Stationary Patterns in a Two-Protein Reaction-Diffusion System

Machine learning-aided design and screening of an emergent protein function in synthetic cells

Recently, utilization of Machine Learning (ML) has led to astonishing progress in computational protein design, bringing into reach the targeted engineering of proteins for industrial and biomedical applications. However, the design of proteins for emergent functions of core relevance to cells, such as the ability to spatiotemporally self-organize and thereby structure the cellular space, is still extremely challenging. While on the generative side conditional generative models and multi-state design are on the rise, for emergent functions there is a lack of tailored screening methods as typically needed in a protein design project, both computational and experimental. Here we describe a proof-of-principle of how such screening, in silico and in vitro, can be achieved for ML-generated variants of a protein that forms intracellular spatiotemporal patterns. For computational screening we use a structure-based divide-and-conquer approach to find the most promising candidates, while for the subsequent in vitro screening we use synthetic cell-mimics as established by Bottom-Up Synthetic Biology. We then show that the best screened candidate can indeed completely substitute the wildtype gene in Escherichia coli. These results raise great hopes for the next level of synthetic biology, where ML-designed synthetic proteins will be used to engineer cellular functions.

A programmable reaction-diffusion system for spatiotemporal cell signaling circuit design

Cells self-organize molecules in space and time to generate complex behaviors, but we lack synthetic strategies for engineering spatiotemporal signaling. We present a programmable reaction-diffusion platform for designing protein oscillations, patterns, and circuits in mammalian cells using two bacterial proteins, MinD and MinE (MinDE). MinDE circuits act like "single-cell radios," emitting frequency-barcoded fluorescence signals that can be spectrally isolated and analyzed using digital signal processing tools. We define how to genetically program these signals and connect their spatiotemporal dynamics to cell biology using engineerable protein-protein interactions. This enabled us to construct sensitive reporter circuits that broadcast endogenous cell signaling dynamics on a frequency-barcoded imaging channel and to build control signal circuits that synthetically pattern activities in the cell, such as protein condensate assembly and actin filamentation. Our work establishes a paradigm for visualizing, probing, and engineering cellular activities at length and timescales critical for biological function.

Protein-Assisted Large-Scale Assembly and Differential Patterning of DNA Origami Lattices

Nanofabrication has experienced a big boost with the invention of DNA origami, enabling the production and assembly of complex nanoscale structures that may be able to unlock fully new functionalities in biology and beyond. The remarkable precision with which these structures can be designed and produced is, however, not yet matched by their assembly dynamics, which can be extremely slow, particularly when attached to biological templates, such as membranes. Here, the rapid and controlled formation of DNA origami lattices on the scale of hundreds of micrometers in as little as 30 minutes is demonstrated, utilizing active patterning by the E.coli Min protein system, thereby yielding a remarkable improvement over conventional passive diffusion-based assembly methods. Various patterns, including spots, inverse spots, mazes, and meshes can be produced at different scales, tailored through the shape and density of the assembled structures. The differential positioning accomplished by Min-induced diffusiophoresis even allows the introduction of "pseudo-colors", i.e., complex core-shell patterns, by simultaneously patterning different DNA origami species. Beyond the targeted functionalization of biological surfaces, this approach may also be promising for applications in plasmonics, catalysis, and molecular sensing.

Insights into the assembly and regulation of the bacterial divisome

The ability to split one cell into two is fundamental to all life, and many bacteria can accomplish this feat several times per hour with high accuracy. Most bacteria call on an ancient homologue of tubulin, called FtsZ, to localize and organize the cell division machinery, the divisome, into a ring-like structure at the cell midpoint. The divisome includes numerous other proteins, often including an actin homologue (FtsA), that interact with each other at the cytoplasmic membrane. Once assembled, the protein complexes that comprise the dynamic divisome coordinate membrane constriction with synthesis of a division septum, but only after overcoming checkpoints mediated by specialized protein-protein interactions. In this Review, we summarize the most recent evidence showing how the divisome proteins of Escherichia coli assemble at the cell midpoint, interact with each other and regulate activation of septum synthesis. We also briefly discuss the potential of divisome proteins as novel antibiotic targets.

