Movable Finite Automata (MFA) models for biological systems. I: Bacteriophage assembly and operation

A new class of models, called Movable Finite Automata (MFA) models, is introduced. MFA models are physically realistic, but still share some of the features of cellular automata that make the latter easy to handle mathematically and computationally. They are found to be quite versatile in modeling the self-organization of biological systems. Their use in simulating the interaction of protein molecules in the self-assembly and operation of the T4 bacteriophage is described. The results of these simulations carried out on a microcomputer, are given.     

A simulation of T4 bacteriophage assembly and operation

A model is presented for the self-assembly and operation of a bacteriophage comparable with the T4 bacteriophage that infects Escherichia coli. The model treats protein molecules as simple units obeying the principle free energy minimization, and exhibiting the properties of quasi-equivalence and conformational switching. A computer program incorporating the model has been developed. The results of simulation using this program are presented.     

Internal motion of DNA in bacteriophages

We have investigated internal motion of DNA in bacteriophages by measuring fluorescence anisotropy decays of intercalated ethidium. The results showed large suppression of the internal motion of the inner DNA; the interhelix interaction of the DNA in the phage head is considered to enhance the effective viscosity of the DNA rod and to restrict the angle of the internal motion. Considering that the observed internal motion arises mainly from torsional motion of the DNA, we have calculated the movable angles of the torsional motion (the standard deviation of the torsional motion) of the DNA in the phage heads. The magnitude of the calculated movable angles indicates the extent of suppression of the DNA movement in the phage head; in lambda wild type phage, the DNA is packed most rigidly in the head and the motion is found to be restricted most severely. In a deletion mutant of lambda phage, whose inner DNA content is deficient by 17.6%, steric hindrance from the interhelix DNA interaction is decreased, and the DNA can move more easily. In T4 wild type phage, although the extent of condensation of the inner DNA is the same as that in lambda wild type phage, the DNA was fairly mobile. The presence of glucosylated hydroxymethylcytosine is suggested to influence the rigidity of the inner DNA or packaging mode of the DNA in the T4 head.     

Hybrid dynamic/static method for large-scale simulation of metabolism

Background  

Many computer studies have employed either dynamic simulation or metabolic flux analysis (MFA) to predict the behaviour of biochemical pathways. Dynamic simulation determines the time evolution of pathway properties in response to environmental changes, whereas MFA provides only a snapshot of pathway properties within a particular set of environmental conditions. However, owing to the large amount of kinetic data required for dynamic simulation, MFA, which requires less information, has been used to manipulate large-scale pathways to determine metabolic outcomes.     

Evolutionary design on a budget: robustness and optimality of bacteriophage T7

Exploring how biological systems have been 'designed' by evolution to achieve robust behaviours is now a subject of increasing research effort. Yet, it still remains unclear how environmental factors may contribute to this process. This issue is addressed by employing a detailed computer model for the intracellular growth of phage T7. More than 150 000 in silico T7 mutants were generated and the rates and efficiencies of their growth in two host environments, namely, a realistic environment that offered finite host resources for the synthesis of phage functions and a hypothetical environment where the phage was supplied infinite host resources, were evaluated. Results revealed two key properties of phage T7. First, T7 growth was overall robust with respect to perturbations in its parameters, but fragile with respect to changes in the ordering of its genetic elements. Secondly, the wild-type T7 had close to optimal fitness in the finite environment. Furthermore, a strong correlation was found between fitness and growth efficiency in the finite environment. The results underscore the potential importance of the environment in shaping robust design of a biological system. In particular, the strong correlation between fitness and growth efficiency suggests that T7 may have evolved to maximise its growth rate by minimising waste of finite resources.     

