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A crowd density forecasting task aims to predict how the crowd density map will change in the future from observed past crowd density maps. However, the past crowd density maps are often incomplete due to the miss-detection of pedestrians, and it is crucial to develop a robust crowd density forecasting model against the miss-detection. This paper presents a MAsked crowd density Completion framework for crowd density forecasting (CrowdMAC), which is simultaneously trained to forecast future crowd density maps from partially masked past crowd density maps (i.e., forecasting maps from past maps with miss-detection) while reconstructing the masked observation maps (i.e., imputing past maps with miss-detection). Additionally, we propose Temporal-Density-aware Masking (TDM), which non-uniformly masks tokens in the observed crowd density map, considering the sparsity of the crowd density maps and the informativeness of the subsequent frames for the forecasting task. Moreover, we introduce multi-task masking to enhance training efficiency. In the experiments, CrowdMAC achieves state-of-the-art performance on seven large-scale datasets, including SDD, ETH-UCY, inD, JRDB, VSCrowd, FDST, and

Occlusion is one of the fundamental challenges in crowd counting. In the community, various data-driven approaches have been developed to address this issue, yet their effectiveness is limited. This is mainly because most existing crowd counting datasets on which the methods are trained are based on passive cameras, restricting their ability to fully sense the environment. Recently, embodied navigation methods have shown significant potential in precise object detection in interactive scenes. These methods incorporate active camera settings, holding promise in addressing the fundamental issues in crowd counting. However, most existing methods are designed for indoor navigation, showing unknown performance in analyzing complex object distribution in large scale scenes, such as crowds. Besides, most existing embodied navigation datasets are indoor scenes with limited scale and object quantity, preventing them from being introduced into dense crowd analysis. Based on this, a novel task, Embodied Crowd Counting (ECC), is proposed. We first build up an interactive simulator, Embodied Crowd Counting Dataset (ECCD), which enables large scale scenes and large object quantity. A prior proba

We show how the quality of decisions based on the aggregated opinions of the crowd can be conveniently studied using a sample of individual responses to a standard IQ questionnaire. We aggregated the responses to the IQ questionnaire using simple majority voting and a machine learning approach based on a probabilistic graphical model. The score for the aggregated questionnaire, Crowd IQ, serves as a quality measure of decisions based on aggregating opinions, which also allows quantifying individual and crowd performance on the same scale. We show that Crowd IQ grows quickly with the size of the crowd but saturates, and that for small homogeneous crowds the Crowd IQ significantly exceeds the IQ of even their most intelligent member. We investigate alternative ways of aggregating the responses and the impact of the aggregation method on the resulting Crowd IQ. We also discuss Contextual IQ, a method of quantifying the individual participant's contribution to the Crowd IQ based on the Shapley value from cooperative game theory.

Modeling and reproducing crowd behaviors are important in various domains including psychology, robotics, transport engineering and virtual environments. Conventional methods have focused on synthesizing momentary scenes, which have difficulty in replicating the continuous nature of real-world crowds. In this paper, we introduce a novel method for automatically generating continuous, realistic crowd trajectories with heterogeneous behaviors and interactions among individuals. We first design a crowd emitter model. To do this, we obtain spatial layouts from single input images, including a segmentation map, appearance map, population density map and population probability, prior to crowd generation. The emitter then continually places individuals on the timeline by assigning independent behavior characteristics such as agents' type, pace, and start/end positions using diffusion models. Next, our crowd simulator produces their long-term locomotions. To simulate diverse actions, it can augment their behaviors based on a Markov chain. As a result, our overall framework populates the scenes with heterogeneous crowd behaviors by alternating between the proposed emitter and simulator. Not

Traditionally, the term crowd was used almost exclusively in the context of people who self-organized around a common purpose, emotion or experience. Today, however, firms often refer to crowds in discussions of how collections of individuals can be engaged for organizational purposes. Crowdsourcing, the use of information technologies to outsource business responsibilities to crowds, can now significantly influence a firms ability to leverage previously unattainable resources to build competitive advantage. Nonetheless, many managers are hesitant to consider crowdsourcing because they do not understand how its various types can add value to the firm. In response, we explain what crowdsourcing is, the advantages it offers and how firms can pursue crowdsourcing. We begin by formulating a crowdsourcing typology and show how its four categories (crowd-voting, micro-task, idea and solution crowdsourcing) can help firms develop crowd capital, an organizational-level resource harnessed from the crowd. We then present a three-step process model for generating crowd capital. Step one includes important considerations that shape how a crowd is to be constructed. Step two outlines the capabi