Forceful patterning: theoretical principles of mechanochemical pattern formation

Biological pattern formation is essential for generating and maintaining spatial structures from the scale of a single cell to tissues and even collections of organisms. Besides biochemical interactions, there is an important role for mechanical and geometrical features in the generation of patterns. We review the theoretical principles underlying different types of mechanochemical pattern formation across spatial scales and levels of biological organization.

Coarsening and wavelength selection far from equilibrium: A unifying framework based on singular perturbation theory

Intracellular protein patterns are described by (nearly) mass-conserving reaction-diffusion systems. While these patterns initially form out of a homogeneous steady state due to the well-understood Turing instability, no general theory exists for the dynamics of fully nonlinear patterns. We develop a unifying theory for nonlinear wavelength-selection dynamics in (nearly) mass-conserving two-component reaction-diffusion systems independent of the specific mathematical model chosen. Previous work has shown that these systems support an extremely broad band of stable wavelengths, but the mechanism by which a specific wavelength is selected has remained unclear. We show that an interrupted coarsening process selects the wavelength at the threshold to stability. Based on the physical intuition that coarsening is driven by competition for mass and interrupted by weak source terms that break strict mass conservation, we develop a singular perturbation theory for the stability of stationary patterns. The resulting closed-form analytical expressions enable us to quantitatively predict the coarsening dynamics and the final pattern wavelength. We find excellent agreement with numerical results throughout the diffusion- and reaction-limited regimes of the dynamics, including the crossover region. Further, we show how, in these limits, the two-component reaction-diffusion systems map to generalized Cahn-Hilliard and conserved Allen-Cahn dynamics, therefore providing a link to these two fundamental scalar field theories. The systematic understanding of the length-scale dynamics of fully nonlinear patterns in two-component systems provided here builds the basis to reveal the mechanisms underlying wavelength selection in multicomponent systems with potentially several conservation laws.

Protein-Based Patterning to Spatially Functionalize Biomimetic Membranes

The bottom-up reconstitution of proteins for their modular engineering into synthetic cellular systems can reveal hidden protein functions in vitro. This is particularly evident for the bacterial Min proteins, a paradigm for self-organizing reaction-diffusion systems that displays an unexpected functionality of potential interest for bioengineering: the directional active transport of any diffusible cargo molecule on membranes. Here, the MinDE protein system is reported as a versatile surface patterning tool for the rational design of synthetically assembled 3D systems. Employing two-photon lithography, microswimmer-like structures coated with tailored lipid bilayers are fabricated and demonstrate that Min proteins can uniformly pattern bioactive molecules on their surface. Moreover, it is shown that the MinDE system can form stationary patterns inside lipid vesicles, which allow the targeting and distinctive clustering of higher-order protein structures on their inner leaflet. Given their facile use and robust function, Min proteins thus constitute a valuable molecular toolkit for spatially patterned functionalization of artificial biosystems like cell mimics and microcarriers.

The mechanism of MinD stability modulation by MinE in Min protein dynamics

The patterns formed both in vivo and in vitro by the Min protein system have attracted much interest because of the complexity of their dynamic interactions given the apparent simplicity of the component parts. Despite both the experimental and theoretical attention paid to this system, the details of the biochemical interactions of MinD and MinE, the proteins responsible for the patterning, are still unclear. For example, no model consistent with the known biochemistry has yet accounted for the observed dual role of MinE in the membrane stability of MinD. Until now, a statistical comparison of models to the time course of Min protein concentrations on the membrane has not been carried out. Such an approach is a powerful way to test existing and novel models that are difficult to test using a purely experimental approach. Here, we extract time series from previously published fluorescence microscopy time lapse images of in vitro experiments and fit two previously described and one novel mathematical model to the data. We find that the novel model, which we call the Asymmetric Activation with Bridged Stability Model, fits the time-course data best. It is also consistent with known biochemistry and explains the dual MinE role via MinE-dependent membrane stability that transitions under the influence of rising MinE to membrane instability with positive feedback. Our results reveal a more complex network of interactions between MinD and MinE underlying Min-system dynamics than previously considered.

