Optimality and cooperativity in superselective surface binding by multivalent DNA nanostars.

Weak multivalent interactions govern a large variety of biological processes like cell-cell adhesion and virus-host interactions. These systems distinguish sharply between surfaces based on receptor density, known as superselectivity. Present experimental studies typically involve tens or hundreds of interactions, resulting in a high entropic contribution leading to high selectivities. However, if, and if so how, systems with few ligands, such as multi-domain proteins and bacteriophages binding to their host, show superselective behavior is an open question. Here, we address this question with a multivalent experimental model system based on star shaped branched DNA nanostructures (DNA nanostars) with each branch featuring a single stranded overhang that binds to complementary receptors on a target surface. Each DNA nanostar possesses a fluorophore, to directly visualize DNA nanostar surface adsorption by total internal reflection fluorescence microscopy (TIRFM). We observe that DNA nanostars can bind superselectively to surfaces and bind optimally at a valency of three, for a given binding strength and concentration. We explain this optimum by extending the current theory with interactions between DNA nanostar binding sites (ligands). Our results add to the understanding of multivalent interactions, by identifying cooperative mechanisms that lead to optimal selectivity, and providing quantitative values for the relevant parameters. These findings inspire additional design rules which improve future work on selective targeting in directed drug delivery.

Quantification of GTPase Cycling Rates of GTPases and GTPase:Effector Mixtures Using GTPase Glo Assays.

In different cellular activities such as signal transduction, cell division, and intracellular transportation, small guanosine triphosphatases (GTPases) take on a vital role. Their function involves hydrolysis of guanosine triphosphate (GTP) to guanosine diphosphate (GDP). In this article, we explain the application of a commercially available GTPase assay-the GTPase Glo assay by Promega-for investigation of GTPase-effector interactions. We provide experimental protocols together with an analysis model and software to obtain GTPase cycling rates of GTPases and GTPase:effector mixtures. GTPase cycling rates refer to the rates by which a GTPase completes an entire GTPase cycle. These rates enable quantification of the strength of GTPase effectors in a concentration-dependent fashion, as well as quantification of the combined effect of two effectors, independent of which GTPase cycle step they are affecting. © 2024 The Authors. Current Protocols published by Wiley Periodicals LLC. Basic Protocol: Conducting GTPase Glo assays Support Protocol 1: Analyzing GTPase assays to correlate luminescence with remaining GTP Support Protocol 2: Fitting GTPase assay data to obtain GTPase cycling rates.

Perspectives on polarity - exploring biological asymmetry across scales.

In this Perspective, Journal of Cell Science invited researchers working on cell and tissue polarity to share their thoughts on unique, emerging or open questions relating to their field. The goal of this article is to feature 'voices' from scientists around the world and at various career stages, to bring attention to innovative and thought-provoking topics of interest to the cell biology community. These voices discuss intriguing questions that consider polarity across scales, evolution, development and disease. What can yeast and protists tell us about the evolution of cell and tissue polarity in animals? How are cell fate and development influenced by emerging dynamics in cell polarity? What can we learn from atypical and extreme polarity systems? How can we arrive at a more unified biophysical understanding of polarity? Taken together, these pieces demonstrate the broad relevance of the fascinating phenomenon of cell polarization to diverse fundamental biological questions.

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.

Pleiotropy drives evolutionary repair of the responsiveness of polarized cell growth to environmental cues.

The ability of cells to translate different extracellular cues into different intracellular responses is vital for their survival in unpredictable environments. In Saccharomyces cerevisiae, cell polarity is modulated in response to environmental signals which allows cells to adopt varying morphologies in different external conditions. The responsiveness of cell polarity to extracellular cues depends on the integration of the molecular network that regulates polarity establishment with networks that signal environmental changes. The coupling of molecular networks often leads to pleiotropic interactions that can make it difficult to determine whether the ability to respond to external signals emerges as an evolutionary response to environmental challenges or as a result of pleiotropic interactions between traits. Here, we study how the propensity of the polarity network of S. cerevisiae to evolve toward a state that is responsive to extracellular cues depends on the complexity of the environment. We show that the deletion of two genes, BEM3 and NRP1, disrupts the ability of the polarity network to respond to cues that signal the onset of the diauxic shift. By combining experimental evolution with whole-genome sequencing, we find that the restoration of the responsiveness to these cues correlates with mutations in genes involved in the sphingolipid synthesis pathway and that these mutations frequently settle in evolving populations irrespective of the complexity of the selective environment. We conclude that pleiotropic interactions make a significant contribution to the evolution of networks that are responsive to extracellular cues.

