Bacterial choices for the consumption of multiple resources for current and future needs.

Microorganisms differ in their effectiveness in uptake and selection of substances that they bring in from the environment. They also differ in how they balance the allocation of nutrients for immediate and for delayed use. Moreover, they may not take up resources as fast as they seemingly could, and they may extrude derivatives of substances just pumped in. A good deal of these apparent choices must reside in the uptake systems and the linkage of these with the cell's intermediate metabolism. An important feature is that a resource may vary in concentration from time to time, nutrient to nutrient, and habitat to habitat. This variation must have been critical to the evolution of regulatory processes. Some possibilities for the combined uptake and consumption are considered for substrates serving the same (homologous) and different (heterologous) roles for the bacterium. From the membrane transport processes diagrammed in Fig. 1c and Fig. 2 and corresponding computer program given in Appendix A, the combined effect of uptake processes and cell growth can be studied. The model can be modified for various alternate models to study the possible control of cellular uptake and metabolism for the range of ecological roles of the bacterium.

Evidence that the cell wall of Bacillus subtilis is protonated during respiration.

Several independent experiments suggest that cell walls of Bacillus subtilis are protonated during growth. When cells were grown in the presence of fluorescein-labeled dextran to saturate the cell walls, centrifuged, and suspended in PBS, fluorescence-activated cell sorter analyses revealed the bacteria were only poorly fluorescent. In contrast, when the bacteria were purged with N(2) to dissipate protonmotive force (pmf) fluorescence became intense. Upon reconstitution of the pmf with phenazine methosulfate, glucose, and oxygen, fluorescence declined. Another approach used pH-dependent chemical modification of cell walls. The walls of respiring B. subtilis cells were amenable to carboxylate modification by [(14)C]ethanolamine and 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide. The carbodiimide activation of carboxylate groups occurs only in acidic conditions. Upon dissipation of pmf the walls were refractory to chemical modification. Ammonium groups can be condensed with FITC in alkaline medium, but the condensation is very slow in acidic buffers. It was found that the derivatization of the walls with FITC could occur in the absence of pmf. The use of pH-dependent fluorophores and pH-dependent chemical modification reactions suggest that cell walls of respiring B. subtilis cells have a relatively low pH environment. This study shows a bacterium has a protonated compartment. Acidification of cell walls during growth may be one means of regulating autolytic enzymes.

Can synchronous cultures of bacteria be manufactured?

The bacterial cell cycle is simpler and different than that of the typical eukaryotic cell cycle. The selective pressure during evolution has been directed to achieve optimal growth of the individual free-living microbial cell instead of a variety of replication rates of the differentiated cell within an entire multicellular organism. This means that for most bacterial cells division depends more critically on their success in acquiring and using resources than is the case for most eukaryotic cells. The further implication is that bacterial cells somehow measure their own success in growth and from this 'decide' when they should attempt cell cycle events such as cell division and chromosome replication. On the assumption that bacterial division is responsive, directly or indirectly, to cell size, the cell cycle is analyzed here through Monte Carlo simulations. The results are used to consider the possibility of generating bacterial cultures growing synchronous. Because the precision of the size-at-division is surprisingly good, it appears that some organisms, at least, have a sensory mechanism that responds to their success in cell growth. It is known that the division size of some strains, however, is more precisely regulated than in others. Also, some strains are more precise in dividing the mother's cell cytoplasm to give the same sized daughters. Because some strains are much more precise than others, the possibility is raised that useful synchrony could be obtained with selected strains that are precise in these two aspects. These cultures would useful in studying other aspect of the physiology of cell growth.

Oligotrophs versus copiotrophs.

Bacteria can grow rapidly, yet there are some that grow slowly under apparent optimal conditions. These organisms are usually present in environments with low levels of nutrients, and are not found in conditions of more plentiful nutrients. They are known as "oligotrophs"in contrast to "copiotrophs", which are common in environments with greater nutritional opportunities. This essay asks why do the oligotrophs not occupy richer environments, and why are copiotrophs not more prevalent in chronic starvation environments?

Length distribution of the peptidoglycan chains in the sacculus of Escherichia coli.