This study enhances a crowd density estimation algorithm originally designed for image-based analysis by adapting it for video-based scenarios. The proposed method integrates a denoising probabilistic model that utilizes diffusion processes to generate high-quality crowd density maps. To improve accuracy, narrow Gaussian kernels are employed, and multiple density map outputs are generated. A regression branch is incorporated into the model for precise feature extraction, while a consolidation mechanism combines these maps based on similarity scores to produce a robust final result. An event-driven sampling technique, utilizing the Farneback optical flow algorithm, is introduced to selectively capture frames showing significant crowd movements, reducing computational load and storage by focusing on critical crowd dynamics. Through qualitative and quantitative evaluations, including overlay plots and Mean Absolute Error (MAE), the model demonstrates its ability to effectively capture crowd dynamics in both dense and sparse settings. The efficiency of the sampling method is further assessed, showcasing its capability to decrease frame counts while maintaining essential crowd events. B

Part 1 The crowd: the fear of being touched the open and closed crowd the discharge destructiveness the eruption persecution domestication of crowds in the world religions panic the crowd as a ring the attributes of the crowd rhythm stagnation slowness, or the remoteness of the goal invisible crowds classification of crowds according to their prevailing emotion baiting crowds flight crowds prohibition crowds reversal crowds feast crowds the double crowd - men and women, the living and the dead the double crowd - war crowd crystals crowd symbols - fire, the sea, rain, rivers, forest, corn, wind, sand, the heap, stone heaps, treasure. Part 2 The pack: the pack - kinds of pack hunting pack the war pack the lamenting pack the increase pack the communion inward and tranquil packs the pack's determination, the historical premanence of packs packs in the ancestor legends of the Aranda temporary formation among the Aranda. Part 3 The pack and religion: the transmutation of packs hunting and the forest among the Lele of Kasai the war booty and the Jivaros the rain dances of the Pueblo Indians on the dynamics of war, the first death, the triumph Islam as a religion of war the religions of lament the Muharram festival of the Shiites Catholicism and the crowd the Holy Fire in Jerusalem. Part 4 The crowd in history: national crowd symbols - the English, the Dutch, the Germans, the French, the Swiss, the Spaniards, the Italians, the Jews Germany and Versailles inflation and the crowd the nature of the parliamentary system distribution and increase, socialism and production the self-destruction of the Xosas. Part 5 The entrails of power: seizing and incorporation the hand - the patience of the hand, the finger exercises of monkeys, the hands and the birth of objects, destructiveness in monkeys and men, the killers are always the powerful on the psychology of eating. Part 6 The survivor: the survivor survival and invulnerability survival as a passion the rules as survivor the escape of Josephus the despot's hostility to survivors, rulers and their successors forms of survival the survivor in primitive belief the resentment of the dead epidemics cemetries immortality. Part 7 Elements of power. Part content.

Detection-based methods have been viewed unfavorably in crowd analysis due to their poor performance in dense crowds. However, we argue that the potential of these methods has been underestimated, as they offer crucial information for crowd analysis that is often ignored. Specifically, the area size and confidence score of output proposals and bounding boxes provide insight into the scale and density of the crowd. To leverage these underutilized features, we propose Crowd Hat, a plug-and-play module that can be easily integrated with existing detection models. This module uses a mixed 2D-1D compression technique to refine the output features and obtain the spatial and numerical distribution of crowd-specific information. Based on these features, we further propose region-adaptive NMS thresholds and a decouple-then-align paradigm that address the major limitations of detection-based methods. Our extensive evaluations on various crowd analysis tasks, including crowd counting, localization, and detection, demonstrate the effectiveness of utilizing output features and the potential of detection-based methods in crowd analysis.

Crowd simulation is a research area widely used in diverse fields, including gaming and security, assessing virtual agent movements through metrics like time to reach their goals, speed, trajectories, and densities. This is relevant for security applications, for instance, as different crowd configurations can determine the time people spend in environments trying to evacuate them. In this work, we extend WebCrowds, an authoring tool for crowd simulation, to allow users to build scenarios and evaluate them through a set of metrics. The aim is to provide a quantitative metric that can, based on simulation data, select the best crowd configuration in a certain environment. We conduct experiments to validate our proposed metric in multiple crowd simulation scenarios and perform a comparison with another metric found in the literature. The results show that experts in the domain of crowd scenarios agree with our proposed quantitative metric.

Most state-of-the-art crowd counting methods use color (RGB) images to learn the density map of the crowd. However, these methods often struggle to achieve higher accuracy in densely crowded scenes with poor illumination. Recently, some studies have reported improvement in the accuracy of crowd counting models using a combination of RGB and thermal images. Although multimodal data can lead to better predictions, multimodal data might not be always available beforehand. In this paper, we propose the use of generative adversarial networks (GANs) to automatically generate thermal infrared (TIR) images from color (RGB) images and use both to train crowd counting models to achieve higher accuracy. We use a Pix2Pix GAN network first to translate RGB images to TIR images. Our experiments on several state-of-the-art crowd counting models and benchmark crowd datasets report significant improvement in accuracy.

