Water activity in subaerial microbial biofilms on stone monuments.

Stone monuments can be difficult environments for life, particularly with respect to liquid water access. Nevertheless, microbial communities are found on them with apparent ubiquity. A variety of strategies for access to liquid water have been proposed. Regardless of their water-retention mechanisms details, though, we argue that water activity (a key indicator for cell viability) is constrained by environmental conditions, largely independently of community structure, and is predicted by the local temperature and relative humidity. However, direct measurement of water activity in SABs, particularly those growing on stone surfaces, is difficult. A method for estimating water activity within SABs is presented that uses a minimally invasive combination of conservative sampling, weather data, confocal imaging, and mathematical modeling. Applying the methodology to measurements from the marble roofs of the Federal Hall National Memorial and of the Thomas Jefferson Memorial, estimations are made for water activity in their subaerial stone communities over the course of an approximately one year period.

Mathematical modeling of dispersal phenomenon in biofilms.

A mathematical model for dispersal phenomenon in multispecies biofilm based on a continuum approach and mass conservation principles is presented. The formation of dispersed cells is modeled by considering a mass balance for the bulk liquid and the biofilm. Diffusion of these cells within the biofilm and in the bulk liquid is described using a diffusion-reaction equation. Diffusion supposes a random character of mobility. Notably, biofilm growth is modeled by a hyperbolic partial differential equation while the diffusion process of dispersed cells by a parabolic partial differential equation. The two are mutually connected but governed by different equations that are coupled by two growth rate terms. Three biological processes are discussed. The first is related to experimental observations on starvation induced dispersal [1]. The second considers diffusion of a non-lethal antibiofilm agent which induces dispersal of free cells. The third example considers dispersal induced by a self-produced biocide agent.

Diffusive transport through a model host-biofilm system.

Free-living biofilms have been subject to considerable attention, and basic physical principles for them are generally accepted. Many host-biofilm systems, however, consist of heterogeneous mixtures of aggregates of microbes intermixed with host material and are much less studied. Here we analyze a key property, namely reactive depletion, in such systems and argue that two regimes are possible: (1) a homogenizable mixture of biofilm and host that in important ways acts effectively like a homogeneous macrobiofilm and (2) a distribution of separated microbiofilms within the host with independent local microenvironments.

Modeling multispecies biofilms including new bacterial species invasion.

A mathematical model for multispecies biofilm evolution based on continuum approach and mass conservation principles is presented. The model can describe biofilm growth dynamics including spatial distribution of microbial species, substrate concentrations, attachment, and detachment, and, in particular, is able to predict the biological process of colonization of new species and transport from bulk liquid to biofilm (or vice-versa). From a mathematical point of view, a significant feature is the boundary condition related to biofilm species concentrations on the biofilm free boundary. These data, either for new or for already existing species, are not required by this model, but rather can be predicted as results. Numerical solutions for representative examples are obtained by the method of characteristics. Results indicate that colonizing bacteria diffuse into biofilm and grow only where favorable environmental conditions exist for their development.

Mathematical model of biofilm induced calcite precipitation.

Microbially modulated carbonate precipitation is a fundamentally important phenomenon of both engineered and natural environments. In this paper, we propose a mixture model for biofilm induced calcite precipitation. The model consists of three phases - calcite, biofilm and solvent - which satisfy conservation of mass and momentum laws with addition of a free energy of mixing. The model also accounts for chemistry, mechanics, thermodynamics, fluid and electrodiffusion transport effects. Numerical simulations qualitatively capturing the dynamics of this process and revealing effects of kinetic parameters and external flow conditions are presented.

Senescence can explain microbial persistence.

It has been known for many years that small fractions of persister cells resist killing in many bacterial colony-antimicrobial confrontations. These persisters are not believed to be mutants. Rather it has been hypothesized that they are phenotypic variants. Current models allow cells to switch in and out of the persister phenotype. Here, a different explanation is suggested for persistence, namely senescence. Using a mathematical model including age structure, it is shown that senescence provides a natural explanation for persistence-related phenomena, including the observations that the persister fraction depends on growth phase in batch culture and dilution rate in continuous culture.

Description of mechanical response including detachment using a novel particle model of biofilm/flow interaction.

Bacterial biofilms, while made up of microbial-scale objects, also function as meso- and macroscale materials. In particular, macro-scale material properties determine how biofilms respond to large-scale mechanical stresses, e.g. fluid shear. Viscoelastic and other constitutive properties influence biomass structure (through growth and fluid shear stresses) by erosion and sloughing detachment. In this paper, using the immersed boundary method, biofilm is modelled by a system of viscoelastic, breakable springs embedded in a fluid flow, evolving according to the basic physical laws of conservation of mass and momentum. We demonstrate in the context of computer simulation biofilm deformation and detachment under fluid shear stress.

Role of cohesion in the material description of biofilms.

Biofilm structure plays an important role in biofilm function and control. It is thus important to determine the extent to which mechanics may determine structure in biofilms. We consider a generic qualitative constitutive description of biofilm incorporating as assumptions a small number of fundamental physical properties of biofilm viscoelasticity and cohesion. Implications of cohesive energy on biofilm structure are then explored. Steady solutions and energy minima are studied and it is demonstrated that cohesion energy leads naturally to a free surface film state. It is found that in many circumstances, biofilms could be subject to heterogeneity formation via spinodal decomposition. Such material heterogeneity may have important implications for structural stability in biofilms both on short and long time scales.

Commonality of elastic relaxation times in biofilms.

