Characterization of facilitated diffusion of tumor suppressor p53 along DNA using single-molecule fluorescence imaging

Stick, Slide, or Bounce: Charge Density Controls Nanoparticle Diffusion

The diffusion and interaction dynamics of charged nanoparticles (NPs) within charged polymer networks are crucial for understanding various biological and biomedical applications. Using a combination of coarse-grained molecular dynamics simulations and experimental diffusion studies, we investigate the effects of the NP size, relative surface charge density (ζ), and concentration on the NP permeation length and time. We propose a scaling law for the relative diffusion of NPs with respect to concentration and ζ, highlighting how these factors influence the NP movement within the network. The analyses reveal that concentration and ζ significantly affect NP permeation length and time, with ζ being critical, as critical as concentration. This finding is corroborated by controlled release experiments. Further, we categorize NP dynamics into sticking, sliding, and bouncing regimes, demonstrating how variations in ζ, concentration, and NP size control these behaviors. Through normalized attachment time (NAT) analyses, we elucidate the roles of electrostatic interactions, steric hindrance, and hydrodynamic forces in governing NP dynamics. These insights provide guidance for optimizing NP design in targeted drug delivery and advanced material applications, enhancing our understanding of NP behavior in complex environments.

Nonspecific vs. specific DNA binding free energetics of a transcription factor domain protein

Transcription factor (TF) proteins regulate gene expression by binding to specific sites on the genome. In the facilitated diffusion model, an optimized search process is achieved by the TF alternating between 3D diffusion in the bulk and 1D diffusion along DNA. While undergoing 1D diffusion, the protein can switch from a search mode for fast diffusion along nonspecific DNA to a recognition mode for stable binding to specific DNA. It was recently noticed that, for a small TF domain protein, reorientations on DNA happen between the nonspecific and specific DNA binding. We here conducted all-atom molecular dynamics simulations with steering forces to reveal the protein-DNA binding free energetics, confirming that the search and recognition modes are distinguished primarily by protein orientations on the DNA. As the binding free energy difference between the specific and nonspecific DNA system slightly deviates from that being estimated directly from dissociation constants on 15-bp DNA constructs, we hypothesize that the discrepancy can come from DNA sequences flanking the 6-bp central binding sites that impact on the dissociation kinetics measurements. The hypothesis is supported by a simplified spherical protein-DNA model along with stochastic simulations and kinetic modeling.

Single-molecule characterization of target search dynamics of DNA-binding proteins in DNA-condensed droplets

Target search models of DNA-binding proteins in cells typically consider search mechanisms that include 3D diffusion and 1D sliding, which can be characterized by single-molecule tracking on DNA. However, the finding of liquid droplets of DNA and nuclear components in cells cast doubt on extrapolation from the behavior in ideal non-condensed DNA conditions to those in cells. In this study, we investigate the target search behavior of DNA-binding proteins in reconstituted DNA-condensed droplets using single-molecule fluorescence microscopy. To mimic nuclear condensates, we reconstituted DNA-condensed droplets using dextran and PEG polymers. In the DNA-condensed droplets, we measured the translational movement of four DNA-binding proteins (p53, Nhp6A, Fis and Cas9) and p53 mutants possessing different structures, sizes, and oligomeric states. Our results demonstrate the presence of fast and slow mobility modes in DNA-condensed droplets for the four DNA-binding proteins. The slow mobility mode capability is correlated strongly to the molecular size and the number of DNA-binding domains on DNA-binding proteins, but only moderately to the affinity to single DNA segments in non-condensed conditions. The slow mobility mode in DNA-condensed droplets is interpreted as a multivalent interaction mode of the DNA-binding protein to multiple DNA segments.

Dynamic transcription regulation at the single-molecule level

Cell fate changes during development, differentiation, and reprogramming are largely controlled at the transcription level. The DNA-binding transcription factors (TFs) often act in a combinatorial fashion to alter chromatin states and drive cell type-specific gene expression. Recent advances in fluorescent microscopy technologies have enabled direct visualization of biomolecules involved in the process of transcription and its regulatory events at the single-molecule level in living cells. Remarkably, imaging and tracking individual TF molecules at high temporal and spatial resolution revealed that they are highly dynamic in searching and binding cognate targets, rather than static and binding constantly. In combination with investigation using techniques from biochemistry, structure biology, genetics, and genomics, a more well-rounded view of transcription regulation is emerging. In this review, we briefly cover the technical aspects of live-cell single-molecule imaging and focus on the biological relevance and interpretation of the single-molecule dynamic features of transcription regulatory events observed in the native chromatin environment of living eukaryotic cells. We also discuss how these dynamic features might shed light on mechanistic understanding of transcription regulation.

