negative turgor pressure, P_t, in leaf cells are water saving and homeostasis of reactants. This paper advances methods for detecting the occurrence of negative P_t in leaves. Biomechanical models of pressure‐volume (PV) curves predict that negative P_t does not change the linearity of PV curve plots of inverse balance pressure, P_B, versus relative water loss, but it does predict changes in either the y‐intercept or the x‐intercept of the plots depending on where cell collapse occurs in the P_B domain because of negative P_t. PV curve analysis of Robinia leaves revealed a shift in the x‐intercept (x‐axis is relative water loss) of PV curves, caused by negative P_t of palisade cells. The low x‐intercept of the PV curve was explained by the non‐collapse of palisade cells in Robinia in the P_B domain. Non‐collapse means that P_t smoothly falls from positive to negative values with decreasing cell volume without a dramatic change in slope. The magnitude of negative turgor in non‐collapsing living cells was as low as ?1.3 MPa and the relative volume of the non‐collapsing cell equaled 58% of the total leaf cell volume. This study adds to the growing evidence for negative P_t.     

DURATION OF MITOSIS AND SEPARATE MITOTIC PHASES COMPARED TO NUCLEAR DNA CONTENT IN ERYTHROBLASTS OF FOUR VERTEBRATES

The passage of a wave of tritiated. thymidine-labelled cells through each of the phases of mitosis is analysed in erythroblasts of four vertebrates species, selected because of their widely differing diploid DNA content. Mitotic time (t_m) and relative durations of separate mitotic phases as well as that of the G₂ period are thus accurately determined. Mean duration of t_m appears to vary according to the species specific DNA amount. This relation is approximately the same as for S, for G₁ and for the generation time, which have been previously determined.     

Calcium-mobilizing agonists stimulate anion fluxes in cultured endothelial cells from human umbilical vein

Intracellular ion concentrations were determined in split skins of Rana pipiens using the technique of electron microprobe analysis. Based on the 1 min Br uptake from the apical bath, two types of mitochondria-rich (MR) cells could be distinguished: active cells which rapidly exchanged their anions with the apical bath and inactive cells which did not. Br uptake and frequency of active MR cells were closely correlated with the skin conductance, g _t. Replacing Cl in the apical bath with an impermeant anion significantly lowered g _t and the Br uptake and Na concentration of active cells. Even larger reductions were observed after apical amiloride (0.1 mm). The inhibition of the Br uptake was reversible by voltage clamping (100 mV, inside positive). Cl removal and amiloride also led to some shrinkage of active cells. The results suggest that the active cell is responsible for a large part of g _t. Inactive MR cells had much lower Br and Na concentrations which were not significantly affected by Cl removal, amiloride, or voltage clamping. Principal cells, which represent the main cell type of the epithelium, showed only a minimal Br uptake from the apical side which was not correlated with g _t. Moreover, Cl removal had no effect on the Na, Br, and Cl concentrations of principal cells.I wish to thank Cathy Langford for her excellent technical assistance. Financial support was provided by National Institutes of Health grants DK35717 and 1S10-RR0-234501.     