We focus on robot navigation in crowded environments. To navigate safely and efficiently within crowds, robots need models for crowd motion prediction. Building such models is hard due to the high dimensionality of multiagent domains and the challenge of collecting or simulating interaction-rich crowd-robot demonstrations. While there has been important progress on models for offline pedestrian motion forecasting, transferring their performance on real robots is nontrivial due to close interaction settings and novelty effects on users. In this paper, we investigate the utility of a recent state-of-the-art motion prediction model (S-GAN) for crowd navigation tasks. We incorporate this model into a model predictive controller (MPC) and deploy it on a self-balancing robot which we subject to a diverse range of crowd behaviors in the lab. We demonstrate that while S-GAN motion prediction accuracy transfers to the real world, its value is not reflected on navigation performance, measured with respect to safety and efficiency; in fact, the MPC performs indistinguishably even when using a simple constant-velocity prediction model, suggesting that substantial model improvements might be ne

Crowd algorithms often assume workers are inexperienced and thus fail to adapt as workers in the crowd learn a task. These assumptions fundamentally limit the types of tasks that systems based on such algorithms can handle. This paper explores how the crowd learns and remembers over time in the context of human computation, and how more realistic assumptions of worker experience may be used when designing new systems. We first demonstrate that the crowd can recall information over time and discuss possible implications of crowd memory in the design of crowd algorithms. We then explore crowd learning during a continuous control task. Recent systems are able to disguise dynamic groups of workers as crowd agents to support continuous tasks, but have not yet considered how such agents are able to learn over time. We show, using a real-time gaming setting, that crowd agents can learn over time, and `remember' by passing strategies from one generation of workers to the next, despite high turnover rates in the workers comprising them. We conclude with a discussion of future research directions for crowd memory and learning.

In crowd behavior understanding, a model of crowd behavior need to be trained using the information extracted from video sequences. Since there is no ground-truth available in crowd datasets except the crowd behavior labels, most of the methods proposed so far are just based on low-level visual features. However, there is a huge semantic gap between low-level motion/appearance features and high-level concept of crowd behaviors. In this paper we propose an attribute-based strategy to alleviate this problem. While similar strategies have been recently adopted for object and action recognition, as far as we know, we are the first showing that the crowd emotions can be used as attributes for crowd behavior understanding. The main idea is to train a set of emotion-based classifiers, which can subsequently be used to represent the crowd motion. For this purpose, we collect a big dataset of video clips and provide them with both annotations of "crowd behaviors" and "crowd emotions". We show the results of the proposed method on our dataset, which demonstrate that the crowd emotions enable the construction of more descriptive models for crowd behaviors. We aim at publishing the dataset wit

Dense pedestrian crowds may pose significant safety risks, yet their underlying dynamics remain insufficiently understood to reliably prevent accidents. In these environments, physical interactions and contact forces fundamentally shape the dynamics of the crowd. However, accurately describing these interindividual interactions requires specific modeling and analytical approaches. This chapter reviews paradigms and models used to represent pedestrian dynamics in various contexts, highlighting the transition from classical approaches to models tailored for dense crowd conditions. We argue that further investigation is needed, featuring new experimental studies and new modeling paradigms, to better capture the complex dynamics that emerge in high-density situations.

Multi-modal crowd counting involves estimating crowd density from both visual and thermal/depth images. This task is challenging due to the significant gap between these distinct modalities. In this paper, we propose a novel approach by introducing an auxiliary broker modality and on this basis frame the task as a triple-modal learning problem. We devise a fusion-based method to generate this broker modality, leveraging a non-diffusion, lightweight counterpart of modern denoising diffusion-based fusion models. Additionally, we identify and address the ghosting effect caused by direct cross-modal image fusion in multi-modal crowd counting. Through extensive experimental evaluations on popular multi-modal crowd-counting datasets, we demonstrate the effectiveness of our method, which introduces only 4 million additional parameters, yet achieves promising results. The code is available at https://github.com/HenryCilence/Broker-Modality-Crowd-Counting.

Crowd movement simulation is crucial for pedestrian safety management and facility design. Data-driven models offer the potential to improve realism and predictive accuracy, but most are developed for a single scenario, limiting their flexibility. We propose a data-driven crowd simulation model that incorporates refined visual-information extraction and explicit exit cues, aiming to improve flexibility across multiple scenarios by more effectively capturing core navigational features. The model is tested on four fundamental modules (bottleneck, corridor, corner, and T-junction) and further evaluated in a composite scenario using a modular approach. Results show that our model performs well across these scenarios, aligning with pedestrian movement in real-world experiments, and outperforms the classical knowledge-driven model in these scenarios. The research outcomes can provide inspiration for the development of data-driven crowd simulation models and advance the application of data-driven approaches.