Single-Molecule Microscopy Meets Molecular Dynamics Simulations for Characterizing the Molecular Action of Proteins on DNA and in Liquid Condensates

DNA-binding proteins trigger various cellular functions and determine cellular fate. Before performing functions such as transcription, DNA repair, and DNA recombination, DNA-binding proteins need to search for and bind to their target sites in genomic DNA. Under evolutionary pressure, DNA-binding proteins have gained accurate and rapid target search and binding strategies that combine three-dimensional search in solution, one-dimensional sliding along DNA, hopping and jumping on DNA, and intersegmental transfer between two DNA molecules. These mechanisms can be achieved by the unique structural and dynamic properties of these proteins. Single-molecule fluorescence microscopy and molecular dynamics simulations have characterized the molecular actions of DNA-binding proteins in detail. Furthermore, these methodologies have begun to characterize liquid condensates induced by liquid-liquid phase separation, e.g., molecular principles of uptake and dynamics in droplets. This review discusses the molecular action of DNA-binding proteins on DNA and in liquid condensate based on the latest studies that mainly focused on the model protein p53.

Direct visualization of the effect of DNA structure and ionic conditions on HU-DNA interactions

Architectural DNA–binding proteins are involved in many important DNA transactions by virtue of their ability to change DNA conformation. Histone-like protein from E. coli strain U93, HU, is one of the most studied bacterial architectural DNA–binding proteins. Nevertheless, there is still a limited understanding of how the interactions between HU and DNA are affected by ionic conditions and the structure of DNA. Here, using optical tweezers in combination with fluorescent confocal imaging, we investigated how ionic conditions affect the interaction between HU and DNA. We directly visualized the binding and the diffusion of fluorescently labelled HU dimers on DNA. HU binds with high affinity and exhibits low mobility on the DNA in the absence of Mg²⁺; it moves 30-times faster and stays shorter on the DNA with 8 mM Mg²⁺ in solution. Additionally, we investigated the effect of DNA tension on HU–DNA complexes. On the one hand, our studies show that binding of HU enhances DNA helix stability. On the other hand, we note that the binding affinity of HU for DNA in the presence of Mg²⁺ increases at tensions above 50 pN, which we attribute to force-induced structural changes in the DNA. The observation that HU diffuses faster along DNA in presence of Mg²⁺ compared to without Mg²⁺ suggests that the free energy barrier for rotational diffusion along DNA is reduced, which can be interpreted in terms of reduced electrostatic interaction between HU and DNA, possibly coinciding with reduced DNA bending.

Testing mechanisms of DNA sliding by architectural DNA-binding proteins: dynamics of single wild-type and mutant protein molecules in vitro and in vivo

Architectural DNA-binding proteins (ADBPs) are abundant constituents of eukaryotic or bacterial chromosomes that bind DNA promiscuously and function in diverse DNA reactions. They generate large conformational changes in DNA upon binding yet can slide along DNA when searching for functional binding sites. Here we investigate the mechanism by which ADBPs diffuse on DNA by single-molecule analyses of mutant proteins rationally chosen to distinguish between rotation-coupled diffusion and DNA surface sliding after transient unbinding from the groove(s). The properties of yeast Nhp6A mutant proteins, combined with molecular dynamics simulations, suggest Nhp6A switches between two binding modes: a static state, in which the HMGB domain is bound within the minor groove with the DNA highly bent, and a mobile state, where the protein is traveling along the DNA surface by means of its flexible N-terminal basic arm. The behaviors of Fis mutants, a bacterial nucleoid-associated helix-turn-helix dimer, are best explained by mobile proteins unbinding from the major groove and diffusing along the DNA surface. Nhp6A, Fis, and bacterial HU are all near exclusively associated with the chromosome, as packaged within the bacterial nucleoid, and can be modeled by three diffusion modes where HU exhibits the fastest and Fis the slowest diffusion.

