Christina Kuttler

Technische Universität München | TUM · Department of Mathematical Modelling

Formulating tumor models that predict growth under therapy is vital for improving patient-specific treatment plans. In this context, we present our recent work on simulating non-small-scale cell lung cancer (NSCLC) in a simple, deterministic setting for two different patients receiving an immunotherapeutic treatment. At its core, our model consists...

Quorum sensing is a widespread process in bacteria that controls collective behaviours in response to cell density. Populations of cells coordinate gene expression through the perception of self-produced chemical signals. Although this process is well-characterized genetically and biochemically, quantitative information about network properties, in...

A mathematical model for bacterial growth and control by antibiotics treatment, including Quorum sensing as a special kind of communication, is introduced. We aim in setting up a flexible model structure allowing for fast simulations and overview about the general behavior. The deterministic approach can be used for in silico studies of bacterial c...

The use of external enzymes provides an alternative way of reducing communication in pathogenic bacteria that may lead to the degradation of their signal and the loss of their pathogeneity. The present study considers an optimal control problem for the semilinear reaction-diffusion model of bacterial quorum sensing under the impact of external enzy...

We extend a previously presented mesoscopic (i.e. colony scale) mathematical model of the reaction of bacterial biofilms to antibiotics. In that earlier model, exposure to antibiotics evokes two responses: inactivation as the antibiotics kill the bacteria, and inducing a quorum sensing based stress response mechanism upon exposure to small subletha...

Survival of living tumor cells underlies many influences such as nutrient saturation, oxygen level, drug concentrations or mechanical forces. Data-supported mathematical modeling can be a powerful tool to get a better understanding of cell behavior in different settings. However, under consideration of numerous environmental factors mathematical mo...

Survival of living tumor cells underlies many influences such as nutrient saturation, oxygen level, drug concentrations or mechanical forces. Data-supported mathematical modeling can be a powerful tool to get a better understanding of cell behavior in different settings. However, under consideration of numerous environmental factors mathematical mo...

In this work, we present and analyse a system of coupled partial differential equations, which models tumour growth under the influence of subdiffusion, mechanical effects, nutrient supply and chemotherapy. The subdiffusion of the system is modelled by a time fractional derivative in the equation governing the volume fraction of the tumour cells. T...

Background Cancer is one of the leading death causes globally with about 8.2 million deaths per year and an increase in numbers in recent years. About 90% of cancer deaths do not occur due to primary tumors but due to metastases, of which most are not clinically identifiable because of their relatively small size at primary diagnosis and limited te...

Background: Cancer is one of the leading death causes globally with about 8.2 million deaths per year and an increase in numbers in recent years. About 90% of cancer deaths do not occur due to primary tumors but due to metastases, of which most are not clinically identifiable because of their relatively small size at primary diagnosis and limited t...

Introduction: Esophageal motility disorders have a severe impact on patients' quality of life. While high-resolution manometry (HRM) is the gold standard in the diagnosis of esophageal motility disorders, intermittently occurring muscular deficiencies often remain undiscovered if they do not lead to an intense level of discomfort or cause sufferin...

Background: Cancer is one of the leading death causes globally with about 8.2 million deaths per year and an increase in numbers in recent years. About 90% of cancer deaths do not occur due to primary tumors but due to metastases, of which most are not clinically identifiable because of their relatively small size at primary diagnosis and limited t...

In this work, we present a model for tumour growth in terms of reaction-diffusion equations with mechanical coupling and time fractional derivatives. We prove the existence and uniqueness of the weak solution. Numerical results illustrate the effect of the fractional derivative and the influence of the fractional parameter.

The bacterium Staphylococcus aureus is an important human pathogen, which plays a crucial role in a large number of hospital-acquired infections. We study pattern formation in colonies of this bacterium under laboratory conditions.

In ecology, G-functions can be employed to define a growth function G for a population b, which can then be universally applied to all individuals or groups b i within this population. We can further define a strategy v i for every group b i . Examples for strategies include diverse behaviour such as number of offspring, habitat choice, and time of...

The focus of this paper is to develop a new partial differential equation model for the pattern formation of the human pathogen Staphylococcus aureus, starting from a newly developed model of selected gene regulation mechanisms. In our model, we do not only account for the bacteria densities and nutrient concentrations, but also for the quorum sens...

Quorum sensing (QS) in Pseudomonas aeruginosa coordinates the expression of virulence factors, such as exoproteases and siderophores, that are public goods utilized by the whole population of bacteria, regardless of whether they invested or not in their production. These public goods can be used by QS defective mutants for growth and since these mu...