The stress-bearing fabric of bacteria is made of peptidoglycan. This crosslinked fabric is formed from disaccharide pentapeptide units that are transported through the cytoplasmic membrane and then polymerized in two directions: (i) to form oligoglycan chains; and (ii) to cross link these chains by tail-to-tail bonds from the muropeptides to the protruding peptides of other chains. The distribution of the glycan chain lengths is reminiscent of the "most probable distribution of polymer chemistry. Of course, the process is more complex than solely the random addition of units to growing chains. The complexity precludes mathematical analysis, but computer modeling of the Monte Carlo type is capable of including a range of possibilities. At each time point a specified number of disaccharides are singly added to the muramic acid residue ends of existing chains chosen at random. The transfer is in exchange for the cleavage of pyrophosphate bactoprenol that transported the disaccharide pentapeptide through the membrane. The progam then selects, again at random, which chain to cleave and between which two disaccharides of the chain the cleavage event is to occur. The cleavage generates an N -acetyl 1,6 anhydro-muramic acid end and a non-reducing N -acetyl glucosamine end. The simulation can be modified so that the program does not cleave off a disaccharide next to either end of the chain. Comparisons are shown with the experimental results of Obermann & H]oltje (1994. Microbiology140, 79-87.) They obtained their data by taking the results with normal growing cells and subtracting the similar data from minicells to estimate the chain length distribution in the cylinder part of the cell. In its most basic form the computer simulation has only one fitted parameter, K, which is the number of disaccharides added to the murein for every internal cleavage event. In this form the fitting to the experimental results is poor. One possible reason for this is that the tension on the chains, and therefore the probability of being cleaved by autolysins varies with orientation of the chain on the cylinder surface. It is well known that the tension in the cylindrical wall is twice as large in the circumferential direction as in the axial one, so one class would consist of those chains aligned longitudinally, subject to lower stress, and would have a higher energy of activation for autolysis than chains aligned circumferentially. A good fit is obtained on the assumption that there are only two classes of chains; one more likely to be cleaved than the other. The key point is that only two processes: adding of disaccharide pentapeptides at random to glycan chains and cleavage between the disaccharides at random, together with the assumption that the wall is less easily hydrolysed in the axial direction is sufficient to account for the experimental distribution.

The exoskeleton of bacterial cells (the sacculus): still a highly attractive target for antibacterial agents that will last for a long time.

Most bacteria are entirely surrounded by a strong cell wall held together by covalent bonds of strength similar to those holding the atoms in a diamond together. This exoskeleton is a coat of armor or corset and is usually called a sacculus. It protects the bacterium from the stresses resulting from the higher osmotic pressure of the cytoplasm when compared with its environment. This strategy of constructing an external mechanical support has the weakness that the wall barrier has to be cleaved and new wall material inserted outside of the cell proper in order for the bacterium to grow and divide. Because of the unique chemistry and the necessity of selectively cleaving old stress-bearing wall for growth, the wall of the bacterial cell has been a key target for chemotherapeutic treatment of bacterial diseases. Currently, many infectious organisms are becoming resistant to overused antibiotics. Still the wall is a good target, and there could possibly be several entirely new classes of antibiotics targeted toward other parts of wall metabolism and function. The essential autolysins may be a particularly relevant target. To find chemotherapeutic agents we must use and extend our present understanding of the structural mechanics of bacterial wall and their biophysics, biochemistry, and physiology. Moreover, if we use our knowledge of biophysics/genetics and of the evolution of antibiotic resistance mutations that occurred millions of years ago, as well as our knowledge of ones that have arisen recently, quite novel antibiotics may be designed.

Penicillin binding proteins, beta-lactams, and lactamases: offensives, attacks, and defensive countermeasures.

A strong outer covering of peptidoglycan (the sacculus) is essential for most bacteria. Beta-lactams have evolved billions of years ago and can block saccular growth of the organism. This led to the evolution of beta-lactamases and resistant penicillin binding proteins (PBPs). With the introduction of lactam antibiotics by the pharmaceutical industry, resistance genes in nature were laterally transferred to antibiotic-treated disease-causing organisms and additional modification of beta-lactamase genes and of the regulatory genes of the mecA region took place. However, it can be concluded that very little of either type of resistance mechanisms represents new basic evolution against the penicillin type antibiotics. In the last 60 years the resistant bacteria in the main arose by movement of genes from other organisms, from minor genetic changes, and from alteration of the regulation of synthesis.

Simulation of the conformation of the murein fabric: the oligoglycan, penta-muropeptide, and cross-linked nona-muropeptide.

