Cross-diffusion induced patterns for a single-step enzymatic reaction

Several different enzymes display an apparent diffusion coefficient that increases with the concentration of their substrate. Moreover, their motion becomes directed in substrate gradients. Currently, there are several competing models for these transport dynamics. Here, we use mathematical modeling and numerical simulations to analyze whether the enzymatic reactions can generate a significant feedback from enzyme transport onto the substrate profile. We find that this feedback can generate spontaneous spatial patterns in the enzyme distribution, with just a single-step catalytic reaction. However, patterns are formed only for a subclass of transport models. For such models, nonspecific repulsive interactions between the enzyme and the substrate, or attractive interactions between the enzyme and the product, cause the enzyme to accumulate in regions of low substrate concentration. Reactions then amplify local substrate and product fluctuations, causing enzymes to further accumulate where substrate is low. Experimental analysis of this pattern formation process could discriminate between different transport models.

Slower growth of Escherichia coli leads to longer survival in carbon starvation due to a decrease in the maintenance rate

Fitness of bacteria is determined both by how fast cells grow when nutrients are abundant and by how well they survive when conditions worsen. Here, we study how prior growth conditions affect the death rate of Escherichia coli during carbon starvation. We control the growth rate prior to starvation either via the carbon source or via a carbon‐limited chemostat. We find a consistent dependence where death rate depends on the prior growth conditions only via the growth rate, with slower growth leading to exponentially slower death. Breaking down the observed death rate into two factors, maintenance rate and recycling yield, reveals that slower growing cells display a decreased maintenance rate per cell volume during starvation, thereby decreasing their death rate. In contrast, the ability to scavenge nutrients from carcasses of dead cells (recycling yield) remains constant. Our results suggest a physiological trade‐off between rapid proliferation and long survival. We explore the implications of this trade‐off within a mathematical model, which can rationalize the observation that bacteria outside of lab environments are not optimized for fast growth.

Dynamics of the Buckling Transition in Double-Stranded DNA and RNA

DNA under torsional strain undergoes a buckling transition that is the fundamental step in plectoneme nucleation and supercoil dynamics, which are critical for the processing of genomic information. Despite its importance, quantitative models of the buckling transition, in particular to also explain the surprising two-orders-of-magnitude difference between the buckling times for RNA and DNA revealed by single-molecule tweezers experiments, are currently lacking. Additionally, little is known about the configurations of the DNA during the buckling transition because they are not directly observable experimentally. Here, we use a discrete worm-like chain model and Brownian dynamics to simulate the DNA/RNA buckling transition. Our simulations are in good agreement with experimentally determined parameters of the buckling transition. The simulations show that the buckling time strongly and exponentially depends on the bending stiffness, which accounts for more than half the measured difference between DNA and RNA. Analyzing the microscopic conformations of the chain revealed by our simulations, we find clear evidence for a solenoid-shaped transition state and a curl intermediate. The curl intermediate features a single loop and becomes increasingly populated at low forces. Taken together, the simulations suggest that the worm-like chain model can account semiquantitatively for the buckling dynamics of both DNA and RNA.

Heterogeneous Timing of Gene Induction as a Regulation Strategy

In response to environmental changes, cells often adapt by up-regulating genes to synthesize proteins that generate a benefit in the new environment. Several such cases of gene induction have been reported where the timing was heterogeneous, with some cells responding early and others responding late, although the microbial population was genetically homogeneous and the environment was well mixed. Here, we explore under which conditions heterogeneous timing of gene induction could be advantageous for the population as a whole. We base our study on a mathematical model that accounts for the cost of protein synthesis in terms of resources, which cells must provide immediately, whereas the associated benefit accumulates only slowly over the protein lifetime. Due to this delayed benefit, gene induction can be a risky investment, if resources are scarce and the environment fluctuates rapidly and unpredictably. Unprofitable gene induction then depletes the remaining limiting resource needed for maintenance of cell viability. We show that whenever gene induction is associated with a transient risk but beneficial in the long run, the stochastic timing of gene induction maximizes the reproductive success of a population. In particular, in an environment of stochastic periods of famine and feast, an optimum emerges from a trade-off between short-term growth, favoring rapid and homogeneous responses, and long-term survival, favoring a broadly heterogeneous response. Our analysis suggests that the optimal variability of induction times is just as large as the time required for the amortization of the initial investment into protein synthesis.