Intensity of microcarrier collisions in turbulent flow

A model is developed, allowing estimation of the share of inelastic interparticle collisions in total energy dissipation for stirred suspensions. The model is restricted to equal-sized, rigid, spherical particles of the same density as the surrounding Newtonian fluid. A number of simplifying assumptions had to be made in developing the model. According to the developed model, the share of collisions in energy dissipation is small.List of Symbols b parameter in velocity distribution function (Eq. (28)) - c _K factor in Kolmogoroff spectrum law (Eq. (20)) - D _t(r _p ) m²/s characteristic dispersivity at particle radius scale (Eq. (13)) - E(k, t) m³/s² energy spectrum as function of k and t (Eq. (16)) - E _K (k) m³/s² energy spectrum as function of k in Kolmogoroff-region (Eq. (20)) - E _p dimensionless mean kinetic energy of a colliding particle (Eq. (36)) - E _cp dimensionless kinetic energy exchange in a collision (Eq. (37)) - G(x, s) dimensionless energy spectrum as function of x and s (Eq. (16)) - G _B(x) dimensionless energy spectrum as function of x for boundary region (Eq. (29)) - G _K(x) dimensionless energy spectrum as function of x for Kolmogoroff-region (Eq. (21)) - g m/s² gravitational acceleration - I _cp dimensionless collision intensity per particle (Eq. (38)) - I _cv dimensionless volumetric collision intensity (Eq. (39)) - k l/m reciprocal of length scale of velocity fluctuations (Eq. (17)) - K dimensionless viscosity (Eq. (13)) - n(2) dimensionless particle collision rate (Eq. (12)) - n(r) l/s particle exchange rate as function of distance from observatory particle center (Eq. (7)) - r m vector describing position relative to observatory particle center (Eq. (2)) - r m scalar distance to observatory particle center (Eq. (3)) - r _pm particle radius (Eq. (1)) - s dimensionless time (Eq. (10)) - SC kg/ms³ Severity of collision (Eq. (1)) - t s time (Eq. (2)) - u(r, t) m/s velocity vector as function of position vector and time (Eq. (2)) - u(r, t) m/s magnitude of velocity vector as function of position vector and time (Eq. (3)) - u _r(r, t) m/s radial component of velocity vector as function of position vector and time (Eq. (3)) - u _r (r, t) m/s magnitude of radial component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s latitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s magnitude of latitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s longitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s magnitude of longitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u _gsm/s superficial gas velocity - u(r) m/s root mean square velocity as function of distance from observatory particle center (Eq. (3)) - u_r(r) m/s root mean square radial velocity component as function of distance from observatory particle center (Eq. (4)) - u (r) m/s root mean square latitudinal velocity component as function of distance from observatory particle center (Eq. (4)) - u (r) m/s Root mean square longitudinal velocity component as function of distance from observatory particle center (Eq. (4)) - w(x) dimensionless root mean square velocity as function of dimensionless distance from observatory particle center (Eq. (11)) - V _pm³ particle volume (Eq. (36)) - w(2) dimensionless root mean square collision velocity (Eq. (34)) - w ^* parameter in boundary layer velocity equation (Eq. (24)) - x dimensionless distance to particle center (Eq. (9)) - x ^* value of x where G _Band G _K-curves touch (Eq. (32)) - x _K dimensionless micro-scale (Kolmogoroff-scale) of turbulence (Eq. (15)) - volumetric particle hold-up - m²/s³ energy dissipation per unit of mass - m²/s kinematic viscosity - kg/m³ density - (r) m³/s fluid-exchange rate as function of distance to observatory particle center - Latitudinal co-ordinate (Eq. (5)) - Longitudinal co-ordinate (Eq. (5))     

ANALYSIS OF INTESTINAL CELL PROLIFERATION AFTER GUANETHIDINE-INDUCED SYMPATHECTOMY

Neonatal administration of guanethidine-sulfate results in an alteration of the cell proliferative pattern of the small intestinal epithelium of the young adult rat. Sympathectomy with guanethidine has previously been shown to depress mitotic, labelling, and total cellular migration indices while increasing the generation cycle time (T_C) of small intestinal crypt cells as measured by a stathmokinetic method. The present study showed that the G₁, S and G₂ phases of the crypt cell cycle are altered by sympathectomy, G₁ accounting for most of the increase in T_C. In addition, the percentage of [³H]-thymidine labelled crypt cells is reduced and the duration of crypt cell transit is lengthened by guanethidine-induced sympathectomy.     

The cell kinetics of the epidermis and follicular epithelium of the rat: variations with age and body site