Engineering of the genome editing protein Cas9 to slide along DNA

The genome editing protein Cas9 faces engineering challenges in improving off-target DNA cleavage and low editing efficiency. In this study, we aimed to engineer Cas9 to be able to slide along DNA, which might facilitate genome editing and reduce off-target cleavage. We used two approaches to achieve this: reducing the sliding friction along DNA by removing the interactions of Cas9 residues with DNA and facilitating sliding by introducing the sliding-promoting tail of Nhp6A. Seven engineered mutants of Cas9 were prepared, and their performance was tested using single-molecule fluorescence microscopy. Comparison of the mutations enabled the identification of key residues of Cas9 to enhance the sliding along DNA in the presence and absence of single guide RNA (sgRNA). The attachment of the tail to Cas9 mutants enhanced sliding along DNA, particularly in the presence of sgRNA. Together, using the proposed approaches, the sliding ability of Cas9 was improved up to eightfold in the presence of sgRNA. A sliding model of Cas9 and its engineering action are discussed herein.

What Are the Molecular Requirements for Protein Sliding along DNA?

DNA-binding proteins rely on linear diffusion along the longitudinal DNA axis, supported by their nonspecific electrostatic affinity for DNA, to search for their target recognition sites. One may therefore expect that the ability to engage in linear diffusion along DNA is universal to all DNA-binding proteins, with the detailed biophysical characteristics of that diffusion differing between proteins depending on their structures and functions. One key question is whether the linear diffusion mechanism is defined by translation coupled with rotation, a mechanism that is often termed sliding. We conduct coarse-grained and atomistic molecular dynamics simulations to investigate the minimal requirements for protein sliding along DNA. We show that coupling, while widespread, is not universal. DNA-binding proteins that slide along DNA transition to uncoupled translation–rotation (i.e., hopping) at higher salt concentrations. Furthermore, and consistently with experimental reports, we find that the sliding mechanism is the less dominant mechanism for some DNA-binding proteins, even at low salt concentrations. In particular, the toroidal PCNA protein is shown to follow the hopping rather than the sliding mechanism.

The disordered DNA-binding domain of p53 is indispensable for forming an encounter complex to and jumping along DNA

The tumor suppressor p53 utilizes a facilitated diffusion mechanism to search for and bind to target DNA sequences. Sub-millisecond single-molecule fluorescence tracking demonstrated that p53 forms a short-lived encounter complex to DNA then converts to the long-lived complex that can move and jump along DNA during the target search. To reveal the role of each DNA-binding domain of p53 in these processes, we investigated two p53 mutants lacking either of two DNA-binding domains; structured core and disordered C-terminal domains, using sub-millisecond single-molecule fluorescence microscopy. We found that the C-terminal domain is required for the encounter complex formation and conversion to the long-lived complex. The long-lived complex is stabilized by the core domain as well as the C-terminal domain. Furthermore, only the C-terminal domain participates in the jump of p53 along DNA at a high salt concentration. We propose that the flexible C-terminal domain of p53 is twined around DNA, which can form the encounter complex, convert to the long-lived complex, and enable p53 to land on DNA after the jump.

The HMGB chromatin protein Nhp6A can bypass obstacles when traveling on DNA

DNA binding proteins rapidly locate their specific DNA targets through a combination of 3D and 1D diffusion mechanisms, with the 1D search involving bidirectional sliding along DNA. However, even in nucleosome-free regions, chromosomes are highly decorated with associated proteins that may block sliding. Here we investigate the ability of the abundant chromatin-associated HMGB protein Nhp6A from Saccharomyces cerevisiae to travel along DNA in the presence of other architectural DNA binding proteins using single-molecule fluorescence microscopy. We observed that 1D diffusion by Nhp6A molecules is retarded by increasing densities of the bacterial proteins Fis and HU and by Nhp6A, indicating these structurally diverse proteins impede Nhp6A mobility on DNA. However, the average travel distances were larger than the average distances between neighboring proteins, implying Nhp6A is able to bypass each of these obstacles. Together with molecular dynamics simulations, our analyses suggest two binding modes: mobile molecules that can bypass barriers as they seek out DNA targets, and near stationary molecules that are associated with neighboring proteins or preferred DNA structures. The ability of mobile Nhp6A molecules to bypass different obstacles on DNA suggests they do not block 1D searches by other DNA binding proteins.