Regulation of reaction fluxes via enzyme sequestration and co-clustering

Experimental observations suggest that cells change the intracellular localization of key enzymes to regulate the reaction fluxes in enzymatic networks. In particular, cells appear to use sequestration and co-clustering of enzymes as spatial regulation strategies. These strategies should be equally useful to achieve rapid flux regulation in synthetic biomolecular systems. Here, we leverage a theoretical model to analyse the capacity of enzyme sequestration and co-clustering to control the reaction flux in a branch of a reaction–diffusion network. We find that in both cases, the response of the system is determined by two dimensionless parameters, the ratio of total activities of the competing enzymes and the ratio of diffusion to reaction timescales. Using these dependencies, we determine the parameter range for which sequestration and co-clustering can yield a biologically significant regulatory effect. Based on the known kinetic parameters of enzymes, we conclude that sequestration and co-clustering represent a viable regulation strategy for a large fraction of metabolic enzymes, and suggest design principles for reaction flux regulation in natural or synthetic systems.

Death Rate of E. coli during Starvation Is Set by Maintenance Cost and Biomass Recycling

To break down organismal fitness into molecular contributions, costs and benefits of cellular components must be analyzed in all phases of the organism’s life cycle. Here, we establish the required quantitative approach for the death phase of the model bacterium Escherichia coli. We show that in carbon starvation, an exponential decay of viability emerges as a collective phenomenon, with viable cells recycling nutrients from cell carcasses to maintain viability. The observed collective death rate is determined by the maintenance rate of viable cells and the amount of nutrients recovered from dead cells. Using this relation, we study the cost of a wasteful enzyme during starvation and the benefit of the stress response sigma factor RpoS. While the enzyme increases maintenance and thereby the death rate, RpoS improves biomass recycling, decreasing the death rate. Our approach thus enables quantitative analyses of how cellular components affect the survival of non-growing cells.


TUM Press Release (deutsch)

TUM Press Release (english)

A global resource allocation strategy governs growth transition kinetics of Escherichia coli

A grand challenge of systems biology is to predict the kinetic responses of living systems to perturbations starting from the underlying molecular interactions. Changes in the nutrient environment have long been used to study regulation and adaptation phenomena in microorganisms and they remain a topic of active investigation. Although much is known about the molecular interactions that govern the regulation of key metabolic processes in response to applied perturbations, they are insufficiently quantified for predictive bottom-up modelling. Here we develop a top-down approach, expanding the recently established coarse-grained proteome allocation models from steady-state growth into the kinetic regime. Using only qualitative knowledge of the underlying regulatory processes and imposing the condition of flux balance, we derive a quantitative model of bacterial growth transitions that is independent of inaccessible kinetic parameters. The resulting flux-controlled regulation model accurately predicts the time course of gene expression and biomass accumulation in response to carbon upshifts and downshifts (for example, diauxic shifts) without adjustable parameters. As predicted by the model and validated by quantitative proteomics, cells exhibit suboptimal recovery kinetics in response to nutrient shifts owing to a rigid strategy of protein synthesis allocation, which is not directed towards alleviating specific metabolic bottlenecks. Our approach does not rely on kinetic parameters, and therefore points to a theoretical framework for describing a broad range of such kinetic processes without detailed knowledge of the underlying biochemical reactions.