We present a mathematical model of biofilm response to antibiotics, controlled by a quorum sensing system that confers increased resistance. The model is a highly nonlinear system of partial differential equations that we investigate in computer simulations. Our results suggest that an adaptive, quorum sensing-controlled, mechanism to switch betwee...

Although bacteria are unicellular organisms, they use a sophisticated mechanism to cooperate with other bacteria which allows them to carry out multicellular-like processes, such as swarming, biofilm formation, induce infections, luminescence, etc. This mechanism is known as quorum sensing (QS) and it functions through the individual release, diffu...

A central question to biology is how pathogenic bacteria initiate acute or chronic infections. Here we describe a genetic program for cell-fate decision in the opportunistic human pathogen Staphylococcus aureus, which generates the phenotypic bifurcation of the cells into two genetically identical but different cell types during the course of an in...

Gene quantification and differential expression analysis of BRcells and DRcells. This data table contains the table for gene-wise quantification calculated for different cDNA libraries used in this study. DESeq analysis data for library comparisons.

Genome-wide analysis of DRcell and BRcell sorted subpopulations. Library specific variations are 0, showing that no statistically significant genetic differences were found between BRcells and DRcells genomes.

Functional classification of annotated genes. Gene Ontology classification of annotated genes that showed significant log2fold change value for differential expression generated by DESeq analysis. Aureowiki functional classification of the annotated genes that showed significant log2fold change value for differential expression generated by DESeq c...

Hypergeometric analysis for library comparison comprising the log2fold values for differentially expressed genes that were shown to be expressed by DESeq analysis comparison of DRcells+ against BRcells+ sample sets. Hypergeometric analysis probability and hypergeometric analysis heatmap comparison.

List of strains used in this study.

List of plasmids and plasmids used in this study.

Bacteria are not just primitive stupid organisms, being only interested in divide themselves as fast as possible. Many bacterial species have developed a special kind of communication called quorum sensing which helps them to coordinate their behavior. This phenomenon is run and controlled by a special gene regulation system. It is based on product...

We prove existence and uniqueness of weak and classical solutions to certain semi-linear parabolic systems with Robin boundary conditions using the coupled upper-lower solution approach. Our interest lies in cross-dependencies on the gradient parts of the reaction term, which prevents the straight-forward application of standard theorems. Such cros...

Many bacteria have developed a possibility to recognise aspects of their environment or to communicate with each other by chemical signals. The so-called Quorum sensing (QS) is a special case of this kind of communication. Such an extracellular signalling via small diffusible compounds (called autoinducers) is known for many bacterial species, incl...

Quorum sensing is a bacterial cell-to-cell communication mechanism and is based on gene regulatory networks, which control and regulate the production of signaling molecules in the environment. In the past years, mathematical modeling of quorum sensing has provided an understanding of key components of such networks, including several feedback loop...

Bacterial communication is enabled through the collective release and sensing of signalling molecules in a process called quorum sensing. Cooperative processes can easily be destabilized by the appearance of cheaters, who contribute little or nothing at all to the production of common goods. This especially applies for planktonic cultures. In this...

Cell-to-cell signalling via small diffusible molecules, usually termed quorum sensing (QS), represents a common behaviour in bacteria. This signalling regulates life style switches in many, if not most symbiotic microbial species either beneficial or pathogenic for their eukaryotic hosts, but is also involved in controlling environmental processes...

Background: Cell dispersal (or detachment) is part of the developmental cycle of microbial biofilms. It can be externally or internally induced, and manifests itself in discrete sloughing events, whereby many cells disperse in an instance, or in continuous slower dispersal of single cells. One suggested trigger of cell dispersal is quorum sensing,...

Pseudomonas syringae is a plant-pathogen which, through the signalling system quorum sensing (QS), controls virulence. In this paper, we use the integral of a non-negative stochastic process to study the QS state of the bacterial colonies it forms when living on leaf surfaces.We investigate the extent to which factors such as water availability and...

This chapter gives an introduction into the most basic models for the dynamics of ecosystems. Starting with the simplest case of one single homogeneous population which inhabits an ecosystem, we proceed to two-population models. They are prototypes for the different interaction patterns between species: one species may predate upon the other, the t...