Abstract The skin from rats of differing age was used to quantify variations in the cell kinetics of the epidermis and the follicular epithelium of different body sites. Four parameters were assessed, namely the basal cell density (BCD), the labelling index (LI), the duration of DNA synthesis (t_s) and the basal cell turnover time (t^T). The BCDs of the epidermis of the dorsum and the upper surface of the foot were similar in rats of 7, 14 and 52 weeks of age, but there was an indication of a progressive decline with increasing age in the BCD of the epidermis of the ear and tail. There were no age-related changes in the length of t_s in any of the four body regions. The rate of cell proliferation, as indicated by the values of the LI and t_T, was relatively rapid in the epidermis of the dorsum, foot and tail of rats aged 7 weeks (LI > 12%; t_T < 80 h). In rats aged 14 weeks this rate of proliferation was maintaned in the epidermis of the dorsum. However, in the foot and tail the rate of cell proliferation was decreased (LI < 10%; t^T > 85 h). A fall in the rate of proliferation of the epidermis of the dorsum was only seen in 52-week-old animals. In these animals the rates of proliferation in the foot and tail were similar to those at the age of 14 weeks. In the epidermis of the ear there was no appreciable change in the rate of cell proliferation with age. The values of the cell kinetic parameters varied in the different body sites. For example, in 52-week-old animals values for t_T were relatively short in the epidermis of the tail and foot and appreciably longer in the epidermis of the dorsum and ear. Considered overall, values for the cell kinetic parameters of the epidermis were comparable with those for the follicular epithelium. The only major differences between the epidermis and the follicular epithelium were in the upper surface of the foot at 7 weeks of age, and in the tail at 7 and 14 weeks of age, where the LI was higher and the t_T shorter in the epidermis than in the follicular epithelium. The relevance of the observed age- and body-site-related variations in the cell kinetics of the epidermis are discussed in relation to previously described differential changes in the radiosensitivity of the skin in this strain of rat.     

A NEW METHOD FOR THE ESTIMATION OF CELL CYCLE PHASES

A method is described, which is applicable to cell renewal systems with an anatomical structure in which all cell locations may be uniquely mapped. Its use is demonstrated on the rat incisor inner enamel epithelium, which forms a one cell thick column in the sagittally sectioned tooth. Cells born in the apical part of the column migrate toward the distal end of the tooth, where they mature. As the cells migrate along the column, they traverse the various cell cycle phases. The present study has been designed to estimate the probability of a cell being in a given phase; all cells touching the basement membrane were numbered, and the number of cells separating any two cells was taken as a measure of distance. Since generally all cells move in one direction (lateral cell migration may occur), it is possible to solve the problem with the aid of functions describing the renewal counting stochastic process in which cell distance serves as an independent variable. The method predicts labelled cell and mitotic rates which agree with those estimated in the usual way. It was then utilized to estimate the fraction of cells in G₂.     

Physical properties of microbial suspensions

A way of characterizing cell size distribution in suspensions of single-cell microorganisms is suggested, based on the first and second moments around origin. Suspension density may be predicted on the basis of the mixing law and the density of microbial dry matter, for suspensions ofSaccharomyces cerevisiae, Candida lipolytica, andAspergillus niger. Newtonian viscosities were correlated using regression analysis by η=Aexp(BC _m)exp(D/t); another correlation is presented for the calculation of surface tension in single-cell microbial suspensions. All the relations are valid in the range of concentrations up to 15% (w/v) and for temperatures between 15° and 35°C. The formulae presented may be used in other hydraulic studies.     

Generalizations of the Roginsky-Zeldovich (or Elovich) equation for charge transport across biological surfaces

The Roginsky-Zeldovich (or Elovich) equation, which is −dx/dt=m exp (nx) (x=substrate concentration,t=time,m andn=constants), describes the kinetics of various biological electron and ion transport processes, and has been derived from the concept of charge transport across an activation energy barrier at an interface between dissimilar phases, driven by a difference in redox or ion potentials, with the simplifying assumptions that charge carrier concentration is constant, backward current across the interface is zero, and diffusion of substrate is fast. If charge carrier concentration is proportional to substrate concentration, then the kinetic equation is −dx/dt=mx exp (nx). If backward current is not zero, then −dx/dt=m ₁ exp (n ₁x) −m ₂ exp (n ₂ x), wherem ₁,m ₂,n ₁ andn ₂ are constants. Kinetic equations for interfacial charge transport in the presence of a significant substrate diffusion potential are also derived.     