The structure and conformation of the sacculus of bacteria at a scale much larger than just the component disaccharide penta-muropeptide is not well known and is crucially important for the understanding of bacterial growth and cell wall function. By computer simulations, the minimal energy conformations and the energy needed for stretching the component parts were found. The oligosaccharide chain, modeled as (GlcNAc-MurNAc)8 when under no tension, can assumed a variety of nearly iso-energetic conformations. These included a variety of bends and kinks, with the chain forming an irregular random coil. In the most relaxed and minimal energy state, the D-lactyl groups of the MurNAc (N-acetyl muramic acid) residues protruded at about an angle of 90 degrees relative to the D-lactyl groups of their immediate MurNAc neighbors in the same chain. The cell wall penta-muropeptide precursor is identical for Escherichia coli and Bacillus subtilis; it also adopted many conformations, each of an energy almost equal to the global minimum. The cross-bridged structure of the tail-to-tail linkage of disaccharide nona-muropeptide has a second type of association, in addition to the covalent cross-bridge, which has not been considered before. This is the ionic interaction between the free D-Ala and the free amino group of the m-A2 pm. In vivo, when the cross-bridge is stretched (in the computer to simulate growth), this pairing dissociates. The possible biological significance of this is that it exposes the underlying 'tail-to-tail' peptide bond to autolysis and will expose both the ends of the m-A2 pm and the D-AlaD-Ala groups that may then be able to react with nascent penta-muropeptides to form trimers. This suggests a new model for growth of the bacterial cell wall that depends on changes in the chemical conformation of the cross-bridge structure as it comes to bear stress.

The re-incarnation, re-interpretation and re-demise of the transition probability model.

There are two classes of models for the cell cycle that have both a deterministic and a stochastic part; they are the transition probability (TP) models and sloppy size control (SSC) models. The hallmark of the basic TP model are two graphs: the alpha and beta plots. The former is the semi-logarithmic plot of the percentage of cell divisions yet to occur, this results in a horizontal line segment at 100% corresponding to the deterministic phase and a straight line sloping tail corresponding to the stochastic part. The beta plot concerns the differences of the age-at-division of sisters (the beta curve) and gives a straight line parallel to the tail of the alpha curve. For the SC models the deterministic part is the time needed for the cell to accumulate a critical amount of some substance(s). The variable part differs in the various variants of the general model, but they do not give alpha and beta curves with linear tails as postulated by the TP model. This paper argues against TP and for an elaboration of SSC type of model. The main argument against TP is that it assumes that the probability of the transition from the stochastic phase is time invariant even though it is certain that the cells are growing and metabolizing throughout the cell cycle; a fact that should make the transition probability be variable. The SSC models presume that cell division is triggered by the cell's success in growing and not simply the result of elapsed time. The extended model proposed here to accommodate the predictions of the SSC to the straight tailed parts of the alpha and beta plots depends on the existence of a few percent of the cell in a growing culture that are not growing normally, these are growing much slower or are temporarily quiescent. The bulk of the cells, however, grow nearly exponentially. Evidence for a slow growing component comes from experimental analyses of population size distributions for a variety of cell types by the Collins-Richmond technique. These subpopulations existence is consistent with the new concept that there are a large class of rapidly reversible mutations occurring in many organisms and at many loci serving a large range of purposes to enable the cell to survive environmental challenges. These mutations yield special subpopulations of cells within a population. The reversible mutational changes, relevant to the elaboration of SSC models, produce slow-growing cells that are either very large or very small in size; these later revert to normal growth and division. The subpopulations, however, distort the population distribution in such a way as to fit better the exponential tails of the alpha and beta curves of the TP model.

Attachment of the chromosome to the cell poles: the strategy for the growth of bacteria in two and three dimensions.

Bacteria such as Staphylococcus, Lampropedia, and Sarcina develop in characteristic two-or three-dimensional groups of cells. We propose here a model of how bacteria may generate such groupings by an extension of an earlier model for rod-shaped bacteria. No other mechanism for forming two- or three-dimensional structures of groups of cells has been proposed. Our earlier model for division of rod-shaped bacteria into nearly equal-sized daughters assumed that the origin and terminus DNA were attached at a critical time to polar wall sites. While such binding was speculative 20 years ago, it has now been established that the DNA for the origin of replication, at least during some part of the cell cycle is located in the pole for several different bacteria. Evidence is also building showing that the terminus DNA region is sometimes located at a position in the cell that will develop into two new poles. Here, a new extension of the concept that polar sites bind specifically origin and terminus DNA of the chromosome is presented that can explain how division takes place in one and then in another dimension to form two-dimensional tablets of four cells or large planar arrays. A further possible extension to three dimensions to generate octets of cells is proposed.