In contrast to the previous chapter “Mathematical Ecology”, dealing exclusively with compartmental models without any further structure, the complexity of the models is now larger, even though the basic questions still concern the conditions for survival respectively long-term dynamics. In this chapter, an individual is characterised by more proper...

In the present chapter, we discuss two different approaches to model evolution. The first focuses on genes. The presence of different gene variations indicates different discrete levels of fitness, i.e., of reproductive success. We will look at this kind of models (Hardy-Weinberg, Wright model and Fisher-Wright-Haldane model) first. The second appr...

This chapter gives an introduction into the most basic models for the dynamics of ecosystems. Starting with the simplest case of one single homogeneous population which inhabits an ecosystem, we proceed to two-population models. They are prototypes for the different interaction patterns between species: one species may predate upon the other, the t...

Chemical and biochemical networks can be viewed as dynamical systems. The properties of these systems can be complex and sometimes also surprising. Examples are enzyme kinetics, cells that interact and react to their environment by means of regulatory pathways, pattern on the skin of cows, leopards or snails are created by means of biochemical reac...

Compartmental models form the back-bone of mathematical biology. In this chapter, we introduce some of the basic tools to understand how to formulate and handle compartmental models in different situations, and which questions are possible to answer. We focus on linear models and independent entities. Nonlinear models will be discussed in the follo...

We start off with the description of a single ganglion (a neuronal cell, nerve cell), that is stimulated by a given input. Experiments show basically that a certain minimal activation is necessary to provoke a reaction. This reaction has a form of one spike in case of a short input signal, or periodic spiking in case of a constant input. This behav...

This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models, and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, bioc...

We introduce and study a degenerate reaction-diffusion system that can serve as a model prototype for the pattern formation of a bacterial multicellular community where the bacteria produce biofilm, grow and spread in the presence of a nutrient. Under proper conditions on the reaction terms, we prove the global existence and the uniqueness of solut...

Abstract Quorum sensing, a special kind of cell-cell communication, has originally been described for well-mixed homogeneous bacterial cultures. However, recent perception supports its ecological relevance for spatially heterogeneous distributed cells, like colonies and biofilms. New experimental techniques allow for single cell analysis under thes...

In this interdisciplinary approach, the dynamics of production and degradation of the quorum sensing signal 3-oxo-decanoylhomoserine lactone were studied for continuous cultures of Pseudomonas putida IsoF. The signal concentrations were quantified over time by use of monoclonal antibodies and ELISA. The results were verified by use of ultra-high-pe...

A novel class of state-dependent delay equations is derived from the balance laws of age-structured population dynamics, assuming that birth rates and death rates, as functions of age, are piece-wise constant and that the length of the juvenile phase depends on the total adult population size. The resulting class of equations includes also neutral...

We consider the uptake of various carbon sources by microorganisms based on four fundamental assumptions: (1) the uptake of nutrient follows a saturation characteristics (2) substrate processing has a benefit but comes at costs of maintaining the process chain (3) substrate uptake is controlled and (4) evolution optimized the control of substrate u...

A general framework for age-structured predator-prey systems is introduced. Individuals are distinguished into two classes, juveniles and adults, and several possible interactions are considered. The initial system of partial differential equations is reduced to a system of (neutral) delay differential equations with one or two delays. Thanks to th...

Background: Tumor angiogenesis is the process of vessel arousal and growth, initiated by chemical substances secreted by adjacent tissue of a tumor. After the tumor has reached a certain size, oxygen and nutrient supply cannot be accomplished alone by diffusion and the tumor forms new vessels from the adjacent tissue, which sprout and invade the tu...

Autoinducer signals enable coordinated behaviour of bacterial populations, a phenomenon originally described as quorum sensing. Autoinducer systems are often controlled by environmental substances as nutrients or secondary metabolites (signals) from neighbouring organisms. In cell aggregates and biofilms gradients of signals and environmental subst...

Background Diabetes mellitus is a group of metabolic diseases with increased blood glucose concentration as the main symptom. This can be caused by a relative or a total lack of insulin which is produced by the β‐cells in the pancreatic islets of Langerhans. Recent experimental results indicate the relevance of the β‐cell cycle for the development...

Pseudomonas syringae is a gram-negative bacterium which lives on leaf surfaces. Its growth has been described using epifluorescence microscopy and image analysis; it was found to be growing in aggregates of a wide range of sizes. We develop a stochastic model to describe aggregate distribution and determine the mechanisms generating experimental ob...

