Calculation of thermodynamic properties of protein in Escherichia coli K-12 grown on succinic acid, energy changes accompanying protein anabolism, and energetic role of ATP in protein synthesis

Using an average of the results from three methods of calculation, estimations are made of the thermodynamic properties of a unit carbon formula weight (UCFW) of Escherichia coli K-12 protein. These resulted in values fro DeltaG(f) of -38.09 kJ (-9.10 kcal)/ UCFW, for DeltaH(f) of -68.18 kJ (-16.29 kcal)/UCFW, and for DeltaS(f) of -94.2 J (-22.5 cal)/UCFW deg. The absolute entropy of one UCFW of E. coli K-12 protein is calculated to be 73.8 J/UCFW deg. Using these values, the corresponding changes in thermodynamic properties accompanying the anabolism of protein by this microorganism to from one UCFW of protein by this microorganism to from one UCFW of protein are calculated to be 1.97 kJ (0.47 kcal)/UCFW for DeltaG, 0.75 kJ (0.18 kcal)/UCFW for DeltaH, and -4.09 J (-0.98 cal)/UCFW deg for DeltaS. All these values are sufficiently close to zero that they may be considered to be so. The question is raised as to the quantity of ATP energy conserved within the substance of the protein as it is synthesized from succinic acid. It is calculated that only 3.8% of the total free energy available from ATP that is required during protein anabolism can have been conserved within the substance of the protein, there being a net conversion of the remaninder into heat and entropy.     

An alternate method of calculating the heat of growth of Escherichia coli K-12 on succinic acid

The DeltaH(f) (0) unit weight of a complex substance such as a biological macromolecule is almost always obtained by means of combustion analysis. In theory, this can also be done by summing the DeltaH(f) (0) values for the monomers comprising the macromolecule plus the enthalpic energies involved in their polymerization. The enthalpy of formation of one unit-carbon formula weight of dried Escherichia coli K-12 cells was determined by summing the values of the enthalpies of formation of the quantities of monomers in the major classes of macromolecules substances comprising the cellular biomass and the enthalpic energies involved in their polymerizations. To this value was added the enthalpy of formation of the cellular ions in their aqueous standard states, per unit-carbon formula weight of cellular substance and the enthalpy change with respect to the ionization of the protein amino acid side chains. If it is assumed that the cellular fabric is insoluble and that the ions are soluble, the sum of the enthalpies of formation of all the cellular components should closely approximate the enthalpy of formation of one unit-carbon formula weight equivalent of living cells. Using this value, a calculation of the enthalpy change accompanying anabolism shows this latter to be effectively zero, indicating that the heat of growth (anabolism plus catabolism) is equal to that calculated for catabolism alone. This conclusion is in accord with those of several investigators who have used manometry or direct calorimetry.     

Microcalorimetric measurement of the enthalpy of binding of rabbit skeletal myosin subfragment 1 and heavy meromyosin to F-actin

The heat of binding of rabbit skeletal myosin subfragment 1 (myosin-S1) and heavy meromyosin (HMM) to F-actin has been measured by batch calorimetry. Proton release measurements in unbuffered solutions indicate that less than 0.1 mol of protons is absorbed or released per mol of myosin head bound to actin. Hence, the measured heats are approximately equal to the enthalpy of myosin-S1 and HMM binding to actin. The enthalpy of binding of myosin-S1 to actin was +22 +/- 3 and +27 +/- 5 kJ/mol of myosin-S1 in two series of experiments at 12 degrees C and +26 +/- 5 kJ/mol of myosin-S1 at 0 degrees C, indicating that delta Cp for this reaction in the range of 0-12 degrees C is small (-80 J/mol/K). The enthalpy of binding of HMM to actin at 12 degrees C was found to be +26 +/- 1 kJ/mol of myosin head. The enthalpies determined here and the equilibrium constants obtained from the literature for measurements at 20 degrees C under identical solvent conditions were used to estimate the entropy of the association of myosin S1 and HMM with F-actin: +235 J/mol/K for myosin-S1 and +190 J/mol of myosin head/K for HMM. Thermodynamic parameters of the interaction of myosin-S1 with actin and ADP or AMP-PNP can be evaluated using the enthalpy of association of myosin-S1 with actin determined here, together with literature values for the equilibrium constants and enthalpies of binding of these nucleotides to myosin-S1. The calculated enthalpies of binding of ADP or AMP-PNP to actomyosin-S1 are small and negative.     