Bacteriophage latent-period evolution as a response to resource availability

Bacteriophages (phages) modify microbial communities by lysing hosts, transferring genetic material, and effecting lysogenic conversion. To understand how natural communities are affected it is important to develop predictive models. Here we consider how variation between models--in eclipse period, latent period, adsorption constant, burst size, the handling of differences in host quantity and host quality, and in modeling strategy--can affect predictions. First we compare two published models of phage growth, which differ primarily in terms of how they model the kinetics of phage adsorption; one is a computer simulation and the other is an explicit calculation. At higher host quantities (approximately 10(8) cells/ml), both models closely predict experimentally determined phage population growth rates. At lower host quantities (10(7) cells/ml), the computer simulation continues to closely predict phage growth rates, but the explicit model does not. Next we concentrate on predictions of latent-period optima. A latent-period optimum is the latent period that maximizes the population growth of a specific phage growing in the presence of a specific quantity and quality of host cells. Both models predict similar latent-period optima at higher host densities (e.g., 17 min at 10(8) cells/ml). At lower host densities, however, the computer simulation predicts latent-period optima that are much shorter than those suggested by explicit calculations (e.g., 90 versus 1,250 min at 10(5) cells/ml). Finally, we consider the impact of host quality on phage latent-period evolution. By taking care to differentiate latent-period phenotypic plasticity from latent-period evolution, we argue that the impact of host quality on phage latent-period evolution may be relatively small.     

Bacteriophage Latent-Period Evolution as a Response to Resource Availability

Bacteriophages (phages) modify microbial communities by lysing hosts, transferring genetic material, and effecting lysogenic conversion. To understand how natural communities are affected it is important to develop predictive models. Here we consider how variation between models—in eclipse period, latent period, adsorption constant, burst size, the handling of differences in host quantity and host quality, and in modeling strategy—can affect predictions. First we compare two published models of phage growth, which differ primarily in terms of how they model the kinetics of phage adsorption; one is a computer simulation and the other is an explicit calculation. At higher host quantities (~10⁸ cells/ml), both models closely predict experimentally determined phage population growth rates. At lower host quantities (10⁷ cells/ml), the computer simulation continues to closely predict phage growth rates, but the explicit model does not. Next we concentrate on predictions of latent-period optima. A latent-period optimum is the latent period that maximizes the population growth of a specific phage growing in the presence of a specific quantity and quality of host cells. Both models predict similar latent-period optima at higher host densities (e.g., 17 min at 10⁸ cells/ml). At lower host densities, however, the computer simulation predicts latent-period optima that are much shorter than those suggested by explicit calculations (e.g., 90 versus 1,250 min at 10⁵ cells/ml). Finally, we consider the impact of host quality on phage latent-period evolution. By taking care to differentiate latent-period phenotypic plasticity from latent-period evolution, we argue that the impact of host quality on phage latent-period evolution may be relatively small.     

Transfection of Escherichia coli Spheroplasts II. Relative Infectivity of Native, Denatured, and Renatured Lambda, T7, T5, T4, and P22 Bacteriophage DNAs

The change of infectivity of phage DNAs after heat and alkali denaturation (and renaturation) was measured. T7 phage DNA infectivity increased 4- to 20-fold after denaturation and decreased to the native level after renaturation. Both the heavy and the light single strand of T7 phage DNA were about five times as infective as native T7 DNA. T4 and P22 phage DNA infectivity increased 4- to 20-fold after denaturation and increased another 10- to 20-fold after renaturation. These data, combined with other authors' results on the relative infectivity of various forms of phiX174 and lambda DNAs give the following consistent pattern of relative infectivity. Covalently closed circular double-stranded DNA, nicked circular double-stranded DNA, and double-stranded DNA with cohesive ends are all equally infective and also most highly infectious for Escherichia coli lysozyme-EDTA spheroplasts; linear or circular single-stranded DNAs are about 1/5 to 1/20 as infective; double-stranded DNAs are only 1/100 as infective. Two exceptions to this pattern were noted: lambda phage DNA lost more than 99% of its infectivity after alkaline denaturation; this infectivity could be fully recovered after renaturation. This behavior can be explained by the special role of the cohesive ends of the phage DNA. T5 phage DNA sometimes showed a transient increase in infectivity at temperatures below the completion of the hyperchròmic shift; at higher temperatures, the infectivity was completely destroyed. T5 DNA denatured in alkali lost more than 99.9% of its infectivity; upon renaturation, infectivity was sometimes recovered. This behavior is interpreted in terms of the model of T5 phage DNA structure proposed by Bujard (1969). The results of the denaturation and renaturation experiments show higher efficiencies of transfection for the following phage DNAs (free of single-strand breaks): T4 renatured DNA at 10(-3) instead of 10(-5) for native DNA; renatured P22 DNA at 3 x 10(-7) instead of 3 x 10(-9) for native DNA; and denatured T7 DNA at 3 x 10(-6) instead of 3 x 10(-7) for native DNA.     