Quorum sensing (QS) describes the capability of microbes to communicate with each other by the aid of small molecules. Here we investigate the dynamics of QS-regulated gene expression induced by acylhomoserine lactones (AHLs) in Pseudomonas putida IsoF containing a green fluorescent protein-based AHL reporter. The fluorescence time course of indivi...

In this work we present a mathematical model for tumor growth based on the biology of the cell cycle. For an appropriate description of the effects of phase-specific drugs, it is necessary to look at the cell cycle and its phases. Our model reproduces the dynamics of three different tumor cell populations: quiescent cells, cells during the interpha...

Acidovorax radicis N35, isolated from surface‐sterilized wheat roots (Triticum aestivum), showed irreversible phenotypic variation in nutrient broth, resulting in a differing colony morphology. In addition to the wild‐type form (rough colony type), a phenotypic variant form (smooth colony type) appeared at a frequency of 3.2 × 10−3 per cell per gen...

Acidovorax radicis N35, isolated from surface-sterilized wheat roots (Triticum aestivum), showed irreversible phenotypic variation in nutrient broth, resulting in a differing colony morphology. In addition to the wild-type form (rough colony type), a phenotypic variant form (smooth colony type) appeared at a frequency of 3.2 × 10(-3) per cell per g...

Biofilms are microbial communities encased in a layer of extracellular polymeric substances (EPS). The EPS matrix provides several functional purposes for the biofilm, such as protecting bacteria from environmental stresses, and providing mechanical stability. Quorum sensing is a cell-cell communication mechanism used by several bacterial taxa to c...

The bacterial strain Pseudomonas putida IsoF, isolated from a tomato rhizosphere, possesses a quorum sensing regulation system, which allows the bacteria to recognise aspects of their environment or to communicate with each other by the so-called autoinducer molecules. In an experimental study, the time series of the autoinducer production did not...

The biocontrol strain Pseudomonas putida IsoF, which was isolated from a tomato rhizosphere, is a known N-acyl-homoserine lactone (AHL) producer with only one LuxI/LuxR-like quorum-sensing (QS) system. The production and degradation of AHLs were analysed in different growth phases of the bacterium. Using the analytical tools of ultra performance li...

Quorum sensing is a type of cell to cell communication used to coordinate behavior in groups based on population density. We present a mathematical model of this phenomenon in bacterial biofilms, consisting of a nonlinear diffusion reaction system. The model includes production and spatial spreading of biomass, conversion of down-regulated biomass...

We develop a simple model for the random distribution of a gene product. It is assumed that the only source of variance is due to switching transcription on and off by a random process. Under the condition that the transition rates between on and off are constant we find that the amount of mRNA follows a scaled Beta distribution. Additionally, a si...

Autoinducer sensing, also known as quorum sensing, is the communication of bacteria by autoinducer (small signaling molecules). Cells respond on extremely low concentrations of autoinducer: only one or two molecules per cell are sufficient. At this signal level a high degree of noise is inherent. We ask for the mechanism that is able to overcome th...

Many bacteria developed a possibility to recognise aspects of their environment or to communicate with each other by chemical signals. An important strategy is the so-called quorum sensing (QS), a regulatory mechanism for the gene expression, where the bacteria measure their own cell density by means of this signalling pathway. One of the best-stud...

Loss of Hes7 function leads to irregular somite formation demonstrating that Hes7 is a crucial component of the segmentation clock during somitogenesis. Experiments revealed that not only the repressor functionality but also the half-life of the protein is crucial for oscillatory expression of Hes7 and regular somite formation. Numerical integratio...

We propose that bacteria release diffusible autoinducers as proxies for testing the efficiency of producing extracellular effectors (efficiency sensing).

Cell-based immunotherapy in settings of allogeneic stem cell transplantation or donor leukocyte infusion has curative potential, especially in hematologic malignancies. However, this approach is severely restricted due to graft-versus-host disease (GvHD). This limitation may be overcome if target antigens are molecularly defined and effector cells...

Derivatives of N-acylhomoserine lactones (HSLs) with different alkanoyl side chains occur as quorum or diffusion sensing molecules in gram-negative bacteria and their quantitative chemical analysis became important as a possible way to follow regulation processes of their pathogenicity towards plants and animals. The lactone-ring of HSLs is chemica...

Quorum sensing faces evolutionary problems from non-producing or over-producing cheaters. Such problems are circumvented in diffusion sensing, an alternative explanation for quorum sensing. However, both explanations face the problems of signalling in complex environments such as the rhizosphere where, for example, the spatial distribution of cells...