The strategy of Myxococcus xanthus for group cooperative behavior.

New evidence has been presented from our laboratory that the gliding bacterium, Myxococcus xanthus, does not home by chemotaxis toward a nutrient source. Our experiments, those of others, and the theory presented here combine to suggest a model, called the 'Pied Piper' model. It hypothesizes a gene that has a high mutation rate forward and back (say something in excess 10(-4) mutations per cell generation) which leads to switching between two motility states. Occasionally rare organisms become genetically, but reversibly, changed so that they move unidirectionally instead of mostly forward and back as do the bulk of the cells. When such a 'leader' cell arises, it continues to move in its original orientation, and causes a cohort of cells to move together away from the bulk of the cells. That is, in the less common mutational state it counteracts the usual tendency to just move forward and backward achieving little net movement. The assumption of a genetic element that mutates in a reversible way is suggested by numerous cases of reversible switches now known in a wide range of bacteria serving a variety of functions. A second aspect of the model is that mechanisms exist that cause cells to move in the same direction as their nearby neighbors. This process results in a regular spacing of bands of cells to form mounds in the absence of a leader. The action of C-factor, a factor-secreted by the cells which has been largely studied in the laboratory of Dale Kaiser, and extracellular fibrils, (rod-shaped protein and carbohydrate bodies) largely studied in the laboratory of Martin Dworkin, may be key elements in coordinating (or linking) the movements of neighboring cells. Based on the assumption of the absence of chemotaxis, computer simulations of pattern formation for gliding bacterial swarms and flares are consistent with observed behaviors and thus are additional evidence that chemotactic motility of the type exhibited by Escherichia coli, is not necessary for the group movements of M. xanthus. Some tests for this model are suggested.

The three-for-one model for gram-negative wall growth: a problem and a possible solution.

The murein wall in Gram-negative bacteria is so thin that the mechanism of growth is necessarily complicated. From analytical data of murein components, Höltje suggested a model for the growth mechanism that would lead to safe wall enlargement. The model depended on the formation of trimers of peptidoglycan disaccharides linked via their pentapeptides. In the 'three-for-one' model three oligopeptidoglycan chains are linked to each other in the usual linkages between the carboxyl group of D-alanine residues and the epsilon-amino group of diaminopimelic acid residues; these are designated 'tail-to-tail' linkages. This three-chained raft is then linked to the stress-bearing wall via the formation of trimers, defined as three peptide chains linked together by tail-to-tail linkages. Then by autolyzing the oldest bonds in each trimer, the old chain is excised and the raft becomes part of the stress-bearing wall and the wall is enlarged. There is a problem with the three-for-one model in that it demands a precise fitting of the prefabricated raft of three crosslinked chains to a stress-bearing chain in the wall fabric to allow the series of trimer linkages to form. Because the wall, when bearing stress, must be pulled into a 'honeycomb' structure, the end-to-end distance would be shortened. The possibility is raised here that the glycan chains in the stress-bearing wall are stretched to a sufficient degree by the cell's turgor pressure to compensate for its zig-zag structure; this could allow the model to function. A calculation is presented that assumes that the area of the pores in the fabric, called tessera, is maximized by the cell's turgor pressure. In this case the glycan chain must stretch 10% (and the end-to-end distance of peptide strands stretch 28%) so that the end-to-end distance of a glycan chain in the stress-bearing wall and the unstretched nascent wall can be the same and permit indefinite stable growth.

The biophysics of the gram-negative periplasmic space.