A tractable physical model for the yeast polarity predicts epistasis and fitness.

Accurate phenotype prediction based on genetic information has numerous societal applications, such as crop design or cellular factories. Epistasis, when biological components interact, complicates modelling phenotypes from genotypes. Here we show an approach to mitigate this complication for polarity establishment in budding yeast, where mechanistic information is abundant. We coarse-grain molecular interactions into a so-called mesotype, which we combine with gene expression noise into a physical cell cycle model. First, we show with computer simulations that the mesotype allows validation of the most current biochemical polarity models by quantitatively matching doubling times. Second, the mesotype elucidates epistasis emergence as exemplified by evaluating the predicted mutational effect of key polarity protein Bem1p when combined with known interactors or under different growth conditions. This example also illustrates how unlikely evolutionary trajectories can become more accessible. The tractability of our biophysically justifiable approach inspires a road-map towards bottom-up modelling complementary to statistical inferences. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.

Towards evolutionary predictions: Current promises and challenges.

Evolution has traditionally been a historical and descriptive science, and predicting future evolutionary processes has long been considered impossible. However, evolutionary predictions are increasingly being developed and used in medicine, agriculture, biotechnology and conservation biology. Evolutionary predictions may be used for different purposes, such as to prepare for the future, to try and change the course of evolution or to determine how well we understand evolutionary processes. Similarly, the exact aspect of the evolved population that we want to predict may also differ. For example, we could try to predict which genotype will dominate, the fitness of the population or the extinction probability of a population. In addition, there are many uses of evolutionary predictions that may not always be recognized as such. The main goal of this review is to increase awareness of methods and data in different research fields by showing the breadth of situations in which evolutionary predictions are made. We describe how diverse evolutionary predictions share a common structure described by the predictive scope, time scale and precision. Then, by using examples ranging from SARS-CoV2 and influenza to CRISPR-based gene drives and sustainable product formation in biotechnology, we discuss the methods for predicting evolution, the factors that affect predictability and how predictions can be used to prevent evolution in undesirable directions or to promote beneficial evolution (i.e. evolutionary control). We hope that this review will stimulate collaboration between fields by establishing a common language for evolutionary predictions.

Complexity and self-organization in the evolution of cell polarization.

Cellular life exhibits order and complexity, which typically increase over the course of evolution. Cell polarization is a well-studied example of an ordering process that breaks the internal symmetry of a cell by establishing a preferential axis. Like many cellular processes, polarization is driven by self-organization, meaning that the macroscopic pattern emerges as a consequence of microscopic molecular interactions at the biophysical level. However, the role of self-organization in the evolution of complex protein networks remains obscure. In this Review, we provide an overview of the evolution of polarization as a self-organizing process, focusing on the model species Saccharomyces cerevisiae and its fungal relatives. Moreover, we use this model system to discuss how self-organization might relate to evolutionary change, offering a shift in perspective on evolution at the microscopic scale.

Evolved interactions stabilize many coexisting phases in multicomponent liquids.

Phase separation has emerged as an essential concept for the spatial organization inside biological cells. However, despite the clear relevance to virtually all physiological functions, we understand surprisingly little about what phases form in a system of many interacting components, like in cells. Here we introduce a numerical method based on physical relaxation dynamics to study the coexisting phases in such systems. We use our approach to optimize interactions between components, similar to how evolution might have optimized the interactions of proteins. These evolved interactions robustly lead to a defined number of phases, despite substantial uncertainties in the initial composition, while random or designed interactions perform much worse. Moreover, the optimized interactions are robust to perturbations, and they allow fast adaption to new target phase counts. We thus show that genetically encoded interactions of proteins provide versatile control of phase behavior. The phases forming in our system are also a concrete example of a robust emergent property that does not rely on fine-tuning the parameters of individual constituents.

Direct visualization of superselective colloid-surface binding mediated by multivalent interactions.

Reliably distinguishing between cells based on minute differences in receptor density is crucial for cell-cell or virus-cell recognition, the initiation of signal transduction, and selective targeting in directed drug delivery. Such sharp differentiation between different surfaces based on their receptor density can only be achieved by multivalent interactions. Several theoretical and experimental works have contributed to our understanding of this "superselectivity." However, a versatile, controlled experimental model system that allows quantitative measurements on the ligand-receptor level is still missing. Here, we present a multivalent model system based on colloidal particles equipped with surface-mobile DNA linkers that can superselectively target a surface functionalized with the complementary mobile DNA-linkers. Using a combined approach of light microscopy and Foerster resonance energy transfer (FRET), we can directly observe the binding and recruitment of the ligand-receptor pairs in the contact area. We find a nonlinear transition in colloid-surface binding probability with increasing ligand or receptor concentration. In addition, we observe an increased sensitivity with weaker ligand-receptor interactions, and we confirm that the timescale of binding reversibility of individual linkers has a strong influence on superselectivity. These unprecedented insights on the ligand-receptor level provide dynamic information into the multivalent interaction between two fluidic membranes mediated by both mobile receptors and ligands and will enable future work on the role of spatial-temporal ligand-receptor dynamics on colloid-surface binding.