Thermodynamics of the reactions catalyzed by the multifunctional enzyme complex tryptophan synthase

The intrinsic enthalpy changes (corrected for hydration of D-glyceraldehyde 3-phosphate) for the reactions catalyzed by the alpha and beta 2 subunits of tryptophan synthase from Escherichia coli have been determined calorimetrically. Cleavage of indoleglycerol phosphate (alpha reaction) was found to be associated with a delta H value of 54.0 +/- 2.5 kJ mol-1, while condensation of indole with L-serine (beta reaction) involved -80.3 +/- 4.6 kJ mol-1'. By direct determination of the enthalpy concomitant with the overall synthesis of tryptophan from indoleglycerol phosphate and L-serine an enthalpy value of -13.4 +/- 5.6 kJ mol-1 was observed. In view of the uncertainties of the literature data used for calculation of the hydration contribution, the agreement between the directly measured delta H value of the overall reaction and the sum of the enthalpies of the alpha and beta reactions is fair. Deamination of L-serine, a side reaction catalyzed preferentially by the isolated beta 2 pyridoxal 5'-phosphate2 subunit, was shown to be associated with an enthalpy change of -7.3 +/- 0.4 kJ mol-1.     

Energetics and volume changes of the intermediates in the photolysis of octopus rhodopsin at a physiological temperature

Enthalpy changes (Delta H) of the photointermediates that appear in the photolysis of octopus rhodopsin were measured at physiological temperatures by the laser-induced transient grating method. The enthalpy from the initial state, rhodopsin, to bathorhodopsin, lumirhodopsin, mesorhodopsin, transient acid metarhodopsin, and acid metarhodopsin were 146 +/- 15 kJ/mol, 122 +/- 17 kJ/mol, 38 +/- 8 kJ/mol, 12 +/- 5 kJ/mol, and 12 +/- 5 kJ/mol, respectively. These values, except for lumirhodopsin, are similar to those obtained for the cryogenically trapped intermediate species by direct calorimetric measurements. However, the Delta H of lumirhodopsin at physiological temperatures is quite different from that at low temperature. The reaction volume changes of these processes were determined by the pulsed laser-induced photoacoustic method along with the above Delta H values. Initially, in the transformation between rhodopsin and bathorhodopsin, a large volume expansion of +32 +/- 3 ml/mol was obtained. The volume changes of the subsequent reaction steps were rather small. These results are compared with the structural changes of the chromophore, peptide backbone, and water molecules within the membrane helixes reported previously.     

Interactions of sodium pentobarbital with D-glucose and L-sorbose transport in human red cells.

Pentobarbital acts as a mixed inhibitor of net D-glucose exit, as monitored photometrically from human red cells. At 30 degrees C the Ki of pentobarbital for inhibition of Vmax of zero-trans net glucose exit is 2.16+/-0.14 mM; the affinity of the external site of the transporter for D-glucose is also reduced to 50% of control by 1. 66+/-0.06 mM pentobarbital. Pentobarbital reduces the temperature coefficient of D-glucose binding to the external site. Pentobarbital (4 mM) reduces the enthalpy of D-glucose interaction from 49.3+/-9.6 to 16.24+/-5.50 kJ/mol (P<0.05). Pentobarbital (8 mM) increases the activation energy of glucose exit from control 54.7+/-2.5 kJ/mol to 114+/-13 kJ/mol (P<0.01). Pentobarbital reduces the rate of L-sorbose exit from human red cells, in the temperature range 45 degrees C-30 degrees C (P<0.001). On cooling from 45 degrees C to 30 degrees C, in the presence of pentobarbital (4 mM), the Ki (sorbose, glucose) decreases from 30.6+/-7.8 mM to 14+/-1.9 mM; whereas in control cells, Ki (sorbose, glucose) increases from 6.8+/-1.3 mM at 45 degrees C to 23.4+/-4.5 mM at 30 degrees C (P<0.002). Thus, the glucose inhibition of sorbose exit is changed from an endothermic process (enthalpy change=+60.6+/-14.7 kJ/mol) to an exothermic process (enthalpy change=-43+/-6.2 7 kJ/mol) by pentobarbital (4 mM) (P<0.005). These findings indicate that pentobarbital acts by preventing glucose-induced conformational changes in glucose transporters by binding to 'non-catalytic' sites in the transporter.     