Redundancy and the role of protein copy numbers in the cell polarization machinery of budding yeast

How can a self-organized cellular function evolve, adapt to perturbations, and acquire new sub-functions? To make progress in answering these basic questions of evolutionary cell biology, we analyze, as a concrete example, the cell polarity machinery of Saccharomyces cerevisiae. This cellular module exhibits an intriguing resilience: it remains operational under genetic perturbations and recovers quickly and reproducibly from the deletion of one of its key components. Using a combination of modeling, conceptual theory, and experiments, we propose that multiple, redundant self-organization mechanisms coexist within the protein network underlying cell polarization and are responsible for the module's resilience and adaptability. Based on our mechanistic understanding of polarity establishment, we hypothesize that scaffold proteins, by introducing new connections in the existing network, can increase the redundancy of mechanisms and thus increase the evolvability of other network components. Moreover, our work gives a perspective on how a complex, redundant cellular module might have evolved from a more rudimental ancestral form.

Phase separation on surfaces in the presence of matter exchange

We present a field theory to describe the composition of a surface spontaneously exchanging matter with its bulk environment. By only assuming matter conservation in the system, we show with extensive numerical simulations that, depending on the matter exchange rates, a complex patterned composition distribution emerges on the surface. For one-dimensional systems we show analytically and numerically that coarsening is arrested and as a consequence domains have a characteristic length scale. Our results show that the causes of heterogeneous lipid composition in cellular membranes may be justified in simple physical terms.

Reconstitution of a Reversible Membrane Switch via Prenylation by One-Pot Cell-Free Expression

Reversible membrane targeting of proteins is one of the key regulators of cellular interaction networks, for example, for signaling and polarization. So-called "membrane switches" are thus highly attractive targets for the design of minimal cells but have so far been tricky to reconstitute in vitro. Here, we introduce cell-free prenylated protein synthesis (CFpPS), which enables the synthesis and membrane targeting of proteins in a single reaction mix including the prenylation machinery. CFpPS can confer membrane affinity to any protein via addition of a 4-peptide motif to its C-terminus and offers robust production of prenylated proteins not only in their soluble forms but also in the direct vicinity of biomimetic membranes. Thus, CFpPS enabled us to reconstitute the prenylated polarity hub Cdc42 and its regulatory protein in vitro, implementing a key membrane switch. We propose CFpPS to be a versatile and effective platform for engineering complex features, such as polarity induction, in synthetic cells.

Bridging scales in a multiscale pattern-forming system

Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological processes inherently involve multiple spatial and temporal scales and transition from one pattern to another over time, rather than progressing from homogeneity to a pattern. To deal with such multiscale systems, coarse-graining methods are needed that allow the dynamics to be reduced to the relevant degrees of freedom at large scales, but without losing information about the patterns at small scales. Here, we present a semiphenomenological approach which exploits mass conservation in pattern formation, and enables reconstruction of information about patterns from the large-scale dynamics. The basic idea is to partition the domain into distinct regions (coarse grain) and determine instantaneous dispersion relations in each region, which ultimately inform about local pattern-forming instabilities. We illustrate our approach by studying the Min system, a paradigmatic model for protein pattern formation. By performing simulations, we first show that the Min system produces multiscale patterns in a spatially heterogeneous geometry. This prediction is confirmed experimentally by in vitro reconstitution of the Min system. Using a recently developed theoretical framework for mass-conserving reaction-diffusion systems, we show that the spatiotemporal evolution of the total protein densities on large scales reliably predicts the pattern-forming dynamics. Our approach provides an alternative and versatile theoretical framework for complex systems where analytical coarse-graining methods are not applicable, and can, in principle, be applied to a wide range of systems with an underlying conservation law.