The Path towards Predicting Evolution as Illustrated in Yeast Cell Polarity.

A bottom-up route towards predicting evolution relies on a deep understanding of the complex network that proteins form inside cells. In a rapidly expanding panorama of experimental possibilities, the most difficult question is how to conceptually approach the disentangling of such complex networks. These can exhibit varying degrees of hierarchy and modularity, which obfuscate certain protein functions that may prove pivotal for adaptation. Using the well-established polarity network in budding yeast as a case study, we first organize current literature to highlight protein entrenchments inside polarity. Following three examples, we see how alternating between experimental novelties and subsequent emerging design strategies can construct a layered understanding, potent enough to reveal evolutionary targets. We show that if you want to understand a cell's evolutionary capacity, such as possible future evolutionary paths, seemingly unimportant proteins need to be mapped and studied. Finally, we generalize this research structure to be applicable to other systems of interest.

Predicting Evolution Using Regulatory Architecture.

The limits of evolution have long fascinated biologists. However, the causes of evolutionary constraint have remained elusive due to a poor mechanistic understanding of studied phenotypes. Recently, a range of innovative approaches have leveraged mechanistic information on regulatory networks and cellular biology. These methods combine systems biology models with population and single-cell quantification and with new genetic tools, and they have been applied to a range of complex cellular functions and engineered networks. In this article, we review these developments, which are revealing the mechanistic causes of epistasis at different levels of biological organization-in molecular recognition, within a single regulatory network, and between different networks-providing first indications of predictable features of evolutionary constraint.

Minimal in vitro systems shed light on cell polarity.

Cell polarity - the morphological and functional differentiation of cellular compartments in a directional manner - is required for processes such as orientation of cell division, directed cellular growth and motility. How the interplay of components within the complexity of a cell leads to cell polarity is still heavily debated. In this Review, we focus on one specific aspect of cell polarity: the non-uniform accumulation of proteins on the cell membrane. In cells, this is achieved through reaction-diffusion and/or cytoskeleton-based mechanisms. In reaction-diffusion systems, components are transformed into each other by chemical reactions and are moving through space by diffusion. In cytoskeleton-based processes, cellular components (i.e. proteins) are actively transported by microtubules (MTs) and actin filaments to specific locations in the cell. We examine how minimal systems - in vitro reconstitutions of a particular cellular function with a minimal number of components - are designed, how they contribute to our understanding of cell polarity (i.e. protein accumulation), and how they complement in vivo investigations. We start by discussing the Min protein system from Escherichia coli, which represents a reaction-diffusion system with a well-established minimal system. This is followed by a discussion of MT-based directed transport for cell polarity markers as an example of a cytoskeleton-based mechanism. To conclude, we discuss, as an example, the interplay of reaction-diffusion and cytoskeleton-based mechanisms during polarity establishment in budding yeast.

Spindle Dynamics Model Explains Chromosome Loss Rates in Yeast Polyploid Cells.

Faithful chromosome segregation, driven by the mitotic spindle, is essential for organismal survival. Neopolyploid cells from diverse species exhibit a significant increase in mitotic errors relative to their diploid progenitors, resulting in chromosome nondisjunction. In the model system Saccharomyces cerevisiae, the rate of chromosome loss in haploid and diploid cells is measured to be one thousand times lower than the rate of loss in isogenic tetraploid cells. Currently it is unknown what constrains the number of chromosomes that can be segregated with high fidelity in an organism. Here we developed a simple mathematical model to study how different rates of chromosome loss in cells with different ploidy can arise from changes in (1) spindle dynamics and (2) a maximum duration of mitotic arrest, after which cells enter anaphase. We apply this model to S. cerevisiae to show that this model can explain the observed rates of chromosome loss in S. cerevisiae cells of different ploidy. Our model describes how small increases in spindle assembly time can result in dramatic differences in the rate of chromosomes loss between cells of increasing ploidy and predicts the maximum duration of mitotic arrest.

Global DNA Compaction in Stationary-Phase Bacteria Does Not Affect Transcription.