Microcalorimetric study of aerobic growth of Cellulomonas sp. 21399 on various carbohydrates

Summary Microcalorimetry was used to study the energetic aerobic growth of Cellulomonas sp. 21399 on glucose, cellobiose and amorphous and crystalline cellulose. The thermochemical aspect of growth on glucose was established with regard to the anabolic contribution. The results obtained allowed the use of glucose as a reference substrate for cellulose degradation. The experimental enthalpy change and the maximum catabolic activity, calculated from the maximum power evolved by the culture, were, respectively,-1079 kJ/mol and 0.85 mmol glucose per hour per dry weight of cells. The growth response on amorphous cellulose was equivalent to that demonstrated on glucose. However, on crystalline cellulose media, Cellulomonas sp. 21399 exhibited eight times less power and the quantity of heat evolved during growth showed that 50% of the cellulose was degraded. Quantitative results and the shape of power-time curves achieved indicate that the structural features of cellulose strongly influence its microbial degradability.     

A thermodynamic study on rA7U7

Ultraviolet absorbance spectroscopy and differential scanning calorimetry were employed to study the heat-induced helix-to-coil transition of the oligoribonucleotide rA7U7. The analysis of concentration-dependent ultraviolet 'melting' profiles was used to derive the van't Hoff transition enthalpy delta HUVvH (-458 kJ/mol cooperative unit). From the DSC data we calculated the calorimetric transition enthalpy delta Hcal (-412.6 kJ/mol duplex) as well as delta HcalvH (-447.9 kJ/mol cooperative unit). For the size of the cooperative unit we obtained lambda approximately 1. In contrast to this result, by means of statistical numerical deconvolution we show that intermediate states are significantly populated; at the maximum the fraction of these states reaches 25.4% of the total population. Therefore, this DSC-deconvolution technique offers a more appropriate way to register amounts of populated intermediate states which are not sufficient to obtain a value of lambda which is essentially lower than unity.     

Comparison of the binding of Na+ and Ca2+ to bovine alpha-lactalbumin

alpha-Lactalbumin is a metal-binding protein which binds Ca2+- and Na+-ions competitively to one specific site, giving rise to a large conformational change of the protein. For this reason, the enthalpy change of binding Ca2+ to apo-alpha-lactalbumin (delta Ho) is strongly dependent on the concentration of Na+ ions in the medium. From that relationship a molar enthalpy of -145 +/- 3 kJ X mol-1 is calculated for the Ca2+-binding at pH 7.4 and 25 degrees C, while a delta Ho of -5 +/- 3 kJ X mol-1 is found to substitute a complexed Na+ by a Ca2+-ion. These measurements also allowed us to calculate a binding constant for Na+ of 195 +/- 18 M-1. The molar enthalpy of Na+-loading was found to be -142 +/- 3 kJ X mol-1, a value very close to delta Ho of the binding of Ca2+ to alpha-lactalbumin. Both enthalpy changes in binding Ca2+ and Na+ are independent of the protein concentration. These exothermic values are in agreement with the hypothesis that both Na+- and Ca2+-ions are able to induce the same conformational change in alpha-lactalbumin upon which hydrophobic regions are removed from the solvent, yielding a less hydrophobic protein. The latter is confirmed by means of affinity measurements of the hydrophobic fluorescent probe 4,4'-bis[1-(phenylamino)-8-naphthalene sulphonate](bis-ANS) to alpha-lactalbumin. The association constant (Ka) decreased from (6.6 +/- 0.5) X 10(4) M-1 in the absence of NaCl to (2.7 +/- 0.2) X 10(4) M-1 in 75 mM NaCl, while the maximum intensity (Imax) of the binary bis-ANS-alpha-lactalbumin complex remained constant at 0.44 +/- 0.02 (arbitrary units). The Ka value of bis-ANS for Ca2+-alpha-lactalbumin was determined at (1.7 +/- 0.2) X 10(4) M-1 and Imax was 0.43 +/- 0.02 (arbitrary units). The difference in hydrophobicity between the two conformational states of the protein was further demonstrated by adsorption experiments of both conformers to phenyl-Sepharose. Apo-alpha-lactalbumin, hydrophobically bound to phenyl-Sepharose, can be eluted by adding Ca2- or Na+-solutions.     