When subject to an osmotic 'up-shock', water flows outward from bacterial cytoplasm of the bacterium. Lipid bilayers can shrink very little in area and therefore must wrinkle to accommodate the smaller volume. The usual consequence is that all the layers of the cell envelope must become wrinkled together because they adhere to each other and must now cover a smaller surface. Plasmolysis spaces are formed if the cytoplasmic membrane (CM) separates from the other components of the wall. However, because the CM bilayer is essentially an incompressible two-dimensional liquid, this constraint restricts the location and shape of plasmolysis spaces. With mild up-shocks they form at the pole and around constricting regions in the cell. Elsewhere their creation requires the formation of endocytotic or exocytotic vesicles. The formation of endocytotic vesicles occurs in animal and plant cells as well as in bacterial cells. With stronger up-shocks tubular structures (Bayer adhesion sites), or other special geometric shapes (e.g., Scheie structures) allow the bilayer to surround an irregular shaped cytoplast. Periosmotic agents, that is, those that extract water from the periplasm as well as the cytoplasm, are molecules such as poly-vinyl-pyrrolidone and alpha-cyclodextrin that are too large to pass through the porins in the outer membrane. They were found to significantly inhibit the formation of plasmolysis spaces. Presumably, they inhibit the plasmolysis process, which requires that extracellular fluid enter between the CM and the outer membrane (OM). In the extreme case, with the dehydrating action of both osmotic agents and periosmotic agents, periplasmic space formation tends to be prevented and a new kind of space develops within the cytoplasm. We have designated these as 'cytoplasmic voids'. These novel structures are not bounded by lipid bilayers, in contrast to the endocytotic vesicles. These new spaces appear to result from the negative turgor pressure generated by the application of the combination of osmotic and periosmotic agents causing bubble formation. Several ideas in the literature about the wall biology (periseptal annuli, leading edge, osmotic pressure in the periplasm) are presented and critiqued. The basic criticism of these is that much of the phenomena can be explained because of the physics of the phospholipid bilayers and osmotic forces and thus does not imply the existence of a special control mechanism to regulate growth and division.

Orientation of the peptidoglycan chains in the sacculus of Escherichia coli.

The organization of chains of oligopeptidoglycan in the saccular wall is of critical importance in the study of the mechanism and physiology of prokaryotic wall growth. The electron microphotographs of De Pedro et al. present new findings and can be used to negate or at least raise questions about the previously accepted conclusion that the glycan chains are oriented transversely to the axis of rod-shaped Escherichia coli. This suggests caution in assuming that the glycan chains in the murein structure are parallel to each other and are perpendicular to the axis of the cell. These results should reopen the question of not only the orientation of the peptidoglycan chains, but the possibility of variability in orientation. Three classes of hypotheses about wall growth are reconsidered and problems with them are presented. The new results from De Pedro's laboratory and the experimental glycan chain length distribution argue against proposed systematic models. These include models that postulate belts or hoops stretched around the circumference of the cell and mechanisms that insert new chains of the length of presumptive "docking" strands in the stress-bearing wall. They are consistent, however, with the surface stress theory that proposes that random enzyme action together with physical forces are involved in the elongation of the rod-shaped Gram-negative wall.

How did bacteria come to be?

Bacteria in the modern taxonomic sense are one of the three Domains. They must have split from the other two after the bulk of the development of biochemistry and cell biology had taken place. Up to the time of the Last Universal Ancestor (LUA) the world had been monophyletic with little stable diversity. This is to say that as advances took place the older forms were eliminated and diversity was only temporary. Two kinds of events could, in principle, permit stable diversity to arise. One kind occurs when two nearly simultaneous, different advances occur, both of which overcome the same problem. While the previous type would be supplanted, if the new types did not compete with each other, new niches and habitats could lead to stable diversity. The second kind is a saltation or macroevolutionary event that greatly expands the biota and reduces previous constraints and thereby drastically reduces competition; this generally leads to a 'species radiation' and results in the development of a spectrum of biological types some of which persist and do not compete with each other. It is proposed that the two splits to yield the three Domains of Bacteria, Archaea, and Eukarya, resulted from one of each of these two processes leading to diversity. One arose from the consequences of cells accumulating substances from the environment, thus increasing their internal osmotic pressure. This resulted in two nearly simultaneous biological solutions: one (Bacteria) was the development of the external sacculus, i.e. the formation of a stress-bearing exoskeleton. The other (Eukarya) was the development of cytoskeletons and mechanoenzymes, i.e. formation of an endoskeleton. The other event causing diversity was the invention of an effective way to tap a new energy source and allow the biomass to increase extensively permitting a radiation of many different types of organisms. I suggest that this seminal advance was the development of methanogenesis. This caused a short-lived expansion and radiation before oxygen-producing photosynthesis allowed a still more major expansion and decreased the number of methanogens. Some details of these processes are elaborated. In particular, the evolutionary process that permitted the development of a sacculus, interpreted in light of the bacterial physiology of today's organisms is presented. It is argued that many great advances arise by developing a number of totally different processes for other purposes that can then each be modified to combine for yet another purpose.