Mode selection mechanism in traveling and standing waves revealed by Min wave reconstituted in artificial cells

Reaction-diffusion coupling (RDc) generates spatiotemporal patterns, including two dynamic wave modes: traveling and standing waves. Although mode selection plays a substantial role in the spatiotemporal organization of living cell molecules, the mechanism for selecting each wave mode remains elusive. Here, we investigated a wave mode selection mechanism using Min waves reconstituted in artificial cells, emerged by the RDc of MinD and MinE. Our experiments and theoretical analysis revealed that the balance of membrane binding and dissociation from the membrane of MinD determines the mode selection of the Min wave. We successfully demonstrated that the transition of the wave modes can be regulated by controlling this balance and found hysteresis characteristics in the wave mode transition. These findings highlight a previously unidentified role of the balance between activators and inhibitors as a determinant of the mode selection of waves by RDc and depict an unexplored mechanism in intracellular spatiotemporal pattern formations.

Building a community to engineer synthetic cells and organelles from the bottom-up

Employing concepts from physics, chemistry and bioengineering, 'learning-by-building' approaches are becoming increasingly popular in the life sciences, especially with researchers who are attempting to engineer cellular life from scratch. The SynCell2020/21 conference brought together researchers from different disciplines to highlight progress in this field, including areas where synthetic cells are having socioeconomic and technological impact. Conference participants also identified the challenges involved in designing, manipulating and creating synthetic cells with hierarchical organization and function. A key conclusion is the need to build an international and interdisciplinary research community through enhanced communication, resource-sharing, and educational initiatives.

Systems of pattern formation within developmental biology

Applications of mathematical models to developmental biology have provided helpful insight into various subfields, ranging from the patterning of animal skin to the development of complex organ systems. Systems involved in patterning within morphology present a unique path to explain self-organizing systems. Current efforts show that patterning systems, notably Reaction-Diffusion and specific signaling pathways, provide insight for explaining morphology and could provide novel applications revolving around the formation of biological systems. Furthermore, the application of pattern formation provides a new perspective on understanding developmental biology and pathology research to study molecular mechanisms. The current review is to cover and take a more in-depth overlook at current applications of patterning systems while also building on the principles of patterning of future research in predictive medicine.

Self-organized protein patterns: The MinCDE and ParABS systems

Self-organized protein patterns are of tremendous importance for biological decision-making processes. Protein patterns have been shown to identify the site of future cell division, establish cell polarity, and organize faithful DNA segregation. Intriguingly, several key concepts of pattern formation and regulation apply to a variety of different protein systems. Herein, we explore recent advances in the understanding of two prokaryotic pattern-forming systems: the MinCDE system, positioning the FtsZ ring precisely at the midcell, and the ParABS system, distributing newly synthesized DNA along with the cell. Despite differences in biological functionality, these two systems have remarkably similar molecular components, mechanisms, and strategies to achieve biological robustness.

Membrane-coated 3D architectures for bottom-up synthetic biology

One of the great challenges of bottom-up synthetic biology is to recreate the cellular geometry and surface functionality required for biological reactions. Of particular interest are lipid membrane interfaces where many protein functions take place. However, cellular 3D geometries are often complex, and custom-shaping stable lipid membranes on relevant spatial scales in the micrometer range has been hard to accomplish reproducibly. Here, we use two-photon direct laser writing to 3D print microenvironments with length scales relevant to cellular processes and reactions. We formed lipid bilayers on the surfaces of these printed structures, and we evaluated multiple combinatorial scenarios, where physiologically relevant membrane compositions were generated on several different polymer surfaces. Functional dynamic protein systems were reconstituted in vitro and their self-organization was observed in response to the 3D geometry. This method proves very useful to template biological membranes with an additional spatial dimension, and thus allows a better understanding of protein function in relation to the complex morphology of cells and organelles.