Quantifying the benefit of a proteome reserve in fluctuating environments

The overexpression of proteins is a major burden for fast-growing bacteria. Paradoxically, recent characterization of the proteome of Escherichia coli found many proteins expressed in excess of what appears to be optimal for exponential growth. Here, we quantitatively investigate the possibility that this overexpression constitutes a strategic reserve kept by starving cells to quickly meet demand upon sudden improvement in growth conditions. For cells exposed to repeated famine-and-feast cycles, we derive a simple relation between the duration of feast and the allocation of the ribosomal protein reserve to maximize the overall gain in biomass during the feast.

Optimal Compartmentalization Strategies for Metabolic Microcompartments

Intracellular compartmentalization of cooperating enzymes is a strategy that is frequently used by cells. Segregation of enzymes that catalyze sequential reactions can alleviate challenges such as toxic pathway intermediates, competing metabolic reactions, and slow reaction rates. Inspired by nature, synthetic biologists also seek to encapsulate engineered metabolic pathways within vesicles or proteinaceous shells to enhance the yield of industrially and pharmaceutically useful products. Although enzymatic compartments have been extensively studied experimentally, a quantitative understanding of the underlying design principles is still lacking. Here, we study theoretically how the size and enzymatic composition of compartments should be chosen so as to maximize the productivity of a model metabolic pathway. We find that maximizing productivity requires compartments larger than a certain critical size. The enzyme density within each compartment should be tuned according to a power-law scaling in the compartment size. We explain these observations using an analytically solvable, well-mixed approximation. We also investigate the qualitatively different compartmentalization strategies that emerge in parameter regimes where this approximation breaks down. Our results suggest that the different sizes and enzyme packings of α- and β-carboxysomes each constitute an optimal compartmentalization strategy given the properties of their respective protein shells.

Inference of gene regulation functions from dynamic transcriptome data

To quantify gene regulation, a function is required that relates transcription factor binding to DNA (input) to the rate of mRNA synthesis from a target gene (output). Such a 'gene regulation function' (GRF) generally cannot be measured because the experimental titration of inputs and simultaneous readout of outputs is difficult. Here we show that GRFs may instead be inferred from natural changes in cellular gene expression, as exemplified for the cell cycle in the yeast S. cerevisiae. We develop this inference approach based on a time series of mRNA synthesis rates from a synchronized population of cells observed over three cell cycles. We first estimate the functional form of how input transcription factors determine mRNA output and then derive GRFs for target genes in the clb2 gene cluster that are expressed during G2/M phase. Systematic analysis of additional GRFs suggests a network architecture that rationalizes transcriptional cell cycle oscillations. We find that a transcription factor network alone can produce oscillations in mRNA expression, but that additional input from cyclin oscillations is required to arrive at the native behaviour of the cell cycle oscillator.

The efficiency of driving chemical reactions by a physical non-equilibrium is kinetically controlled

An out-of-equilibrium physical environment can drive chemical reactions into thermodynamically unfavorable regimes. Under prebiotic conditions such a coupling between physical and chemical non-equilibria may have enabled the spontaneous emergence of primitive evolutionary processes. Here, we study the coupling efficiency within a theoretical model that is inspired by recent laboratory experiments, but focuses on generic effects arising whenever reactant and product molecules have different transport coefficients in a flow-through system. In our model, the physical non-equilibrium is represented by a drift–diffusion process, which is a valid coarse-grained description for the interplay between thermophoresis and convection, as well as for many other molecular transport processes. As a simple chemical reaction, we consider a reversible dimerization process, which is coupled to the transport process by different drift velocities for monomers and dimers. Within this minimal model, the coupling efficiency between the non-equilibrium transport process and the chemical reaction can be analyzed in all parameter regimes. The analysis shows that the efficiency depends strongly on the Damköhler number, a parameter that measures the relative timescales associated with the transport and reaction kinetics. Our model and results will be useful for a better understanding of the conditions for which non-equilibrium environments can provide a significant driving force for chemical reactions in a prebiotic setting.