Microbial physiology and ecology of slow growth.

The uptake capabilities of the cell have evolved to permit growth at very low external nutrient concentrations. How are these capabilities controlled when the substrate concentrations are not extremely low and the uptake systems could import substrate much more rapidly than the metabolic capabilities of the cell might be able to handle? To answer this question, earlier theories for the kinetics of uptake through the cell envelope and steady-state systems of metabolic enzymes are discussed and a computer simulation is presented. The problems to the cell of fluctuating levels of nutrient and too much substrate during continuous culture are discussed. Too much substrate can lead to oligotrophy, substrate-accelerated death, entry into the viable but not culturable state, and lactose killing. The relationship between uptake and growth is considered. Finally, too little substrate may lead to catastrophic attempts at mounting molecular syntheses that cannot be completed.

The permeability of the wall fabric of Escherichia coli and Bacillus subtilis.

To study the overall structure of the peptidoglycan fabric of the sacculi of gram-negative and gram-positive walls, actively growing cultures of Escherichia coli and Bacillus subtilis were treated with boiling sodium dodecyl sulfate solutions. The sacculi were then treated with enzymes to eliminate proteins and nucleic acids. These intact saccoli were probed with fluorescein-labeled dextrans with a range of known molecular weights. The penetration of the probes could be monitored by the negative-staining appearance in the fluorescence microscope. At several chosen times, the molecular weight fraction that allowed barely observable entry of the fluorescein-labeled probe and the molecular weight fraction that penetrated to achieve almost, but not quite, the concentration of probe in the solution external to the sacculi were determined. From three pairs of times and molecular weights that met one or the other of these two criteria, the effective pore size could be calculated. The minimum size of protein molecule that could diffuse through the pores was also calculated. Two mathematical models, which gave essentially the same results, were used to interpret the experimental data: one for the permeation of random coils through a surface containing holes and the other for rigid spheres diffusing through water-filled cylindrical pores. The mean estimate of the effective hole radius in walls from E. coli is 2.06 nm, and that of the effective hole size in walls from B. subtilis is 2.12 nm. These results are supported by experiments in which the loss of preloaded cells was monitored. Various fluorescein-labeled dextran samples were mixed with samples of intact cell walls, held for a long time, and then diluted. The efflux of the dextrans was monitored. Neither large nor small dextrans stained under these conditions. Only with dextran samples of a sufficiently small size were the sacculi filled during the preincubation period, and only with the largest of these could the probe not escape quickly. From the pore (or mesh) size, it can be concluded that the wall fabric of both organisms has few imperfections and that the major passageway is through the smallest possible pore, or "tessera," formed by the maximal cross-linking of the peptides from glycan chain to glycan chain compatible with the degree of rotational flexibility of the chains of repeating disaccharides of N-acetyl muramic acid and N-acetyl glucosamine. A tessera is composed of two chains of eight saccharides cross-linked by two octapeptides. The size of a globular hydrophilic molecule, if it did not bind to wall components, that could pass freely through the meshwork of an unstretched sacculus of either organism is roughly 25 kDa. We stress that this is only a rough estimate, and it may be possible for proteins of less than 50 kDa to pass through the native wall during normal growth conditions.

What size should a bacterium be? A question of scale.

There are living prokaryotes (Bacteria and Archaea) that have cell sizes that range from 0.02-400 microns3. Over this tremendous range, various abilities to cope with the environment are needed. This review attempts to formulate some of the problems and some of the solutions. The smallest size for a free-living organism is suggested to be largely set by the catalytic efficiency of enzymes and protein synthetic machinery. Because of fluctuations in the environment, cells must maintain machinery to cope with various catastrophes; these mechanisms increase the minimum size of the cell. On the other hand, the largest cell is reasonably assumed to be limited by the ability of diffusion to bring nutrients to the appropriate part of the cell and to dispose of waste products. To explore the limitation imposed by diffusion, analysis is developed of diffusion processes through stirred and unstirred media, diffusion through media that contains obstacles, and the effect of size and shape.