In stationary-phase Escherichia coli, Dps (DNA-binding protein from starved cells) is the most abundant protein component of the nucleoid. Dps compacts DNA into a dense complex and protects it from damage. Dps has also been proposed to act as a global regulator of transcription. Here, we directly examine the impact of Dps-induced compaction of DNA on the activity of RNA polymerase (RNAP). Strikingly, deleting the dps gene decompacted the nucleoid but did not significantly alter the transcriptome and only mildly altered the proteome during stationary phase. Complementary in vitro assays demonstrated that Dps blocks restriction endonucleases but not RNAP from binding DNA. Single-molecule assays demonstrated that Dps dynamically condenses DNA around elongating RNAP without impeding its progress. We conclude that Dps forms a dynamic structure that excludes some DNA-binding proteins yet allows RNAP free access to the buried genes, a behavior characteristic of phase-separated organelles.

Patterns of Conservation and Diversification in the Fungal Polarization Network.

The combined actions of proteins in networks underlie all fundamental cellular functions. Deeper insights into the dynamics of network composition across species and their functional consequences are crucial to fully understand protein network evolution. Large-scale comparative studies with high phylogenetic resolution are now feasible through the recent rise in available genomic data sets of both model and nonmodel species. Here, we focus on the polarity network, which is universally essential for cell proliferation and studied in great detail in the model organism, Saccharomyces cerevisiae. We examine 42 proteins, directly related to cell polarization, across 298 fungal strains/species to determine the composition of the network and patterns of conservation and diversification. We observe strong protein conservation for a group of 23 core proteins: >95% of all examined strains/species possess at least 14 of these core proteins, albeit in varying compositions, and non of the individual core proteins is 100% conserved. We find high levels of variation in prevalence and sequence identity in the remaining 19 proteins, resulting in distinct lineage-specific compositions of the network in the majority of strains/species. We show that the observed diversification in network composition correlates with lineage, lifestyle, and genetic distance. Yeast, filamentous and basal unicellular fungi, form distinctive groups based on these analyses, with substantial differences to their polarization network. Our study shows that the fungal polarization network is highly dynamic, even between closely related species, and that functional conservation appears to be achieved by varying the specific components of the fungal polarization repertoire.

Evolutionary dynamics in the fungal polarization network, a mechanistic perspective.

Polarity establishment underlies proper cell cycle completion across virtually all organisms. Much progress has been made in generating an understanding of the structural and functional components of this process, especially in model species. Here we focus on the evolutionary dynamics of the fungal polarization protein network in order to determine general components and mechanistic principles, species- or lineage-specific adaptations and the evolvability of the network. The currently available genomic and proteomic screens in a variety of fungal species have shown three main characteristics: (1) certain proteins, processes and functions are conserved throughout the fungal clade; (2) orthologous functions can never be assumed, as various cases have been observed of homologous loci with dissimilar functions; (3) species have, typically, various species- or lineage-specific proteins incorporated in their polarization network. Further large-scale comparative and experimental studies, including those on non-model species representing the great fungal diversity, are needed to gain a better understanding of the evolutionary dynamics and generalities of the polarization network in fungi.

Optical Tweezers-Based Measurements of Forces and Dynamics at Microtubule Ends.

Microtubules are dynamic cytoskeletal polymers that polymerize and depolymerize while interacting with different proteins and structures within the cell. The highly regulated dynamic properties as well as the pushing and pulling forces generated by dynamic microtubule ends play important roles in processes such as in cell division. For instance, microtubule end-binding proteins are known to affect dramatically the dynamic properties of microtubules, and cortical dyneins are known to mediate pulling forces on microtubule ends. We discuss in this chapter our efforts to reconstitute these systems in vitro and mimic their interactions with structures within the cell using micro-fabricated barriers. Using an optical tweezers setup, we investigate the dynamics and forces of microtubules growing against functionalized barriers in the absence and presence of end-binding proteins and barrier-attached motor proteins. This setup allows high-speed as well as nanometer and piconewton resolution measurements on dynamic microtubules.

Physical and Mathematical Modeling in Experimental Papers.

An increasing number of publications include modeling. Often, such studies help us to gain a deeper insight into the phenomena studied and break down barriers between experimental and theoretical communities. However, combining experimental and theoretical work is challenging for authors, reviewers, and readers. To help maximize the usefulness and impact of combined theoretical and experimental research, this Primer describes the purpose, usefulness, and different types of models and addresses the practical aspect of integrated publications by outlining characteristics of good modeling, presentation, and fruitful collaborations.