Estimation of heat production by cultured cells in suspension using semi-automated flow microcalorimetry

Modifications to a heat conduction flow microcalorimeter are described which allow registration of heat production by cells cultured in suspension. LS cells produced 34 +/- 3 pW per cell. Over an 8.5 h period, cell numbers increased by 9% and heat production per cell by 18%. Oxygen consumption per cell was 0.244 +/- 0.02 mumol min-1 per 10(8) cells and the enthalpy change was -836 kJ/mol O2. An automated pumping system allowed sequential registration of heat production by untreated cells and those exposed to a metabolic inhibitor. The results showed that 0.1 mM 2,4-dinitrophenol caused a greater increase in power (+65% at 1.5 h) than in oxygen consumption (+36%). The opposite occurred in the case of cells treated with 1 mM potassium cyanide, heat dissipation being depressed (-48%) slightly less than oxygen uptake (-52%). The results illustrate the potential of careful calorimetric determinations in studying metabolic events in the growth and division of cells in culture.     

Specific DNA binding by the homeodomain Nkx2.5(C56S): detection of impaired DNA or unfolded protein by isothermal titration calorimetry

Titrations of specific 18-bp duplex DNA with the cardiac-specific homeodomain Nkx2.5(C56S) have utilized an ultrasensitive isothermal titration calorimeter (ITC). As the free DNA nears depletion, we observe large apparent decreases in the binding enthalpy when the DNA is impaired or when the temperature is sufficiently high to produce some unfolding of the free protein. Either effect can be attributed to refolding of the biopolymer that occurs as a result of stabilization due to the large favorable change in free energy on the homeodomain binding to DNA (-49.4 kJ/mol at 298 K). In either case, thermodynamic parameters obtained in such ITC experiments are unreliable. By using a lower temperature (85 vs. 95 degrees C) during the annealing of complementary DNA strands, damage of the 18-bp duplex DNA (T(m) = 72 degrees C) is avoided, and titrations with the homeodomain are normal at temperatures from 10 to 40 degrees C when >95% of the protein is folded. Under the latter conditions, the heat capacity plot is linear with a DeltaC(p) value of -0.80 +/- 0.03 kJ K(-1) mol(-1), which is more negative than that calculated from the burial of solvent accessible surface areas (-0.64 +/- 0.05 kJ K(-1) mol(-1)), consistent with water structures being at the protein-DNA interfaces.     

Binding of NAD+ to pertussis toxin.

The equilibrium dissociation constant of NAD+ and pertussis toxin was determined by equilibrium dialysis and by the quenching of the protein's intrinsic fluorescence on titration with NAD+. A binding constant, Kd, of 24 +/- 2 microM at 30 degrees C was obtained from equilibrium dialysis, consistent with the previously determined value for the Michaelis constant, Km, of 30 +/- 5 microM for NAD+ (when the toxin is catalysing the ADP-ribosylation of water and of dithiothreitol). The intrinsic fluorescence of pertussis toxin was quenched by up to 60% on titration with NAD+, and after correction for dilution and inner filter effects, a Kd value of 27 microM at 30 degrees C was obtained, agreeing well with that found by equilibrium dialysis. The binding constants were measured at a number of temperatures using both techniques, and from this the enthalpy of binding of NAD+ to toxin was determined to be 30 kJ.mol-1, a typical value for a protein-ligand interaction. There is one binding site for NAD+ per toxin molecule.     

Thermodynamics of the Ca2+ binding to bovine alpha-lactalbumin

Bovine alpha-lactalbumin contains one strong Ca2+-binding site. The free energy (delta G0), enthalpy (delta H0), and entropy (delta S0) of binding of Ca2+ to this site have been calculated from microcalorimetric experiments. The enthalpy of binding was dependent on the metal-free bovine alpha-lactalbumin concentration. At 0.8 mg ml-1, metal-free bovine alpha-lactalbumin delta H0 was -110 +/- 6 kJ mol-1. At this concentration the binding constant was estimated from a mathematical analysis of the titration curves to be greater than 10(7) M-1. This means that delta G0 is smaller than -40 kJ mol-1 and delta S0 is less negative than -235 J.K-1 mol-1. The binding of Ca2+ is therefore enthalpy-driven. From binding experiments as a function of temperature, a delta Cp value of -4.1 kJ.K-1 mol-1 was calculated. This value is dependent on the protein concentration. A tentative explanation for this large value is given.     