Bulk-surface coupling identifies the mechanistic connection between Min-protein patterns in vivo and in vitro

Self-organisation of Min proteins is responsible for the spatial control of cell division in Escherichia coli, and has been studied both in vivo and in vitro. Intriguingly, the protein patterns observed in these settings differ qualitatively and quantitatively. This puzzling dichotomy has not been resolved to date. Using reconstituted proteins in laterally wide microchambers with a well-controlled height, we experimentally show that the Min protein dynamics on the membrane crucially depend on the micro chamber height due to bulk concentration gradients orthogonal to the membrane. A theoretical analysis shows that in vitro patterns at low microchamber height are driven by the same lateral oscillation mode as pole-to-pole oscillations in vivo. At larger microchamber height, additional vertical oscillation modes set in, marking the transition to a qualitatively different in vitro regime. Our work reveals the qualitatively different mechanisms of mass transport that govern Min protein-patterns for different bulk heights and thus shows that Min patterns in cells are governed by a different mechanism than those in vitro.

Increasing MinD's Membrane Affinity Yields Standing Wave Oscillations and Functional Gradients on Flat Membranes

The formation of large-scale patterns through molecular self-organization is a basic principle of life. Accordingly, the engineering of protein patterns and gradients is of prime relevance for synthetic biology. As a paradigm for such pattern formation, the bacterial MinDE protein system is based on self-organization of the ATPase MinD and ATPase-activating protein MinE on lipid membranes. Min patterns can be tightly regulated by tuning physical or biochemical parameters. Among the biochemically engineerable modules, MinD's membrane targeting sequence, despite being a key regulating element, has received little attention. Here we attempt to engineer patterns by modulating the membrane affinity of MinD. Unlike the traveling waves or stationary patterns commonly observed in vitro on flat supported membranes, standing-wave oscillations emerge upon elongating MinD's membrane targeting sequence via rationally guided mutagenesis. These patterns are capable of forming gradients and thereby spatially target co-reconstituted downstream proteins, highlighting their functional potential in designing new life-like systems.

Flow Induced Symmetry Breaking in a Conceptual Polarity Model

Important cellular processes, such as cell motility and cell division, are coordinated by cell polarity, which is determined by the non-uniform distribution of certain proteins. Such protein patterns form via an interplay of protein reactions and protein transport. Since Turing’s seminal work, the formation of protein patterns resulting from the interplay between reactions and diffusive transport has been widely studied. Over the last few years, increasing evidence shows that also advective transport, resulting from cytosolic and cortical flows, is present in many cells. However, it remains unclear how and whether these flows contribute to protein-pattern formation. To address this question, we use a minimal model that conserves the total protein mass to characterize the effects of cytosolic flow on pattern formation. Combining a linear stability analysis with numerical simulations, we find that membrane-bound protein patterns propagate against the direction of cytoplasmic flow with a speed that is maximal for intermediate flow speed. We show that the mechanism underlying this pattern propagation relies on a higher protein influx on the upstream side of the pattern compared to the downstream side. Furthermore, we find that cytosolic flow can change the membrane pattern qualitatively from a peak pattern to a mesa pattern. Finally, our study shows that a non-uniform flow profile can induce pattern formation by triggering a regional lateral instability.