Dependence of DNA length on binding affinity between TrpR and trpO of DNA

We scrutinize the length dependency of the binding affinity of bacterial repressor TrpR protein to trpO (specific site) on DNA. A footprinting experiment shows that the longer the DNA length, the larger the affinity of TrpR to the specific site on DNA. This effect termed “antenna effect” might be interpreted as follows: longer DNA provides higher probability for TrpR to access to the specific site aided by one-dimensional diffusion along the nonspecific sites of DNA. We show that, however, the antenna effect cannot be explained while detailed balance holds among three kinetic states, that is, free protein/DNA, nonspecific complexes, and specific complex. We propose a working hypothesis that slow degree(s) of freedom in the system switch(es) different potentials of mean force causing transitions among the three states. This results in a deviation from detailed balance on the switching timescale. We then derive a simple reaction diffusion/binding model that describes the antenna effect on TrpR binding to its target operator. Possible scenarios for such slow degree(s) of freedom in TrpR–DNA complex are addressed.

Transient binding and jumping dynamics of p53 along DNA revealed by sub-millisecond resolved single-molecule fluorescence tracking

Characterization of the target search dynamics of DNA-binding proteins along DNA has been hampered by the time resolution of a standard single-molecule fluorescence microscopy. Here, we achieved the time resolution of 0.5 ms in the fluorescence microscopy measurements by optimizing the fluorescence excitation based on critical angle illumination and by utilizing the time delay integration mode of the electron-multiplying charge coupled device. We characterized the target search dynamics of the tumor suppressor p53 along nonspecific DNA at physiological salt concentrations. We identified a short-lived encounter intermediate before the formation of the long-lived p53–DNA complex. Both the jumps and the one-dimensional diffusion of p53 along DNA were accelerated at higher salt concentrations, suggesting the rotation-uncoupled movement of p53 along DNA grooves and conformational changes in the p53/DNA complex. This method can be used to clarify the unresolved dynamics of DNA-binding proteins previously hidden by time averaging.

Protein Diffusion on Charged Biopolymers: DNA versus Microtubule

Protein diffusion in lower-dimensional spaces is used for various cellular functions. For example, sliding on DNA is essential for proteins searching for their target sites, and protein diffusion on microtubules is important for proper cell division and neuronal development. On the one hand, these linear diffusion processes are mediated by long-range electrostatic interactions between positively charged proteins and negatively charged biopolymers and have similar characteristic diffusion coefficients. On the other hand, DNA and microtubules have different structural properties. Here, using computational approaches, we studied the mechanism of protein diffusion along DNA and microtubules by exploring the diffusion of both protein types on both biopolymers. We found that DNA-binding and microtubule-binding proteins can diffuse on each other's substrates; however, the adopted diffusion mechanism depends on the molecular properties of the diffusing proteins and the biopolymers. On the protein side, only DNA-binding proteins can perform rotation-coupled diffusion along DNA, with this being due to their higher net charge and its spatial organization at the DNA recognition helix. By contrast, the lower net charge on microtubule-binding proteins enables them to diffuse more quickly than DNA-binding proteins on both biopolymers. On the biopolymer side, microtubules possess intrinsically disordered, negatively charged C-terminal tails that interact with microtubule-binding proteins, thus supporting their diffusion. Thus, although both DNA-binding and microtubule-binding proteins can diffuse on the negatively charged biopolymers, the unique molecular features of the biopolymers and of their natural substrates are essential for function.

How p53 Molecules Solve the Target DNA Search Problem: A Review

Interactions between DNA and DNA-binding proteins play an important role in many essential cellular processes. A key function of the DNA-binding protein p53 is to search for and bind to target sites incorporated in genomic DNA, which triggers transcriptional regulation. How do p53 molecules achieve "rapid" and "accurate" target search in living cells? The search dynamics of p53 were expected to include 3D diffusion in solution, 1D diffusion along DNA, and intersegmental transfer between two different DNA strands. Single-molecule fluorescence microscopy enabled the tracking of p53 molecules on DNA and the characterization of these dynamics quantitatively. Recent intensive single-molecule studies of p53 succeeded in revealing each of these search dynamics. Here, we review these studies and discuss the target search mechanisms of p53.