Cerebellar cortex: simulation of recurrent collateral inhibition by means of a neuronal automata assembly. II. Temporal modulation and informational content

A quantitative evaluation of the information content exhibited by a neuronal automata assembly coupled by collateral inhibitory--type rules was undertaken on the results of a computer simulation of this partial model of the cerebellar cortex. By comparison with an uncoupled array the model exhibited two main properties: A markovian type of behavior appears in the functioning of the system in as much as the appearance of a given state is strongly and exclusively correlated to the immediately preceding one. This behavior leads to a decrease in the entropy of the system. This implies that the informational content of the efferent "activity" is significantly higher than that of the afferent one.     

Predictability in Cellular Automata

Modelled as finite homogeneous Markov chains, probabilistic cellular automata with local transition probabilities in (0, 1) always posses a stationary distribution. This result alone is not very helpful when it comes to predicting the final configuration; one needs also a formula connecting the probabilities in the stationary distribution to some intrinsic feature of the lattice configuration. Previous results on the asynchronous cellular automata have showed that such feature really exists. It is the number of zero-one borders within the automaton''s binary configuration. An exponential formula in the number of zero-one borders has been proved for the 1-D, 2-D and 3-D asynchronous automata with neighborhood three, five and seven, respectively. We perform computer experiments on a synchronous cellular automaton to check whether the empirical distribution obeys also that theoretical formula. The numerical results indicate a perfect fit for neighbourhood three and five, which opens the way for a rigorous proof of the formula in this new, synchronous case.     

Effects of Escherichia coli physiology on growth of phage T7 in vivo and in silico

Phage development depends not only upon phage functions but also on the physiological state of the host, characterized by levels and activities of host cellular functions. We established Escherichia coli at different physiological states by continuous culture under different dilution rates and then measured its production of phage T7 during a single cycle of infection. We found that the intracellular eclipse time decreased and the rise rate increased as the growth rate of the host increased. To develop mechanistic insight, we extended a computer simulation for the growth of phage T7 to account for the physiology of its host. Literature data were used to establish mathematical correlations between host resources and the host growth rate; host resources included the amount of genomic DNA, pool sizes and elongation rates of RNA polymerases and ribosomes, pool sizes of amino acids and nucleoside triphosphates, and the cell volume. The in silico (simulated) dependence of the phage intracellular rise rate on the host growth rate gave quantitatively good agreement with our in vivo results, increasing fivefold for a 2.4-fold increase in host doublings per hour, and the simulated dependence of eclipse time on growth rate agreed qualitatively, deviating by a fixed delay. When the simulation was used to numerically uncouple host resources from the host growth rate, phage growth was found to be most sensitive to the host translation machinery, specifically, the level and elongation rate of the ribosomes. Finally, the simulation was used to follow how bottlenecks to phage growth shift in response to variations in host or phage functions.     