Thermodynamic stability of porcine beta-lactoglobulin. A structural relevance.

The proposed biological function of beta-lactoglobulins as transporting proteins assumes a binding ability for ligands and high stability under the acidic conditions of the stomach. This work shows that the conformational stability of nonruminant porcine beta-lactoglobulin (BLG) is not consistent with this hypothesis. Thermal denaturation of porcine BLG was studied by high-sensitivity differential scanning calorimetry within the pH range 2.0-10.0. Dependences of the denaturation temperature and enthalpy on pH were obtained, which reveal a substantial decrease in both parameters in acidic and basic media. The denaturation enthalpy follows a linear dependence on the denaturation temperature. The slope of this line is 9.4 +/- 0.6 kJ.mol-1. K-1,which is close to the denaturation heat capacity increment DeltadCp = 9.6 +/- 0.5 kJ.mol-1.K-1, determined directly from the thermograms. At pH 6.25 the denaturation temperatures of porcine and bovine BLG coincide, at 83.2 degrees C. At this pH the denaturation enthalpy of porcine BLG is 300 kJ.mol-1. The denaturation transition of porcine BLG was shown to be reversible at pH 3.0 and pH 9.0. The transition profile at both pH values follows the two-state model of denaturation. Based on the pH-dependence of the transition temperature and the linear temperature dependence of the transition enthalpy, the excess free energy of denaturation, DeltadGE, of porcine BLG was calculated as a function of pH and compared with that of bovine BLG derived from previously reported data. The pH-dependence of DeltadGE is analysed in terms of the contributions of side-chain H-bonds to the protein stability. Interactions stabilizing native folds of porcine and bovine BLG are discussed.     

Thermodynamics of isomerization reactions involving sugar phosphates

Thermodynamics of isomerization reactions involving sugar phosphates have been studied using heat-conduction microcalorimetry. For the process glucose 6-phosphate2-(aqueous) = fructose 6-phosphate2- (aqueous), K = 0.285 +/- 0.004, delta Go = 3.11 +/- 0.04 kJ.mol-1, delta Ho = 11.7 +/- 0.2 kJ.mol-1, and delta Cop = 44 +/- 11 J.mol-1.K-1 at 298.15 K. For the process mannose 6-phosphate2- (aqueous) = fructose 6-phosphate2- (aqueous), K = 0.99 +/- 0.05, delta Go = 0.025 +/- 0.13 kJ.mol-1, delta Ho = 8.46 +/- 0.2 kJ.mol-1, and delta Cop = 38 +/- 25 J.mol-1.K-1 at 298.15 K. The standard state is the hypothetical ideal solution of unit molality. An approximate result (-14 +/- 5 kJ.mol-1) was obtained for the enthalpy of isomerization of ribulose 5-phosphate (aqueous) to ribose 5-phosphate (aqueous). The data from the literature on isomerization reactions involving sugar phosphates have been summarized, adjusted to a common reference state, and examined for trends and relationships to each other and to other thermodynamic measurements. Estimates are made for thermochemical parameters to predict the state of equilibrium of the several isomerizations considered herein.     

Small angle x-ray scattering of chromatin. Radius and mass per unit length depend on linker length.

Analyses of low angle x-ray scattering from chromatin, isolated by identical procedures but from different species, indicate that fiber diameter and number of nucleosomes per unit length increase with the amount of nucleosome linker DNA. Experiments were conducted at physiological ionic strength to obtain parameters reflecting the structure most likely present in living cells. Guinier analyses were performed on scattering from solutions of soluble chromatin from Necturus maculosus erythrocytes (linker length 48 bp), chicken erythrocytes (linker length 64 bp), and Thyone briareus sperm (linker length 87 bp). The results were extrapolated to infinite dilution to eliminate interparticle contributions to the scattering. Cross-sectional radii of gyration were found to be 10.9 +/- 0.5, 12.1 +/- 0.4, and 15.9 +/- 0.5 nm for Necturus, chicken, and Thyone chromatin, respectively, which are consistent with fiber diameters of 30.8, 34.2, and 45.0 nm. Mass per unit lengths were found to be 6.9 +/- 0.5, 8.3 +/- 0.6, and 11.8 +/- 1.4 nucleosomes per 10 nm for Necturus, chicken, and Thyone chromatin, respectively. The geometrical consequences of the experimental mass per unit lengths and radii of gyration are consistent with a conserved interaction among nucleosomes. Cross-linking agents were found to have little effect on fiber external geometry, but significant effect on internal structure. The absolute values of fiber diameter and mass per unit length, and their dependencies upon linker length agree with the predictions of the double-helical crossed-linker model. A compilation of all published x-ray scattering data from the last decade indicates that the relationship between chromatin structure and linker length is consistent with data obtained by other investigators.     