Biofilms, sticky conglomerations of microorganisms and extracellular polymers, are among the Earth's most common life forms. One component for their survival is an ability to withstand external mechanical stress. Measurements indicate that biofilm elastic relaxation times are approximately the same (about 18 min) over a wide sample of biofilms though other material properties vary significantly. A possible survival significance of this time scale is that it is the shortest period over which a biofilm can mount a phenotypic response to transient mechanical stress.

Effect of heterogeneous structure in mechanically unstressed biofilms on overall growth.

In contrast to their name, biofilms are not always flat and homogeneous but instead often exhibit complex structural heterogeneity. It has been suggested that nonhomogeneous geometry is selected in order to increase biofilm growth rate. A previous study (Dockery and Klapper (2002) SIAM J. Appl. Math., 62, 853-869) of a model biofilm system in a static bulk fluid demonstrated that under some circumstances a flat biofilm-bulk fluid interface is linearly unstable to perturbation due to growth induced forces. Computations indicated that subsequent nonlinear evolution results in fingers and mushrooms of biofilm similar to structures observed in actual biofilms. However, the important complementary issue of biological functionality was not considered. Here a weakly nonlinear analysis of the simple growing biofilm layer model in Dockery and Klapper (2002, SIAM J. Appl. Math., 62, 853-869) is presented. It is argued that, at least in the case of biofilms free of external mechanical stress, overall growth is in fact generally inhibited by the presence of growing perturbations in the linear stage. Hence a more complex explanation of function is necessary.

Biofilm material properties as related to shear-induced deformation and detachment phenomena.

Biofilms of various Pseudomonas aeruginosa strains were grown in glass flow cells under laminar and turbulent flows. By relating the physical deformation of biofilms to variations in fluid shear, we found that the biofilms were viscoelastic fluids which behaved like elastic solids over periods of a few seconds but like linear viscous fluids over longer times. These data can be explained using concepts of associated polymeric systems, suggesting that the extracellular polymeric slime matrix determines the cohesive strength. Biofilms grown under high shear tended to form filamentous streamers while those grown under low shear formed an isotropic pattern of mound-shaped microcolonies. In some cases, sustained creep and necking in response to elevated shear resulted in a time-dependent fracture failure of the "tail" of the streamer from the attached upstream "head." In addition to structural differences, our data suggest that biofilms grown under higher shear were more strongly attached and were cohesively stronger than those grown under lower shears.

Viscoelastic fluid description of bacterial biofilm material properties.

A mathematical model describing the constitutive properties of biofilms is required for predicting biofilm deformation, failure, and detachment in response to mechanical forces. Laboratory observations indicate that biofilms are viscoelastic materials. Likewise, current knowledge of biofilm internal structure suggests modeling biofilms as associated polymer viscoelastic systems. Supporting experimental results and a system of viscoelastic fluid equations with a linear Jeffreys viscoelastic stress-strain law are presented here. This system of equations is based on elements of associated polymer physics and is also consistent with presented and previous experimental results. A number of predictions can be made. One particularly interesting result is the prediction of an elastic relaxation time on the order of a few minutes-biofilm disturbances on shorter time scales produce an elastic response, biofilm disturbances on longer time scales result in viscous flow, i.e., nonreversible biofilm deformation. Although not previously recognized, evidence of this phenomenon is in fact present in recent experimental results.

Remarks on discrete and continuous large-scale models of DNA dynamics.

We present a comparison of the continuous versus discrete models of large-scale DNA conformation, focusing on issues of relevance to molecular dynamics. Starting from conventional expressions for elastic potential energy, we derive elastic dynamic equations in terms of Cartesian coordinates of the helical axis curve, together with a twist function representing the helical or excess twist. It is noted that the conventional potential energies for the two models are not consistent. In addition, we derive expressions for random Brownian forcing for the nonlinear elastic dynamics and discuss the nature of such forces in a continuous system.

Focusing of electric fields in the active site of Cu-Zn superoxide dismutase: effects of ionic strength and amino-acid modification.

In this paper we report the implementation of a finite-difference algorithm which solves the linearized Poisson-Boltzmann equation for molecules of arbitrary shape and charge distribution and which includes the screening effects of electrolytes. The microcoding of the algorithm on an ST-100 array processor allows us to obtain electrostatic potential maps in and around a protein, including the effects of ionic strength, in about 30 minutes. We have applied the algorithm to a dimer of the protein Cu-Zn superoxide dismutase (SOD) and compared our results to those obtained from uniform dielectric models based on coulombic potentials. We find that both the shape of the protein-solvent boundary and the ionic strength of the solvent have a profound effect on the potentials in the solvent. For the case of SOD, the cluster of positive charge at the bottom of the active site channel produces a strongly enhanced positive potential due to the focusing of field lines in the channel-a result that cannot be obtained with any uniform dielectric model. The remainder of the protein is surrounded by a weak negative potential. The electrostatic potential of the enzyme seems designed to provide a large cross-sectional area for productive collisions. Based on the ionic strength dependence of the size of the positive potential region emanating from the active site and the repulsive negative potential barrier surrounding the protein, we are able to suggest an explanation for the ionic strength dependence of the activity of the native and chemically modified forms of the enzyme.

The 'knotting' problem in proteins. Loop penetration.

The 'knotting' problem in proteins is redefined in terms of the more general concept of loop penetration. Disulfide-containing proteins are represented as linear graphs, and it is proposed that proteins with nonplanar graph representations display loop penetrations in their three-dimensional structure. With this argument, it is shown that the occurrence of loop penetration in disulfide-containing proteins is approximately that expected based on the random pairing of sulfhydryl groups. It is argued that loop penetration is not as rare as currently held.