Visualization of dynamic simulations of muscle thin filaments

Following a novel computational formalism, the thin filament of muscle can be modeled by a computational machine containing a large number of finite automata that have one-to-one correspondence with the constituent protein molecules.¹ Computer graphics can be used to visualize the correspondence between the states of finite automata and the configurations of protein molecules according to the structural data. The dynamic simulation of the muscle filament that corresponds to the concurrent state transitions of finite automata can be represented as a sequence of video images. The kinetic and structural knowledge of individual protein molecules is, therefore, integrated into a coherent and functional system. This type of computation and visualization can also be useful for the investigation of molecular structure, function, and interaction in various complex biological systems.     

Inactivation of T4D Bacteriophage by Antiserum Against Bacteriophage Dihydrofolate Reductase

Antiserum was prepared against highly purified T4D bacteriophage-induced dihydrofolate reductase (DFR). This serum not only inactivated the enzyme but also inactivated all strains of T4D examined. T6 was inactivated to a lesser extent, and T2L, T2H, and T5 were unaffected by the antiserum. The phage-killing power of the serum could be blocked by prior incubation with partially purified T4D dfr obtained from host cells unable to make phage structural proteins. These observations confirm earlier results that the phage dfr is a structural component of the phage particle, and they offer new evidence on the manner in which this enzyme in incorporated into the tail structure.     

Effect of Polymyxin on the Bacteriophage Receptors of the Cell Walls of Gram-Negative Bacteria

Treatment of gram-negative bacteria with lethal doses of polymyxin B and colistin resulted in the formation of projections of the outer layer of the cell wall. Phages T3, T4, and T7, which use wall lipopolysaccharide as receptors, were specifically prevented from adsorbing to Escherichia coli B cells treated with polymyxin, whereas phages T1, T2, T5, and T6 were not. In the systems of phage P22C-Salmonella typhimurium LT2 and phage C21-S. typhimurium variant SL1069, the phage were prevented from adsorbing to the host cell treated with the antibiotics. Electron microscopic observations show that phage T2 adsorbed irreversibly to the normal smooth surface between the projections on the outer layer caused by the drug treatment. These results indicate that lipopolysaccharide is affected by polymyxin functionally and morphologically, but lipoprotein is not. The purified lipopolysaccharide showed a ribbon-like structure when viewed face on and showed trilamellar structure when viewed edge on. The lipopolysaccharide from E. coli B was irreversibly adsorbed by phages T3, T4, and T7, but not phage T2. Often, phage T4 adsorbed to both sides of the lipopolysaccharide strand at comparable distances. Phage P22C adsorbed through the spikes of the tail-plates to the lipopolysaccharide from S. typhimurium LT2. Lipopolysaccharide which was treated with low doses of the drug (2.5 to 6.25 mug of polymyxin B per ml to 100 mug of lipopolysaccharide per ml) turned into the coiled form and was partially broken down into short segments with coiled form. The loosely coiled lipopolysaccharide retains both its function as the receptor and its trilamellar structure. Treatment with high doses of the drug (12.5 to 25 mug of polymyxin B per ml to 100 mug of lipopolysaccharide per ml) caused the collapse of the trilamellar structure of the strand. These collapsed lipopolysaccharides became flat and fused with each other, making an amorphous mass, and finally they were broken into small collapsed fragments.     

The Mechanism of Inactivation of T4 Bacteriophage by Tritium Decay

Coliphage T4 was used as a model system to study the mechanism of biological inactivation produced by tritium decay. Experimentally, tritiated precursors were incorporated into phage DNA (thymidine-³H) or into phage protein (³H-amino acids). The ratio of killing efficiencies for decays originating in phage DNA to those originating in phage protein was 2.6. Inactivation by decays from labeled amino acids was assumed to occur exclusively from β-particle irradiation of phage DNA. If decays originating in DNA are due solely to irradiation of DNA, then the killing efficiencies reflect the energy transfer paths in phage DNA for decays originating in phage DNA and in the protein coat. The energy transfer paths were determined for the two cases with the help of a computer and found to be very nearly equal to the experimentally determined ratio (2.6). The killing efficiencies for decays originating in phage DNA were 0.12 and for decays originating in protein 0.046.     

