Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area

Exponential signaling gain at the receptor level enhances signal-to-noise ratio in bacterial chemotaxis

Peer reviewedPublisher PD

The evolution of the bacterial chemotaxis network

Advances in biomolecular technology allow us to sequence entire genomes, but how genes and molecular networks influence the emergence and evolution of phenotypic traits is still unclear. Different fields in biology and medicine are working hard to unravel the relationship between the genome and phenotypes. In this thesis, a new (mechanistic) approach combining systems biology and evolutionary biology is explored to tackle the genotype-phenotype problem. The chemotaxis network of Escherichia coli is used as a model system for its relatively simple network configuration associated with a complex trait such as chemotactic performance. A mathematical model was developed and in silico evolutionary experiments were performed with different environmental conditions. The results show that due to the complexity of the genomic architecture, most individual gene loci have an inconsistent relationship with fitness. In other words, direct relationships between genes and phenotypes are far more complex than just a linear correlation. The reconstruction of the fitness landscape shows that its structure is highly heterogeneous and there are cases in which mutations have unpredictable and inconsistent effects. Another result shows that contrary to static environments, fluctuating environments facilitate the exploration of the fitness landscape. The results in this thesis show the potential of the evolutionary-systems-biology approach, which could help to understand how complex diseases (e.g. cancer or diabetes) develop or how bacteria evolve to become drug resistant

Quantitative Analysis of Information Transfer in Signal Transduction

Biological signal transduction pathways evolved to reliably transmit information from input signals inducing appropriate cellular responses in the process. Along signaling pathways, information is often successively relayed to several types of transmitter molecules. In some cases, particular transmitter molecules do not only receive one kind of information, but several. To this end, information can for instance refer to the identity or quantity of first messengers. By encoding particular bits of information into specific characteristics of such shared transmitters, the information can be decoded downstream. Here, transmitter characteristics may refer to the absolute level of transmitter molecules, the duration of transmitter activation or, in case of activation pulses, the pulse frequency. In this thesis, I analyzed encoding and decoding in two prime examples of signal transduction: calcium signaling in non-excitable cells and Escherichia coli chemotaxis. For this purpose, I present several methods allowing for a quantitative analysis of information transfer, whereas methods are partly based on measures from the field of information theory. With regards to calcium signaling, I focused on the frequency-decoding of calcium oscillations by dependent proteins. Particularly, variations in the quantity of input signals can account for modulations of the calcium oscillation frequency. Several proteins like NFAT, NF-κB, CaMKII and calpain were found to be sensitive to such frequency-modulations. To this end, most frequency-decoding proteins exhibit increased activities for fast calcium oscillations and decreased activities for slow oscillations. I refer to this form of frequency-decoding as high-pass activation. In contrast, the transcription factor NFAT was reported to exhibit an optimal frequency for its activation, while slower or faster frequencies only result in a reduced protein activity. In turn, I refer to this form of frequency-decoding as band-pass activation. On the basis of kinetic models, I identified requirements for high-pass and band-pass activation. In more detail, I employed optimization algorithms aiming at a maximization of the high-pass or band-pass activation distinctness. Among other things, I found that antagonistic, oscillatordependent regulation of the decoder was essential for band-pass activation, whereas regulator species had to be differently responsive to upstream calcium oscillations. Further, I defined favorable parameter margins and confirmed reports on the importance of cooperative protein activation for distinct frequency-decoding. Additionally, I employed channel capacity estimates to quantify the discriminability of particular calcium oscillation frequencies in the presence of realistic stochastic fluctuations. For the application of channel capacity estimations and the interpretation of the resultant estimates, I discuss several possible pitfalls. With regards to Escherichia coli chemotaxis, I focused on the encoding of attractant levels into receptor methylation levels using an established kinetic model. On the basis of results by a collaborateur, encoding was investigated by inferring expected attractant levels from present receptor methylation levels. In addition, I used delayed mutual information estimates to quantify the dynamic processes of memory formation and memory loss. Here, memory formation and memory loss were characterized by targeted transient changes in receptor methylation levels in response to changes in ambient attractant levels. In Escherichia coli chemotaxis, single receptors can be methylated multiple times. By means of the aforementioned methods, I found that, for extreme attractant levels, chemotactic behavior failed due to limitations in the encoding of ambient attractant levels into receptor methylation levels, whereas a reduction of the maximal number of methylations per receptor resulted in severer limitations in the encoding, thus, greater impairments in Escherichia coli chemotaxis. For both examples of signal transduction, I examined information transmission through molecular communication channels. To this end, the input was the variable to be encoded or decoded and the output was the encoding or decoding variable. Changes in model characteristics, such as the model parameterization or network structure, greatly impacted the number of input signals that could be reliably encoded or decoded. Both example systems distinguished themselves by a pronounced ultrasensitivity of the output variable to changes in the input variable. I found that this ultrasensitivity helped in increasing the discriminability between input signals

A Computational Study of E. coli Chemotaxis

Wolde, P.R. ten [Promotor

The spatial evolution of the chemotaxis proteins of the Bacillus subtilis group

The aim of this work was to study spatial evolution of the chemotaxis proteins of a group of plant-associated soil-dwelling bacteria vernacularly referred to as the B. subtilis group. This was achieved by creating homology models for the chemotaxis proteins if a suitable template was available, and by analysing the selective forces (positive, purifying or neutral) acting upon the chemotaxis proteins. Chemotaxis is the phenomenon in which bacteria direct their movement towards more favourable conditions, and is critical for processes such as obtaining nutrients, escaping toxic compounds, host colonization and bio-film formation. Members of the B. subtilis group exhibit different preferences for certain host plants, and it is therefore feasible that their chemotactic machinery are fine-tuned to respond optimally to the conditions of the various niches that the strains inhabit. Homology models were inferred for the plant growth promoting B. amyloliquefaciens FZB42 proteins CheB, CheC, CheD, CheR, CheW and CheY. The interactions between: CheC-CheD, the P1 and P2 domains of CheA with CheY and CheB, and the P4 and P5 domains of CheA with CheW were also modelled. The hydrophobic interactions contributing to intra- and inter-protein contacts were analysed. The models of the interactions between CheB and the various domains of CheA are of particular interest, because to date no structures have been solved that show an interaction between a histidine kinase (such as CheA) and a multidomain response regulator (such as CheB). Furthermore, evidence that phospho-CheB may inhibit the formation of phospho-CheY by competitively binding to the P2 domain of CheA is also presented. Proteins were analysed to determine if individual amino acid sites are under positive, neutral or purifying selection. The Methyl Accepting Chemotaxis Proteins (MCPs), CheA and CheV were also analyzed, but due to a lack of suitable templates, no homology models were constructed. Site-specific positive and purifying selection were estimated by comparing the ratios of non-synonymous to synonymous substitutions at each site in the sequences for the chemotaxis proteins as well as for the receptors McpA, McpB, and McpC. Homology models were coloured according to intensity of selective forces. It was found that the chemotaxis proteins of member of the B. subtilis group are under strong evolutionary constraints, hence it is unlikely that positive selection in these proteins are responsible for the differences in habitat preference that these organism exhibit