Sequential Classification Based on Regression

Let us consider m general populations π₁, …,π_m. Each object belonging to these populations is represented by (p ± 1) characteristics x₁, x₂,…,x_p,y. A certain object, which is an element of one of the m general populations π₁,…,π_m has to be classified into the correct population. It will be assumed that knowledge of the value of the characteristic y would permit its correct classification, but that the observation of this characteristic is expensive, difficult or dangerous, as e.g. in medical applications. y is correlated with a set of p characteristics x₁,x₂,…,x_p, which are observed sequentially. The classification procedure is based on the division of the space of the observed value of characteristics x₁,x₂,…,x_p into nonintersecting areas determined so as to minimize the value of BAYES' risk given by equation (3).     

Gas-phase influence on the mixing in a fluidized bed bio-reactor

Summary The liquid and solids mixing in fluidized bed bio-reactors containing particles with a density only slightly higher than water (1100 kg/m³) is generally consistent with the results found in previous studies for reactors with particles of higher density. The liquid mixing can be described by an axial dispersion model for a large variety of conditions while the solids follow the streamlines of the liquid. In the presence of a gas phase the degree of mixing of both the liquid and the solid phase increased. This effect became larger with increasing reactor diameter. In the extrapolation of laboratory data of three phase fluidized bed bio-reactors to pilot plant systems this effect should be taken into account. The liquid and solids mixing may have a substantial effect on overall conversion rates and on possible microbial stratification in the reactor.Nomenclature Bo Bodenstein number v L/D (-) - D _r diameter of the fluidized bed reactor (m) - D ₁ Dispersion coefficient of the liquid phase (m²/s) - D _g dispersion coefficient of the solid phase (m²/s) - E(in) normalized dye concentration function entering the ideally mixed tank reactor (-) - E(t) normalized dye concentration function as measured (-) - L length of the axial dispersed reactor (m) - t time after dye injection (s) - t _m time constant for microbial selection (s) - t _s solid mixing time constant (s) - t time interval in which a particle migrates within the bed (s) - v _t superficial gas velocity (m/s) - v _g superficial liquid velocity (m/s) - z migration distance of a particle in the bed (m) - ₁ in situ growth rate of a dominant organism (s^-1) - ₂ in situ growth rate of a recessive organism (s^-1) - average residence time in the axial dispersed reactor (s) - _t average residence time in the ideally mixed tank reactor (s)     

A new alcohol dehydrogenase with unique stereospecificity from Pseudomonas sp.

A new nicotinamide cofactor-dependent alcohol dehydrogenase from Pseudomonas strain SBD6 (PADH) was isolated and purified 150-fold to homogeneity using a combination of salt precipitation, anion-exchange chromatography, gel filtration chromatography, and dye matrix chromatography. Approximately 10 mg of pure enzyme can be obtained from 10 g of wet cells. The enzyme has four subunits with a total molecular weight of 162,000. Incubation with the metal chelators 1,10-phenanthroline, 2-aminoethanethiol, hydroxyquinolinesulfonic acid, N-ethylmaleimide, and potassium cyanide result in complete loss of activity. The enzyme is very stable (t_1/2 7 days at pH 7 and 25°C in the absence of 2-propanol and 18 days in the presence of 10% 2-propanol, v/v) and possesses a broad substrate specificity with transfer of the pro-(R) hydride from NADH to the si face of carbonyl substrates to give (R)-alcohols in high enantiomeric excess, a stereochemical process different from that of other known alcohol dehydrogenases. Synthetic scale reductions are facilitated with 2-propanol as a hydride source for the regeneration of NADH. The kinetic mechanism is ordered bi-bi with the cofactor binding first. Based on NAD and 2-propanol, the kinetic parameters of the enzyme were determined to be V_max = 29.9 Units mg⁻¹ at 25°C and pH 8.5, K_m^NAD = 0.36 m and K_m^2-propanol = 0.19 m .     