Microcalorimetric studies of the growth of sulfate-reducing bacteria: energetics of Desulfovibrio vulgaris growth.

The metabolism of Desulfovibrio vulgaris Hildenborough grown on medium containing lactate or pyruvate plus a high concentration of sulfate (36 mM) was studied. Molecular growth yields were 6.7 +/- 1.3 and 10.1 +/- 1.7 g/mol for lactate and pyruvate, respectively. Under conditions in which the energy source was the sole growth-limiting factor, we observed the formation of 0.5 mol of hydrogen per mol of lactate and 0.1 mol of hydrogen per mol of pyruvate. The determination of metabolic end products revealed that D. vulgaris produced, in addition to normal end products (acetic acid, carbon dioxide, hydrogen sulfide) and molecular hydrogen, 2 and 5% of ethanol per mol of lactate and pyruvate, respectively. Power-time curves of growth of D. vulgaris on lactate and pyruvate were obtained, by the microcalorimetric Tian-Calvet apparatus. The enthalpies (delta Hmet) associated with the oxidation of these substrates and calculated from growth thermograms were -36.36 +/- 5 and -70.22 +/- 3 kJ/mol of lactate and pyruvate, respectively. These experimental values were in agreement with the homologous values assessed from the theoretical equations of D. vulgaris metabolism of both lactate and pyruvate. The hydrogen production by this sulfate reducer constitutes an efficient regulatory system of electrons, from energy source through the pathway of sulfate reduction. This hydrogen value may thus facilitate interactions between this strain and other environmental microflora, especially metagenic bacteria.     

Comparative thermodynamic analysis of DNA--protein interactions using surface plasmon resonance and fluorescence correlation spectroscopy

We report a kinetic and thermodynamic analysis of interactions between ssDNA and replication protein A (RPA) using surface plasmon resonance (SPR) and fluorescence correlation spectroscopy (FCS) at variable temperature. The two methods yield different values for the Gibbs free energy but nearly the same value for the reaction enthalpy of ssDNA-RPA complex formation. The Gibbs free energy was determined by SPR and FCS to be -62.6 and -54.7 kJ/mol, respectively. The values for the reaction enthalpy are -64.4 and -66.5 kJ/mol. It is concluded that the difference in Gibbs free energy measured by the two methods is due to different reaction entropies. The entropic contribution to the free energy at 25 degrees C is -1.8 kJ/mol for SPR and -11.8 kJ/mol for FCS. In SPR, the reaction is restricted to two dimensions because of immobilization of the DNA molecules to the sensor surface. In contrast, FCS is able to follow complex formation without spatial restrictions. In consequence, the reaction entropy determined from SPR experiments is lower than for FCS experiments.     

A comparison of the bioscreen method and microscopy for the determination of lag times of individual cells of listeria monocytogenes

Lag phase durations (tLag) of individual Listeria monocytogenes cells were analysed using the NightOwl Molecular Imaging System, and results were compared with mean individual cell lag times (tL) obtained from the detection time (td) method using Bioscreen. With Bioscreen, an average tL of 6.39+/-0.89 h was obtained from five separate experiments. With the NightOwl method, an average tLag of 2.73+/-0.06 h was obtained from three experiments consisting of eight total replicates. Lag values from the NightOwl and Bioscreen are related by the equation: tLag = tL + DT, where DT is the doubling time. The equivalent tLag mean value for the Bioscreen method was 7.11+/-0.84 h. Individual lag times measured by both methods were normally distributed (r2 for Bioscreen and NightOwl ranged from 0.951 to 0.999 and from 0.884 to 0.982, respectively). The results suggest that the NightOwl method can provide accurate estimates of individual cell lag times, which will facilitate the development of combined discrete continuous models for bacterial growth.