Local Self-Enhancement of MinD Membrane Binding in Min Protein Pattern Formation

The proteins MinD, MinE and MinC are constitutive for the spatiotemporal organization of cell division in Escherichia coli, in particular, for positioning the division machinery at mid-cell. To achieve this function, the ATPase MinD and the ATPase-activating protein MinE undergo coordinated pole-to-pole oscillations and have thus become a paradigm for protein pattern formation in biology. The exact molecular mechanisms enabling MinDE self-organization, and particularly the role of cooperativity in the membrane binding of MinD, thought to be a key requirement, have remained poorly understood. However, for bottom-up synthetic biology aiming at a de novo design of key cellular features, elucidating these mechanisms is of great relevance. By combining in vitro reconstitution with rationally guided mutagenesis of MinD, we found that when bound to membranes, MinD displays new interfaces for multimerization, which are distinct from the canonical MinD dimerization site. We propose that these additional transient interactions contribute to the local self-enhancement of MinD at the membrane, while their relative lability maintains the structural plasticity required for MinDE wave propagation. This could represent a powerful structural regulation feature not reported so far for self-organizing proteins.

Design of biochemical pattern forming systems from minimal motifs

Although molecular self-organization and pattern formation are key features of life, only very few pattern-forming biochemical systems have been identified that can be reconstituted and studied in vitro under defined conditions. A systematic understanding of the underlying mechanisms is often hampered by multiple interactions, conformational flexibility and other complex features of the pattern forming proteins. Because of its compositional simplicity of only two proteins and a membrane, the MinDE system from Escherichia coli has in the past years been invaluable for deciphering the mechanisms of spatiotemporal self-organization in cells. Here, we explored the potential of reducing the complexity of this system even further, by identifying key functional motifs in the effector MinE that could be used to design pattern formation from scratch. In a combined approach of experiment and quantitative modeling, we show that starting from a minimal MinE-MinD interaction motif, pattern formation can be obtained by adding either dimerization or membrane-binding motifs. Moreover, we show that the pathways underlying pattern formation are recruitment-driven cytosolic cycling of MinE and recombination of membrane-bound MinE, and that these differ in their in vivo phenomenology.

A non-linear analysis of Turing pattern formation

Reaction-diffusion schemes are widely used to model and interpret phenomena in various fields. In that context, phenomena driven by Turing instabilities are particularly relevant to describe patterning in a number of biological processes. While the conditions that determine the appearance of Turing patterns and their wavelength can be easily obtained by a linear stability analysis, the estimation of pattern amplitudes requires cumbersome calculations due to non-linear terms. Here we introduce an expansion method that makes possible to obtain analytical, approximated, solutions of the pattern amplitudes. We check and illustrate the reliability of this methodology with results obtained from numerical simulations.

The E. coli MinCDE system in the regulation of protein patterns and gradients

Molecular self-organziation, also regarded as pattern formation, is crucial for the correct distribution of cellular content. The processes leading to spatiotemporal patterns often involve a multitude of molecules interacting in complex networks, so that only very few cellular pattern-forming systems can be regarded as well understood. Due to its compositional simplicity, the Escherichia coli MinCDE system has, thus, become a paradigm for protein pattern formation. This biological reaction diffusion system spatiotemporally positions the division machinery in E. coli and is closely related to ParA-type ATPases involved in most aspects of spatiotemporal organization in bacteria. The ATPase MinD and the ATPase-activating protein MinE self-organize on the membrane as a reaction matrix. In vivo, these two proteins typically oscillate from pole-to-pole, while in vitro they can form a variety of distinct patterns. MinC is a passenger protein supposedly operating as a downstream cue of the system, coupling it to the division machinery. The MinCDE system has helped to extract not only the principles underlying intracellular patterns, but also how they are shaped by cellular boundaries. Moreover, it serves as a model to investigate how patterns can confer information through specific and non-specific interactions with other molecules. Here, we review how the three Min proteins self-organize to form patterns, their response to geometric boundaries, and how these patterns can in turn induce patterns of other molecules, focusing primarily on experimental approaches and developments.

Temperature-sensitive protein expression in protocells

We engineered a synthetic temperature regulation toolbox to enable protocells to sense and respond to heat, utilizing RNA thermometers. The thermo-sensitive protocells were generated by encapsulating temperature feedback transcription/translation machinery in droplets. Based on these temperature-sensing devices, the protocells can be operated with logic AND gates, differentially processing temperature stimuli into biological signals.