A Dual-Sensing Receptor Confers Robust Cellular Homeostasis

Cells have evolved diverse mechanisms that maintain intracellular homeostasis in fluctuating environments. In bacteria, control is often exerted by bifunctional receptors acting as both kinase and phosphatase to regulate gene expression, a design known to provide robustness against noise. Yet how such antagonistic enzymatic activities are balanced as a function of environmental change remains poorly understood. We find that the bifunctional receptor that regulates K+ uptake in Escherichia coli is a dual sensor, which modulates its autokinase and phosphatase activities in response to both extracellular and intracellular K+ concentration. Using mathematical modeling, we show that dual sensing is a superior strategy for ensuring homeostasis when both the supply of and demand for a limiting resource fluctuate. By engineering standards, this molecular control system displays a strikingly high degree of functional integration, providing a reference for the vast numbers of receptors for which the sensing strategy remains elusive.

Adsorption-Desorption Kinetics of Soft Particles

Adsorption-desorption processes are ubiquitous in physics, chemistry, and biology. Models usually assume hard particles, but within the realm of soft matter physics the adsorbing particles are compressible. A minimal 1D model reveals that softness fundamentally changes the kinetics: Below the desorption time scale, a logarithmic increase of the particle density replaces the usual Rényi jamming plateau, and the subsequent relaxation to equilibrium can be nonmonotonic and much faster than for hard particles. These effects will impact the kinetics of self-assembly and reaction-diffusion processes.

A New Way of Sensing: Need-Based Activation of Antibiotic Resistance by a Flux-Sensing Mechanism

Sensing of and responding to environmental changes are of vital importance for microbial cells. Consequently, bacteria have evolved a plethora of signaling systems that usually sense biochemical cues either via direct ligand binding, thereby acting as “concentration sensors,” or by responding to downstream effects on bacterial physiology, such as structural damage to the cell. Here, we describe a novel, alternative signaling mechanism that effectively implements a “flux sensor” to regulate antibiotic resistance. more...

Replication-guided nucleosome packing and nucleosome breathing expedite the formation of dense arrays

The condensation of eukaryotic chromatin into DNA entails the formation of dense nucleosome arrays. These are frequently disrupted by transcription and replication, such that reassembly is required.  The kinetics of this reassembly is of central interest. We investigate scenarios that enable to reach densely packed arrays within biologially reasonable timescale and find that nucleosome breathing, stepwise nucleosome assembly as well as replication guided processes expedite the array assembly. more...

Optimal arrangements of enzymes

We study how the spatial arrangement and coordination of enzymes determines the efficiency of a multi-step reaction. These spatial arrangements can be natural (as in biomolecular complexes) or engineered with the modern methods of bio-nanotechnology. In both cases, fundamental functional tradeoffs emerge, which must be characterized to understand the optimization of such systems. more...

Escalation of polymerization in a thermal gradient

In cells, long DNA and RNA polymers are formed with the help of sophisticated enzymes. However, it is unclear how these information-carrying polymers could have spontaneously formed in the "premordial soup" without enzymes. Here, we demonstrate a mutual positive feedback between the chemical polymerization reaction and a physical non-equilibrium process. This feedback circle leads to a dramatic enhancement of the probability to generate long molecules from dilute solutions of monomers. more... 

Toward a unified physical model of nucleosome patterns flanking transcription start sites

The genomes of all eukaryotic organisms are highly packaged into a dynamic structure termed chromatin. On the lowest level of packaging, the structure consists of a "beads-on-a-string" arrangement, where nucleosome "particles" are connected by free DNA "linkers". A large body of recent experimental and theoretical work suggests that this structure can be appropriately described, on a coarse-grained physical level, within the theory of 1D interacting gas systems. In this work, we study which properties are required of such an interacting gas model to yield a "unified" description of nucleosome patterns in different species. more... 

Nanopore Translocation Dynamics of Structured Polynucleotides

Nanopore translocation experiments are increasingly applied to probe the secondary structures of RNA and DNA molecules. We report two vital steps toward establishing nanopore translocation as a tool for the systematic an quantitative analysis of polynucleotide folding. more...