The behaviour of coupled biochemical oscillators as a model of contact inhibition of cellular division

Intercellular communication of molecules between normal cells by tight junctions, and lack of this in some cancer cells (Loewenstein), can explain contact inhibition of cellular division in tissues. A general theory has been based on assuming the continual rise and fall (intrinsic oscillation) of a key substance x in each cell, with the period of the cell cycle. Periods are asynchronous in different cells, and x is exchanged between cells in contact by diffusion. A reduction in the resultant amplitude of fluctuation of x results, so that it does not reach the threshold x_t required for division to ensue; hence contact inhibition.The mathematical model is defined in its simplest form, and the sets of differential equations for arrays of cells are solved, from the isolated cell to the cell in an infinite sheet. The relative probability of division, P, is computed by numerical analysis from the area of resultant curves of x that lies above the threshold x_t. P depends on four dimensionless parameters, the order of coupling n (the number of cells directly communicating with a given cell), the total number of cells N in the aggregate, the communication constant K, and x_t, as a fraction of the amplitude of the intrinsic oscillation. The degree of synchrony, measured by the coefficient of variation σ of the periods, is important. If σ < ± 4%, contact inhibition is much reduced. The theory predicts that a paradoxical “contact-facilitation” is possible for very small aggregates of cells. For a cell in an infinite sheet, the amplitude of oscillation of x is reduced approximately by the factor $\text{1}\text{nK}$. For normal cells K is probably > 1, for cancer cells that lack communication, K is probably «< 1. However, two other basic causes for lack of regulation of tissue growth (cancer) could be excessive intrinsic oscillation of x, cf. x_t, and partial or complete synchronization of groups of cells by some unknown mechanism.     

Regeneration of the Digestive Tube in the Holothurian Apostichopus japonicusafter Evisceration

We performed a TEM study of regeneration of the intestine in the Far Eastern trepang, the holothurian Apostichopus japonicus, after evisceration. The following stages were distinguished in the restoration process of the digestive tube: the growth of connective tissue along the margin of the mesenterium, in the place of rupture; dedifferentiation of cells and their migration and proliferation; the rooting of the esophagus lining into the connective tissue anlage; and the transformation of esophagus cells into cells of the middle part of the intestine. The migration of epithelium into the area of regeneration takes place through a solid cellular layer, without breaking of the cell contacts. The mitotic activity was registered in all stages of restoration; the dividing cells were located chaotically, without the development of a blastema.     

Human oral epithelial cell culture I. Improved conditions for reproducible culture in serum-free medium

Summary Gingival tissue from healthy adult human donors was used as a source of epithelial cells for culture. An overnight incubation of this tissue with dispase facilitated the mechanical separation of the surface epithelium from the underlying fibrous connective tissue. This step minimized culture contamination with fibroblasts. The epithelium was then trypsinized to prepare a single cell suspension. The cell pellets were collected by centrifugation and resuspended in keratinocyte growth medium, incubated at 37° C and 5% CO₂ in a humid atmosphere. Primary cultures grew in small islands that coalesced at confluency. Immunohistochemistry demonstrated uniform staining of the cells with antibodies to keratins of stratified squamous epithelium. Ultrastructurally, the cells contained distinct intermediate filaments. When cells were grown in media with low calcium (0.15 mM), cell-to-cell contacts were via interlacing papillary projections with no desmosomes. However, when cells were grown under physiologic calcium (1.2 mM), desmosomes were prominent and well developed. Cells were maintained in culture for over 100 d (7 passages). This work was supported by Biomedical Research grant RR 05346 from the National Institute of Health, Bethesda, MD, and the University of Washington Graduate School Research Fund.     

Interrelationship among specific rates of cell growth,substrate consumption,and metabolite formation in some simple microbial reactions producing primary metabolites

Applying the carbon balance principle, the interrelationship between ν = μ/Y + m (μ is the specific growth rate of microorganism, v is the specific substrate consumption rate) and π = Aμ B (Luedeking–Piret eqyuation, π is the specific metabolite formation rate) has been established for three types of simple microbial reactions. Equations for the kinetic parameters A and B have been proposed for each of the three types of microbial reactions, Expresses in terms of γ_x, γ_s and γ_p (carbon contents of dry cell, mass, major carbon energy source, and metabolite) as well as the parameters Y and m. Values of both A and B calculated from the proposed equations were compared with their experimental data for lactic acid fragmentation, aerobic SCP production, and alcohol fermentation. The estimated values agreed with the observed ones with reasonably small deviations.