Liquid-like droplet formation by tumor suppressor p53 induced by multivalent electrostatic interactions between two disordered domains

Early in vivo studies demonstrated the involvement of a tumor-suppressing transcription factor, p53, into cellular droplets such as Cajal and promyelocytic leukemia protein bodies, suggesting that the liquid-liquid phase separation (LLPS) might be involved in the cellular functions of p53. To examine this possibility, we conducted extensive investigations on the droplet formation of p53 in vitro. First, p53 itself was found to form liquid-like droplets at neutral and slightly acidic pH and at low salt concentrations. Truncated p53 mutants modulated droplet formation, suggesting the importance of multivalent electrostatic interactions among the N-terminal and C-terminal domains. Second, FRET efficiency measurements for the dimer mutants of p53 revealed that distances between the core domains and between the C-terminal domains were modulated in an opposite manner within the droplets. Third, the molecular crowding agents were found to promote droplet formation, whereas ssDNA, dsDNA, and ATP, to suppress it. Finally, the p53 mutant mimicking posttranslational phosphorylation did not form the droplets. We conclude that p53 itself has a potential to form droplets that can be controlled by cellular molecules and by posttranslational modifications, suggesting that LLPS might be involved in p53 function.

Time-Resolved Diffusion Detection with Microstopped Flow System

The transient grating (TG) method is a powerful technique for monitoring the time dependence of the diffusion coefficient during photochemical reactions. However, the applications of this technique have been limited to photochemical reactions. Here, a microstopped flow (μ-SF) system is developed to expand the technique's applicability. The constructed μ-SF system can be used for a solution with a total volume as small as 3 μL, and mixing times for absorption and diffusion measurements were determined to be 400 μs and 100 ms, respectively. To demonstrate this system with the TG method, an acid-induced denaturation of a photosensor protein, phototropin LOV2 domain with a linker, was studied from the viewpoint of the reactivity. This system can be used not only for time-resolved diffusion measurement but also for conventional absorption or fluorescence detection methods. In particular, this system has a great advantage for a target solution in that only a very small amount is needed.

Direct Observation and Analysis of the Dynamics of the Photoresponsive Transcription Factor GAL4

Herein, the direct visualization of the dynamic interaction between a photoresponsive transcription factor fusion, GAL4-VVD, and DNA using high-speed atomic force microscopy (HS-AFM) is reported. A series of different GAL4-VVD movements, such as binding, sliding, stalling, and dissociation, was observed. Inter-strand jumping on two double-stranded (ds) DNAs was also observed. Detailed analysis using a long substrate DNA strand containing five GAL4-binding sites revealed that GAL4-VVD randomly moved on the dsDNA using sliding and hopping to rapidly find specific binding sites, and then stalled to the specific sites to form a stable complex formation. These results suggest the existence of different conformations of the protein to enable sliding and stalling. This single-molecule imaging system with nanoscale resolution provides an insight into the searching mechanism used by DNA-binding proteins.

Facilitated Diffusion Mechanisms in DNA Base Excision Repair and Transcriptional Activation

Preservation of the coding potential of the genome and highly regulated gene expression over the life span of a human are two fundamental requirements of life. These processes require the action of repair enzymes or transcription factors that efficiently recognize specific sites of DNA damage or transcriptional regulation within a restricted time frame of the cell cycle or metabolism. A failure of these systems to act results in accumulated mutations, metabolic dysfunction, and disease. Despite the multifactorial complexity of cellular DNA repair and transcriptional regulation, both processes share a fundamental physical requirement that the proteins must rapidly diffuse to their specific DNA-binding sites that are embedded within the context of a vastly greater number of nonspecific DNA-binding sites. Superimposed on the needle-in-the-haystack problem is the complex nature of the cellular environment, which contains such high concentrations of macromolecules that the time frame for diffusion is expected to be severely extended as compared to dilute solution. Here we critically review the mechanisms for how these proteins solve the needle-in-the-haystack problem and how the effects of cellular macromolecular crowding can enhance facilitated diffusion processes. We restrict the review to human proteins that use stochastic, thermally driven site-recognition mechanisms, and we specifically exclude systems involving energy cofactors or circular DNA clamps. Our scope includes ensemble and single-molecule studies of the past decade or so, with an emphasis on connecting experimental observations to biological function.