Numerous studies and anecdotes demonstrate the "wisdom of the crowd," the surprising accuracy of a group's aggregated judgments. Less is known, however, about the generality of crowd wisdom. For example, are crowds wise even if their members have systematic judgmental biases, or can influence each other before members render their judgments? If so, are there situations in which we can expect a crowd to be less accurate than skilled individuals? We provide a precise but general definition of crowd wisdom: A crowd is wise if a linear aggregate, for example a mean, of its members' judgments is closer to the target value than a randomly, but not necessarily uniformly, sampled member of the crowd. Building on this definition, we develop a theoretical framework for examining, a priori, when and to what degree a crowd will be wise. We systematically investigate the boundary conditions for crowd wisdom within this framework and determine conditions under which the accuracy advantage for crowds is maximized. Our results demonstrate that crowd wisdom is highly robust: Even if judgments are biased and correlated, one would need to nearly deterministically select only a highly skilled judge be

In recent years, vision-based crowd analysis has been studied extensively due to its practical applications in real world. In this paper, we formulate a novel crowd analysis problem, in which we aim to predict the crowd distribution in the near future given sequential frames of a crowd video without any identity annotations. Studying this research problem will benefit applications concerned with forecasting crowd dynamics. To solve this problem, we propose a global-residual two-stream recurrent network, which leverages the consecutive crowd video frames as inputs and their corresponding density maps as auxiliary information to predict the future crowd distribution. Moreover, to strengthen the capability of our network, we synthesize scene-specific crowd density maps using simulated data for pretraining. Finally, we demonstrate that our framework is able to predict the crowd distribution for different crowd scenarios and we delve into applications including predicting future crowd count, forecasting high-density region, etc.