Chemically Induced Cofactor Requirement for Bacteriophage T4D

The treatment of bacteriophage T4D with 2-hydroxy-5-nitrobenzyl bromide, a specific reagent for alkylating the indole ring of tryptophan residues, converts these particles from a cofactor-independent form to a cofactor-sensitive form. These treated T4D particles phenotypically resemble T4B particles in certain respects. Their ability to form plaques on minimal medium plates is increased by the addition of l-tryptophan and is inhibited by the addition of indole. In liquid medium, their rate of adsorption is dependent on the presence of the cofactor l-tryptophan. l-Tryptophan-requiring phage have been produced by in vitro assembly of treated tail-fiberless particles of a T4D amber mutant plus untreated tail fiber preparation. When treated tail fibers were used with untreated tail-fiberless particles, the newly assembled particles did not require cofactor. A model of the tail structure of all the T-even bacteriophages is presented which postulates that the active configuration of the tail fibers requires that there be either (i) an endogenous tryptophan residue of the phage particle itself or (ii) an exogenously added l-tryptophan molecule complexed with a specific tryptophan receptor site, most likely on the phage base plate.     

The In Vitro Self-Assembly of Supramolecular Structures after the Spontaneous Disassembly of Carotovoricins

The self-assembly of supramolecular structures (empty sheaths and polysheaths of the macromolecular Erwinia carotovora bacteriocins) was studied by electron microscopy in the course of 1- to 2-year incubation of phage particles at 4°C. This study showed that the empty sheaths and polysheaths of the bacteriocins of eight E. carotovora strains spontaneously assemble at the self-assembly centers (or crystallization centers), which have a diameter of 26–65 nm and contain a dense proteinaceous material. The self-assembly center consists of two components, a primer and the structural protein of contracted sheaths. Empty sheaths assembled in the crystallization centers are polar structures synthesized through the stepwise head-to-tail polymerization of monomeric units. The supramolecular structures of two E. carotovora 62A bacteriocins are assembled in a different way. At the early stages of their self-assembly, a reticular structure is formed, which then transforms into very long polysheaths composed of monomers. Along with polysheaths, rounded or lamplike structures 33–117 nm in size composed of the subunits of contracted sheaths are produced. Carotovoricins may serve as suitable objects for the study of the self-assembly of elementary biological structures.     

Electron-microscopic study of the serological affinity between the antigenic components of phages T4 and DDVI.

In an investigation of the antigenic fine structure of phages T4 and DDVI with the use of the neutralization reaction and electron-microscopic observation of the phage-antibody complexes, it has been possible to establish that the head of phage T4 consists of proteins which have antigenic determinants of two types: The first type is identical to the antigens of the head of phage DDVI, and the second type is apparently absent in phage DDVI. The phage DDVI head contains mostly determinants which are common to the phage T4 head, since it was not possible to detect antigenically specific components in the phage DDVI head. The tail sheaths of phage T4 and DDVI appear to be identical in the antigenic respect. A difference has been observed in the fibers and the base plates of the phages investigated. The presence of the following three types of antigens has been established: 1) common to phages T2, T4, and DDVI, 2) common to phages T4 and DDVI, and 3) specific for each phage investigated.     

Towards high throughput metabolic flux analysis in plants

Research on plant metabolism is currently experiencing the common use of various omics methods creating valuable information on the concentrations of the cell's constituents. However, little is known about in vivo reaction rates, which can be determined by Metabolic Flux Analysis (MFA), a combination of isotope labeling experiments and computer modeling of the metabolic network. Large-scale applications of this method so far have been hampered by tedious procedures of tissue culture, analytics, modeling and simulation. By streamlining the workflow of MFA, the throughput of the method could be significantly increased. We propose strategies for these improvements on various sub-steps which will move flux analysis to the medium-throughput range and closer to established methods such as metabolite profiling. Furthermore, this may enable novel applications of MFA, for example screening plant populations for traits related to the flux phenotype.