Mechanisms of Protein Search for Targets on DNA: Theoretical Insights

Protein-DNA interactions are critical for the successful functioning of all natural systems. The key role in these interactions is played by processes of protein search for specific sites on DNA. Although it has been studied for many years, only recently microscopic aspects of these processes became more clear. In this work, we present a review on current theoretical understanding of the molecular mechanisms of the protein target search. A comprehensive discrete-state stochastic method to explain the dynamics of the protein search phenomena is introduced and explained. Our theoretical approach utilizes a first-passage analysis and it takes into account the most relevant physical-chemical processes. It is able to describe many fascinating features of the protein search, including unusually high effective association rates, high selectivity and specificity, and the robustness in the presence of crowders and sequence heterogeneity.

High Free-Energy Barrier of 1D Diffusion Along DNA by Architectural DNA-Binding Proteins

Architectural DNA-binding proteins function to regulate diverse DNA reactions and have the defining property of significantly changing DNA conformation. Although the 1D movement along DNA by other types of DNA-binding proteins has been visualized, the mobility of architectural DNA-binding proteins on DNA remains unknown. Here, we applied single-molecule fluorescence imaging on arrays of extended DNA molecules to probe the binding dynamics of three structurally distinct architectural DNA-binding proteins: Nhp6A, HU, and Fis. Each of these proteins was observed to move along DNA, and the salt concentration independence of the 1D diffusion implies sliding with continuous contact to DNA. Nhp6A and HU exhibit a single sliding mode, whereas Fis exhibits two sliding modes. Based on comparison of the diffusion coefficients and sizes of many DNA binding proteins, the architectural proteins are categorized into a new group distinguished by an unusually high free-energy barrier for 1D diffusion. The higher free-energy barrier for 1D diffusion by architectural proteins can be attributed to the large DNA conformational changes that accompany binding and impede rotation-coupled movement along the DNA grooves.

One-Dimensional Search Dynamics of Tumor Suppressor p53 Regulated by a Disordered C-Terminal Domain

Tumor suppressor p53 slides along DNA and finds its target sequence in drastically different and changing cellular conditions. To elucidate how p53 maintains efficient target search at different concentrations of divalent cations such as Ca²⁺ and Mg²⁺, we prepared two mutants of p53, each possessing one of its two DNA-binding domains, the CoreTet mutant having the structured core domain plus the tetramerization (Tet) domain, and the TetCT mutant having Tet plus the disordered C-terminal domain. We investigated their equilibrium and kinetic dissociation from DNA and search dynamics along DNA at various [Mg²⁺]. Although binding of CoreTet to DNA becomes markedly weaker at higher [Mg²⁺], binding of TetCT depends slightly on [Mg²⁺]. Single-molecule fluorescence measurements revealed that the one-dimensional diffusion of CoreTet along DNA consists of fast and slow search modes, the ratio of which depends strongly on [Mg²⁺]. In contrast, diffusion of TetCT consisted of only the fast mode. The disordered C-terminal domain can associate with DNA irrespective of [Mg²⁺], and can maintain an equilibrium balance of the two search modes and the p53 search distance. These results suggest that p53 modulates the quaternary structure of the complex between p53 and DNA under different [Mg²⁺] and that it maintains the target search along DNA.

Investigating the Influence of Magnesium Ions on p53-DNA Binding Using Atomic Force Microscopy

p53 is a tumor suppressor protein that plays a significant role in apoptosis and senescence, preserving genomic stability, and preventing oncogene expression. Metal ions, such as magnesium and zinc ions, have important influences on p53–DNA interactions for stabilizing the structure of the protein and enhancing its affinity to DNA. In the present study, we systematically investigated the interaction of full length human protein p53 with DNA in metal ion solution by atomic force microscopy (AFM). The p53–DNA complexes at various p53 concentrations were scanned by AFM and their images are used to measure the dissociation constant of p53–DNA binding by a statistical method. We found that the dissociation constant of p53 binding DNA is 328.02 nmol/L in physiological buffer conditions. The influence of magnesium ions on p53–DNA binding was studied by AFM at various ion strengths through visualization. We found that magnesium ions significantly stimulate the binding of the protein to DNA in a sequence-independent manner, different from that stimulated by zinc. Furthermore, the high concentrations of magnesium ions can promote p53 aggregation and even lead to the formation of self-assembly networks of DNA and p53 proteins. We propose an aggregation and self-assembly model based on the present observation and discuss its biological meaning.