Detailed knowledge of the rates, equilibria, and mechanism of biochemical reactions has traditionally been acquired through experiments conducted on solutions containing low concentrations (less than about 1 mg/ml) of total protein, nucleic acid, and/or polysaccharide together with buffer salts, low molecular weight substrates, and cofactors as required. In contrast, biochemical reactions in living systems take place in media containing substantially greater total concentrations (50–400 mg/ml) of macromolecules that may be present in solution and/or in indefinitely large arrays (e.g. cytoskeletal fibers) (1Fulton A.B. Cell. 1982; 30: 345-347Abstract Full Text PDF PubMed Scopus (618) Google Scholar, 2Zimmerman S.B. Trach S.O. J. Mol. Biol. 1991; 222: 599-620Crossref PubMed Scopus (899) Google Scholar). Because no single macromolecular species may be present at high concentration, but all species taken together occupy a significant fraction of the volume of the medium, such media are referred to as "crowded" (3Minton A.P. Wilf J. Biochemistry. 1981; 20: 4821-4826Crossref PubMed Scopus (241) Google Scholar) and/or "confining" (4Minton A.P. Biophys. J. 1992; 63: 1090-1100Abstract Full Text PDF PubMed Scopus (158) Google Scholar) rather than "concentrated," depending upon whether the macrosolutes are soluble and/or structured. Fig.1 provides a schematic illustration of crowding and confinement in eukaryotic cytoplasm. In such media, nonspecific interactions between macrosolutes contribute significantly to the total free energy of the medium. High concentrations of "background" macromolecules that do not participate directly in a particular test reaction have been observed to induce order-of-magnitude or greater changes in the rates and equilibria of numerous test reactions (see below). To properly assess the physiological role of a particular reaction or set of reactions characterized in vitro, it is important to consider the possible influence of crowding and/or confinement upon the reaction in its physiological milieu. A nonspecific interaction between a pair of macromolecules does not depend strongly upon details of the primary, secondary, or tertiary structure(s) of the interacting macromolecules but rather upon global properties such as net charge, dipole or multipole moment, the polarity of surface residues, and macromolecular "shape." Nonspecific interactions may be either repulsive (steric, electrostatic) or attractive (electrostatic, hydrophobic) and are generally substantially weaker on a pairwise basis than specific interactions between reaction partners. The concept of "nonspecific interaction" is widely misunderstood. Many if not most biomedical researchers still regard such interaction as an artifact of a particular experimental system that interferes with the acquisition of meaningful data. Strategies such as extrapolation of results to zero macromolecular concentration are devised for the reduction or elimination of the influence of nonspecific interaction on a test reaction. Although such procedures may be appropriate in certain specific experimental situations, they do not necessarily provide results that are more meaningful in a biological context. On the contrary, significant nonspecific interaction is an unavoidable consequence of crowding and confinement in most or all physiological fluid media. To understand molecular processes in such media one must therefore take account of nonspecific interactions rather than attempt to eliminate them. The contribution of a particular solute species X to the total free energy of the system is a function of an effective concentration, called the thermodynamic activity of X, denoted byax. Thermodynamics teaches that equilibrium constants are generally expressed in terms of equilibrium activities rather than actual concentrations. As a simple example, consider a protein molecule that may reversibly self-associate to form a dimer. The equilibrium association constant for this reaction is K120=(a2/a12), where subscripts 1 and 2 refer to monomer and dimer, respectively. Biochemists are accustomed to seeing equilibrium constants written as ratios of equilibrium concentrations. However, the so-called equilibrium constant written in terms of concentrations,K12, is actually an apparent constant related to the true equilibrium constant, K120 , by K12≡(c2/c2)=K120()(γ12/γ2) γ2), where γi denotes the ratio of effective to actual concentrations of species i, termed the activity coefficient. The activity coefficient has a precise definition in terms of nonspecific solute-solute interaction, lnγi = <gi>/kT, where <gi> denotes the (composition-dependent) equilibrium average free energy of nonspecific interaction between a molecule of species i and all of the other macrosolutes present in the medium, k is the Boltzmann constant, and T is the absolute temperature. Steric repulsion is the most fundamental of all interactions between macromolecules in solution and is always present at finite concentration, independent of the magnitude of additional electrostatic or hydrophobic interactions. Because solute molecules are mutually impenetrable, the presence of a significant volume fraction of macromolecules in the medium places constraints on the placement of an additional molecule of test macrosolute that depend upon the relative sizes, shapes, and concentrations of all macrosolutes in the medium. Fig. 2 depicts a region, demarcated by a square outline, in a solution containing spherical "background" macrosolutes of radius rb, colored black, that occupy ∼30% of the total volume (vtot) of the specified region. The available volume (va,T) is defined to be that part of the volume of the region which may be occupied by the center of massof a molecule of a spherical test species T of radius rt added to the solution. If the test species is very small relative to the background species (Fig. 2 A), then the available volume, indicated inblue, is approximately equal to that part of the total volume not occupied by the background species, i.e. ∼0.7vtot. However, if the size of the test species is comparable with (or larger than) the background species (Fig.2 B), the available volume is substantially smaller, as the center of a molecule of the test species can approach the center of any background molecule to no less than the distance, denoted byrC, at which the surfaces of the two molecules contact each other. 