Dynamic mathematical model development and validation of in vitro Mycobacterium smegmatis growth under nutrient- and pH-stress.

Mycobacterium tuberculosis can exist within a host for lengthy periods, tolerating even antibiotic challenge. This non-heritable, antibiotic tolerant "persister" state, is thought to underlie latent Tuberculosis (TB) infection and a deeper understanding thereof could inform treatment strategies. In addition to experimental studies, mathematical and computational modelling approaches are widely employed to study persistence from both an in vivo and in vitro perspective. However, specialized models (partial differential equations, agent-based, multiscale, etc.) rely on several difficult to determine parameters. In this study, a dynamic mathematical model was developed to predict the response of Mycobacterium smegmatis (a model organism for M. tuberculosis) grown in batch culture and subjected to a range of in vitro environmental stresses. Lag phase dynamics, pH variations and internal nitrogen storage were mechanistically modelled. Experimental results were used to train model parameters using global optimization, with extensive subsequent model validation to ensure extensibility to more complex modelling frameworks. This included an identifiability analysis which indicated that seven of the thirteen model parameters were uniquely identifiable. Non-identifiable parameters were critically evaluated. Model predictions compared to validation data (based on experimental results not used during training) were accurate with less than 16% maximum absolute percentage error, indicating that the model is accurate even when extrapolating to new experimental conditions. The bulk growth model can be extended to spatially heterogeneous simulations such as an agent-based model to simulate in vitro granuloma models or, eventually, in vivo conditions, where distributed environmental conditions are difficult to measure.

Equilibrium unfolding of dimeric desulfoferrodoxin involves a monomeric intermediate: iron cofactors dissociate after polypeptide unfolding.

Here we report the conformational stability of homodimeric desulfoferrodoxin (dfx) from Desulfovibrio desulfuricans (ATCC 27774). The dimer is formed by two dfx monomers linked through beta-strand interactions in two domains; in addition, each monomer contains two different iron centers: one Fe-(S-Cys)(4) center and one Fe-[S-Cys+(N-His)(4)] center. The dissociation constant for dfx was determined to be 1 microM (DeltaG = 34 kJ/mol of dimer) from the concentration dependence of aromatic residue emission. Upon addition of the chemical denaturant guanidine hydrochloride (GuHCl) to dfx, a reversible fluorescence change occurred at 2-3 M GuHCl. This transition was dependent upon protein concentration, in accord with a dimer to monomer reaction [DeltaG(H(2)O) = 46 kJ/mol of dimer]. The secondary structure did not disappear, according to far-UV circular dichroism (CD), until 6 M GuHCl was added; this transition was reversible (for incubation times of < 1 h) and independent of dfx concentration [DeltaG(H(2)O) = 50 kJ/mol of monomer]. Thus, dfx equilibrium unfolding is at least three-state, involving a monomeric intermediate with native-like secondary structure. Only after complete polypeptide unfolding (and incubation times of > 1 h) did the iron centers dissociate, as monitored by disappearance of ligand-to-metal charge transfer absorption, fluorescence of an iron indicator, and reactivity of cysteines to Ellman's reagent. Iron dissociation took place over several hours and resulted in an irreversibly denatured dfx. It appears as if the presence of the iron centers, the amino acid composition, and, to a lesser extent, the dimeric structure are factors that aid in facilitating dfx's unusually high thermodynamic stability for a mesophilic protein.

No cofactor effect on equilibrium unfolding of Desulfovibrio desulfuricans flavodoxin.

Flavodoxins are proteins with an alpha/beta doubly wound topology that mediate electron transfer through a non-covalently bound flavin mononucleotide (FMN). The FMN moiety binds strongly to folded flavodoxin (K(D)=0.1 nM, oxidized FMN). To study the effect of this organic cofactor on the conformational stability, we have characterized apo and holo forms of Desulfovibrio desulfuricans flavodoxin by GuHCl-induced denaturation. The unfolding reactions for both holo- and apo-flavodoxin are reversible. However, the unfolding curves monitored by far-UV circular dichroism and fluorescence spectroscopy do not coincide. For both apo- and holo-flavodoxin, a native-like intermediate (with altered tryptophan fluorescence but secondary structure as the folded form) is present at low GuHCl concentrations. There is no effect on the flavodoxin stability imposed by the presence of the FMN cofactor (DeltaG=20(+/-2) and 19(+/-1) kJ/mol for holo- and apo-flavodoxin, respectively). A thermodynamic cycle, connecting FMN binding to folded and unfolded flavodoxin with the unfolding free energies for apo- and holo-flavodoxin, suggests that the binding strength of FMN to unfolded flavodoxin must be very high (K(D)=0.2 nM). In agreement, we discovered that the FMN remains coordinated to the polypeptide upon unfolding.