Physical limits on cooperative protein-DNA binding and the kinetics of combinatorial transcription regulation

Much of the complexity observed in gene regulation originates from cooperative protein-DNA binding. While studies of the target search of proteins for their specific binding sites on the DNA have revealed design principles for the quantitative characteristics of protein-DNA interactions, no such principles are known for the cooperative interactions between DNA-binding proteins. We consider a simple theoretical model for two interacting transcription factor (TF) species, searching for and binding to two adjacent target sites hidden in the genomic background. more... 

Emergence of information transmission in a prebiotic RNA reactor

A poorly understood step in the transition from a chemical to a biological world is the emergence of self-replicating molecular systems. We study how a precursor for such a replicator might arise in a hydrothermal RNA reactor, which accumulates longer sequences from unbiased monomer influx and random ligation. In the reactor, intra- and intermolecular base pairing locally protects from random cleavage. By analyzing stochastic simulations, we find temporal sequence correlations that constitute a signature of information transmission, weaker but of the same form as in a true replicator. more... 

Quantitative test of statistical positioning

Within the last five years, knowledge about nucleosome organization on the genome has grown dramatically. To a large extent this has been achieved by an increasing number of experimental studies determining nucleosome positions at high resolution over entire genomes. Particular attention has been paid to promoter regions, where a canonical pattern has been established: a nucleosome free region with pronounced adjacent oscillations in the nucleosome density. In our study, we tested to what extent this pattern may be quantitatively described by a minimal physical model, a one-dimensional gas of impenetrable particles, commonly referred to as the “Tonks gas”. more... 

Evolutionary selection of gene regulation mode

Microorganisms employ a wealth of gene regulatory mechanisms to adjust their growth programs to variations in the environment. It was pointed out long ago by Savageau that the particular mode of gene regulation employed may be correlated with the “demand” on the regulated gene, i.e., how frequently the gene product is needed in its natural habitat. An evolutionary “use-it-or-lose-it” principle was proposed to govern the choice of gene regulatory strategies. more... 

Nanopore translocation of structured RNA / DNA

Translocation through nanopores has emerged as a new experimental technique to probe the physical properties of biomolecules. The question of how the typical translocation time for a single unstructured polymer depends on its length has already triggered many theoretical and computational studies. We address this question for structured RNA molecules where the breaking of base-pairing patterns is the main barrier for translocation. more...

Spontaneous Unknotting of a Polymer Confined in a Nanochannel

Chip-based fluidic systems offer enormous prospects for analyzing, sorting, and manipulating complex molecules such as DNA and proteins. To this end, much fundamental research, both experimental and theoretical, is still required. We contribute a theoretical study on an obstacle for these applications: the formation of knots in long polymers, e.g. DNA, upon threading into narrow channels or pores. more... 

Optimal flexibility for conformational transitions in macromolecules

Conformational transitions in macromolecular complexes often involve the reorientation of lever-like structures. Using a simple theoretical model, we show that the rate of such transitions is drastically enhanced if the lever is bendable, e.g. at a localized "hinge". Surprisingly, the transition is fastest with an intermediate flexibility of the hinge. In this intermediate regime, the transition rate is also least sensitive to the amount of "cargo" attached to the lever arm, which could be exploited by molecular motors. To explain this effect, we generalize the Kramers-Langer theory for multi-dimensional barrier crossing to configuration dependent mobility matrices. more... 

Kinetic Accessibility of Buried DNA Sites in Nucleosomes

With help of a light microscope one can see single chromosomes, the closest packed form of DNA. Not only during cell division, but throughout the whole cell cycle, DNA in eucaryotes is packed in one way or another. On the smallest scale, DNA is wrapped around histones and forms nucleosomes. The readout of information - between cell divisions - is controlled by so called transcription factors, which can bind to DNA without ATP consumption. How can that be if DNA is packed? more...