1For markedly non-spherical molecules,rC is a function of the mutual orientations of test and background molecules. For approximately spherical molecules,rC may be treated as a constant equal to the sum of the average radii of test and background molecules. One may visualize this restriction by drawing a circular shell with radiusrC about each background molecule. Then the volume available to the test species, indicated by the blue-colored regions in Fig. 2 B, is that part of the total volume which is not occupied by any background molecule or by any shell. It is evident upon inspection of Fig. 2, A andB, that the available volume is a sensitive function of the relative sizes (and shapes) of test and background molecules and the number density of background molecules. 2Although Fig. 2, A and B,reflects a static distribution of background molecules, these conclusions hold also for a dynamic distribution, assuming equivalence of spatial and time averages. Volume may be excluded to a test particle by the surfaces of immobile structures as well as by individual background macrosolutes (4Minton A.P. Biophys. J. 1992; 63: 1090-1100Abstract Full Text PDF PubMed Scopus (158) Google Scholar, 5Giddings J.C. Kucera E. Russell C.P. Myers M.N. J. Phys. Chem. 1968; 72: 4397-4408Crossref Scopus (439) Google Scholar), as illustrated in Fig. 3, which depicts a pore with square cross-section. 3This pore is one possible idealized representation of a small element of volume bounded by large macromolecular assemblies, such as interstices within a lattice of rodlike fibers or lamellar space between adjacent membrane surfaces. The center of a spherical test molecule whose diameter is comparable with the largest dimension of the pore (Fig. 3 B) is excluded from thepink-colored region, which in this instance represents a significant fraction of the total volume of the solution enclosed in the pore. In a solution of macromolecules interacting exclusively via steric repulsion there exists an extremely simple relationship between the effective and actual concentration of each solute species (6Lebowitz J.L. Helfand E. Praestgaard E. J. Chem. Phys. 1965; 43: 774-779Crossref Scopus (496) Google Scholar), γi ≡ (ai/ci) = (νtot/νa,i), where νtot and νa,i denote the total volume and volume available to speciesi, respectively. The thermodynamic activities of macromolecules in fluid media may be measured by several physical-chemical methods. In Fig. 4, the experimentally measured ratio of the effective to actual concentration of hemoglobin, under experimental conditions comparable with those encountered in a red blood cell, is plotted as a function of the actual concentration. The first remarkable feature of this dependence is its highly non-linear nature; the effective concentration of hemoglobin exceeds the actual concentration by a factor of >10 at 200 g/liter and a factor approaching 100 at 300 g/liter. (For reference, the concentration of hemoglobin within a normal red blood cell typically exceeds 300 g/liter.) The second remarkable feature is that the experimentally measured dependence may be accounted for quantitatively over the entire concentration range by a simple geometrical model for available volume, in which each hemoglobin molecule is represented by a rigid spherical particle of radius ∼29.5 Å, i.e. a particle closely resembling a "shrink-wrapped" hemoglobin molecule (7Ross P.D. Minton A.P. J. Mol. Biol. 1977; 112: 437-452Crossref PubMed Scopus (211) Google Scholar, 8Guttman H.J. Anderson C.F. Record Jr., T.M. Biophys. J. 1995; 68: 835-846Abstract Full Text PDF PubMed Scopus (25) Google Scholar). The ratio of effective to actual concentration (i.e.activity coefficient) of a protein within a polymer gel may be calculated from the extent to which the protein partitions between the gel and bulk solution (4Minton A.P. Biophys. J. 1992; 63: 1090-1100Abstract Full Text PDF PubMed Scopus (158) Google Scholar, 5Giddings J.C. Kucera E. Russell C.P. Myers M.N. J. Phys. Chem. 1968; 72: 4397-4408Crossref Scopus (439) Google Scholar). In Fig. 5, this ratio, measured experimentally in a dextran gel occupying about 3% of total solution volume, is plotted for a variety of globular proteins as a function of molar mass. We note that the dependence of activity coefficient upon molar mass is reasonably independent of the identity of the protein, indicating that it is a property primarily of protein size and is insensitive to small changes in shape or composition. The solid curve was calculated using a simple geometrical model for available volume (9Ogston A.G. J. Phys. Chem. 1970; 74: 668-669Crossref Scopus (56) Google Scholar), in which each protein is modeled as a hard spherical particle with a radius proportional to the cube root of mass, and polymer is modeled as a random matrix of hard cylindrical rods. We present a simple example of how the difference between activity and concentration in a crowded medium may qualitatively influence association equilibria. 4A more complete treatment is presented in Ref.10Minton A.P. Biopolymers. 1981; 20: 2093-2120Crossref Scopus (468) Google Scholar. Consider the dimerization reaction introduced above, with real and apparent equilibrium constants defined in the first two equations. For the sake of illustration, we set the molar mass of A equal to 100,000 and assume that both A andA2 have roughly spherical shape. 5Although the dimer is unlikely to be spherical, its deviation from sphericity will not be so large that treatment as an approximate sphere will introduce a qualitative error into the present estimate (10Minton A.P. Biopolymers. 1981; 20: 2093-2120Crossref Scopus (468) Google Scholar). Using the same geometrical model for excluded volume and the same size and shape parameters used to fit the data in Fig. 5 (9Ogston A.G. J. Phys. Chem. 1970; 74: 668-669Crossref Scopus (56) Google Scholar), the values of γ1 and γ2 may be estimated to be about 3 × 102 and 1 × 104, respectively, for a fractional volume occupancy φ of 0.2, and about 1 × 104 and 1 × 106, respectively, for φ = 0.3. It follows from the second equation that the experimentally observed equilibrium constant,K12, would be expected to exceed K12o (the value ofK12 in the limit of high dilution) by a factor of ∼10 in a medium of φ = 0.2 and ∼100 in a medium of φ = 0.3. Although this estimate is only qualitative, the large magnitude of the predicted effect of excluded volume transcends the crudeness of the theoretical model. Indeed, similar but somewhat more refined predictions have been confirmed, in some cases quantitatively, by experimental observation (see references in Ref. 11Zimmerman S.B. Minton A.P. Annu. Rev. Biophys. Biomol. Struct. 1993; 22: 27-65Crossref PubMed Scopus (1244) Google Scholar and in TableI).Table ISome recent reports of experimentally observed crowding and confinement effects on macromolecular reactionsObservation 1-aPEG, polyethylene glycol.MagnitudeEnhancement of spectrin self-association by PEG, dextran (35Cole N. Ralston G.B. Int. J. Biochem. 1994; 26: 799-804Crossref PubMed Scopus (20) Google Scholar,36Lindner R. Ralston G. Biophys. Chem. 1995; 57: 15-25Crossref PubMed Scopus (43) Google Scholar) 1-bNumbers in parentheses are references.10-fold increase of K12 in 20% dextranEnhancement of actin polymerization by dextran and PEG (37Lindner R. Ralston G. Biophys. Chem. 1997; 66: 57-66Crossref PubMed Scopus (57) Google Scholar)3-fold decrease in solubility in 15% dextranEnhancement of binding of HU protein toE. coli DNA by PEG and non-DNA binding proteins (38Murphy L.D. Zimmerman S.B. Biochim. Biophys. Acta. 1994; 1219: 277-284Crossref PubMed Scopus (74) Google Scholar,39Murphy L.D. Zimmerman S.B. Biophys. Chem. 1995; 57: 71-92Crossref PubMed Scopus (77) Google Scholar)12% PEG increases affinity of DNA for HU by >10-foldStabilization of supercoiled conformations of DNA by PEG (40Naimushin A.N. Quach N. Fujimoto B.S. Schurr J.M. Biopolymers. 2001; 58: 204-217Crossref PubMed Scopus (13) Google Scholar)Sequestration of protein molecules in hydrated sol-gel glass stabilizes them with respect to thermal denaturation (41Eggers D. Valentine J. Protein Sci. 2001; 10: 250-261Crossref PubMed Scopus (358) Google Scholar)T50 for α-lactalbumin increased by >25 °CSelf-association of fibrinogen induced by bovine serum albumin (42Rivas G. Fernández J.A. Minton A.P. Biochemistry. 1999; 38: 9379-9388Crossref PubMed Scopus (145) Google Scholar)Doubling of weight-average molar mass in >5% bovine serum albuminEnhancement by dextran of limited self-association of tubulin under conditions not permitting microtubule assembly>2-fold increase in weight-average molar mass in 10% dextranEnhancement of self-association of FtsZ by bovine serum albumin, hemoglobin (43Rivas G. Fernández J.A. Minton A.P. Proc. Natl. Acad. Sci. U. S. A. 2001; 98: 3150-3155Crossref PubMed Scopus (150) Google Scholar)2-fold increase in weight-average molar mass in 30% albumin or hemoglobinEnhancement of unimolecular condensation of large linear DNA by PEG (44Kidoaki S. Yoshikawa K. Biophys. Chem. 1999; 76: 133-143Crossref PubMed Scopus (27) Google Scholar)>10-fold increase in 2-state equilibrium constant at 18% PEGEnhancement of productive refolding and assembly of GroEL by Ficoll 70 (45Galan A. Sot B. Llorca O. Carrascosa J.L. Valpuesta J.M. Muga A. J. Biol. Chem. 2001; 276: 957-964Abstract Full Text Full Text PDF PubMed Scopus (40) Google Scholar)>3-fold increase in recovery of ATPase activity in presence of >10% FicollReduction in solubility of deoxy sickle cell hemoglobin by dextran (46Bookchin R.M. Balasz T. Wang Z. Josephs R. Lew V.L. J. Biol. Chem. 1999; 274: 6689-6697Abstract Full Text Full Text PDF PubMed Scopus (27) Google Scholar)∼15-fold decrease in 21% dextranEarlier observations are tabulated in Zimmerman and Minton (11Zimmerman S.B. Minton A.P. Annu. Rev. Biophys. Biomol. Struct. 1993; 22: 27-65Crossref PubMed Scopus (1244) Google Scholar).1-a PEG, polyethylene glycol.1-b Numbers in parentheses are references. Open table in a new tab Earlier observations are tabulated in Zimmerman and Minton (11Zimmerman S.B. Minton A.P. Annu. Rev. Biophys. Biomol. Struct. 1993; 22: 27-65Crossref PubMed Scopus (1244) Google Scholar). There are two opposing effects of excluded volume on reaction rates (12Minton A.P. Methods Enzymol. 1998; 295: 127-149Crossref PubMed Scopus (276) Google Scholar). If the overall rate of the reaction is limited by the rate with which a transition state complex decays to products, then crowding would be expected to enhance the relative abundance of the transition state complex and hence the forward reaction rate. Under these conditions, the forward rate constant may be increased by up to the equilibrium enhancement factor, depending upon details of the particular reaction. However, if the overall rate of the reaction is limited by the rate with which reactant molecules encounter each other through diffusional motion, then crowding, which retards diffusional motion (13Ogston A.G. Preston B.N. Wells J.D. Proc. R. Soc. Lond. A. 1973; 353: 297-316Google Scholar, 14Muramatsu N. Minton A.P. Proc. Natl. Acad. Sci. U. S. A. 1988; 85: 2984-2988Crossref PubMed Scopus (137) Google Scholar), would be expected to lower the forward reaction rate. In the limit of high fractional volume occupancy, all association reactions are expected to be diffusion limited and hence slowed by crowding (11Zimmerman S.B. Minton A.P. Annu. Rev. Biophys. Biomol. Struct. 1993; 22: 27-65Crossref PubMed Scopus (1244) Google Scholar). Hence, depending upon the nature of a particular reaction, one of two types of behavior may be observed as the fractional volume occupancy of background molecules increases: the forward rate for a macromolecular association may decrease monotonically or may initially increase, pass through a maximum, and then decrease. A bimodal dependence of reaction rate on crowder concentration has been observed experimentally (15Harrison B. Zimmerman S.B. Nucleic Acids Res. 1986; 14: 1863-1870Crossref PubMed Scopus (24) Google Scholar). Macromolecular crowding and/or confinement by background molecules or structures can in principle affect the equilibrium and kinetics of any macromolecular reaction in which there exists a significant difference between the volume excluded to reactants and the volume excluded to products. Such reactions include self- or heteroassociation, condensation (crystallization, nucleation-controlled fiber formation), binding of macromolecules to specific surface sites, nonspecific surface adsorption, and protein isomerization, including folding/unfolding (4Minton A.P. Biophys. J. 1992; 63: 1090-1100Abstract Full Text PDF PubMed Scopus (158) Google Scholar, 10Minton A.P. Biopolymers. 1981; 20: 2093-2120Crossref Scopus (468) Google Scholar, 11Zimmerman S.B. Minton A.P. Annu. Rev. Biophys. Biomol. Struct. 1993; 22: 27-65Crossref PubMed Scopus (1244) Google Scholar, 16Ralston G.B. J. Chem. Educ. 1990; 67: 857-860Crossref Scopus (82) Google Scholar, 17Minton A.P. Biophys. J. 1995; 68: 1311-1322Abstract Full Text PDF PubMed Scopus (69) Google Scholar, 18Minton A.P. Biophys. J. 2000; 78: 101-109Abstract Full Text Full Text PDF PubMed Scopus (186) Google Scholar). Crowding may also affect enzyme-catalyzed reactions of small molecules if the mechanism of catalysis involves significant conformational change of the enzyme (3Minton A.P. Wilf J. Biochemistry. 1981; 20: 4821-4826Crossref PubMed Scopus (241) Google Scholar,10Minton A.P. Biopolymers. 1981; 20: 2093-2120Crossref Scopus (468) Google Scholar). Many such effects have indeed been observed experimentally. Most of the older observations are cited in Ref. 11Zimmerman S.B. Minton A.P. Annu. Rev. Biophys. Biomol. Struct. 1993; 22: 27-65Crossref PubMed Scopus (1244) Google Scholar, and some more recent observations are listed in Table I. In recent years increased attention has been paid to the functioning of ever larger macromolecular assemblies and systems of interacting components, sometimes referred to as molecular machines (19Alberts B. Cell. 1998; 92: 291-294Abstract Full Text Full Text PDF PubMed Scopus (981) Google Scholar). As larger and more complex systems have come under closer scrutiny, a growing number of biomedical researchers have emphasized the extremely broad ramifications of macromolecular crowding and confinement for biochemistry in the intact cell (see for example Refs.20Garner M.M. Burg M.B. Am. J. Physiol. 1994; 266: C877-C892Crossref PubMed Google Scholar, 21Zimmerman S.B. Murphy L.D. FEBS Lett. 1996; 390: 245-248Crossref PubMed Scopus (114) Google Scholar, 22Martin J. Hartl F.-U. Proc. Natl. Acad. Sci. U. S. A. 1997; 94: 1107-1112Crossref PubMed Scopus (100) Google Scholar, 23Kornberg A. J. Bacteriol. 2000; 182: 3613-3618Crossref PubMed Scopus (77) Google Scholar, 24van den Berg B. Wain R. Dobson C.M. Ellis R.J. EMBO J. 2000; 19: 3870-3875Crossref PubMed Scopus (225) Google Scholar, 25Ellis R.J. Curr. Opin. Struct. Biol. 2001; 11: 114-119Crossref PubMed Scopus (840) Google Scholar). It is becoming more widely appreciated that under physiological conditions of crowding or confinement, the size- and shape-dependent reduction of volume available to every species of macromolecule results in major shifts in the rates and equilibria of a broad range of macromolecular reactions relative to those measured in dilute solution. We now recognize that nonspecific interactions, including (but not limited to) steric repulsion, provide a substantial contribution to the free energy balance of a physiological system such as an intact cell or tissue. It seems likely that the constituent elements of these systems have evolved to function optimally under normal physiological (i.e. crowded and/or confined) conditions and that the proper functioning of the system depends upon maintenance of the free energy balance established under those crowded and/or confined conditions. Excluded volume theory predicts that at the high level of macromolecular fractional volume occupancy characteristic of all living cells (i.e. >0.20–0.30), the reactivity of almost every soluble macromolecular species, dilute as well as concentrated, will depend sensitively upon its available volume, which, in turn, depends sensitively upon the total volume fraction of macromolecules. It follows that relatively small changes in the fractional volume occupancy of the cellular interior are expected to have major effects on the equilibria and kinetics of a broad variety of intracellular reactions (26Minton A.P. Strange K. Cellular and Molecular Physiology of Cell Volume Regulation. Scholar, A.P. Curr. Opin. Struct. Biol. 2000; 10: PubMed Scopus Google Scholar). to understand two very properties of living changes of cellular volume in cells (i.e. concentration of intracellular are with changes in the rates of a broad of intracellular processes that are large to be accounted for on the basis of simple mass S. E. D. Physiol. Rev. 1998; 78: PubMed Scopus Google Scholar). of cell so from to is with one or more widely types of for the maintenance or of cellular volume, and/or in to changes in of the fluid G. and and Scholar). The presented are only a of the that macromolecular crowding and confinement important and in cell and (11Zimmerman S.B. Minton A.P. Annu. Rev. Biophys. Biomol. Struct. 1993; 22: 27-65Crossref PubMed Scopus (1244) Google Scholar, 24van den Berg B. Wain R. Dobson C.M. Ellis R.J. EMBO J. 2000; 19: 3870-3875Crossref PubMed Scopus (225) Google S.B. Biochim. Biophys. 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