Prion diseases are a group of fatal neurodegenerative maladies that can arise spontaneously or be inherited, and that can also be infectious . Despite enormous investments over the last 30 years in searching for a prion virus or virion [2–5], no prion-specific nucleic acids associated with infectious prion particles have ever been identified . A notable shift has occurred in the last few years from debating the question of whether a protein can be infectious to what makes a protein infectious and how many proteins are infectious [7–9]. Elucidating the polymerization mechanisms and structure of misfolded and aggregated isoforms of the prion protein (PrP) will help solving these long-standing research problems.
The discovery of prion disease and the establishment of the protein only hypothesis of prion propagation raised substantial interest in the class of maladies referred to as conformational diseases. Although significant progress has been made in elucidating the mechanisms of polymerization for several amyloidogenic proteins and peptides linked to conformational disorders and solving their fibrillar 3D structures, studies of prion protein amyloid fibrils and their polymerization mechanism have proven to be very difficult. The present minireview introduces the mechanism of branched-chain reaction for describing the peculiar kinetics of prion polymerization and summarizes our current knowledge about the substructure of prion protein amyloid fibrils.
atomic force microscopy
recombinant prion protein
Prion polymerization is a branched-chain reaction
To model prion conversion, two kinetic models has been exploited: the nucleation-polymerization  and the template assisted . These models have been previously discussed in numerous review articles [12–14] and therefore will not be presented here. Although these two models have played an important role in the evolution of our ideas regarding the mechanism of prion conversion, neither of them emphasize the importance of multiplication of the active centers of prion conversion, a key step in prion replication. When studying the kinetics of the in vitro fibril formation, we were surprised to discover that fibrillization of recombinant PrP (rPrP) displays several kinetic features that can not be explained by the nucleation-polymerization or the template assisted models [15,16]. These ‘atypical’ features include: (a) the dramatic effect of reaction volume on the length of the lag-phase; (b) a volume-dependent threshold effect; and (c) the highly cooperative sigmoidal kinetics of polymerization [15,16]. Although these features could not be rationalized within nucleation-polymerization or the template assisted models, they are consistent with the mechanism of branched-chain reactions.
Employing the theory of branched-chain reactions will greatly benefit our understanding of the prion replication mechanism. The first branched-chain processes were described at the beginning of twentieth century and the branched-chain theory was developed shortly afterward in the 1920s by Nikolay Semenov . Although this theory had enormous impact on the developing chemical industry and nuclear sources of energy, the Nobel Prize for this amazing discovery was not awarded until 1956, almost half a century later . A number of odd features including a strong dependence of the reaction rate on the volume or the shape of reaction vessel, the presence of a lag-phase, threshold effects and a strong dependence of the reaction rate on microimpurities observed for this type of reactions raised serious cautions and even jokes among conventional chemists. It took more than 30 years for the chemical community to be convinced that this theory was not heretical. Certainly, the history of developing the branched-chain mechanism and the ‘protein-only’ hypothesis of prion replication share many things in common.
What is more surprising, the theory of branched-chain reactions explains equally well such diverse processes as an atomic explosion or prion replication. Among key characteristics of the branched-chain mechanism is the multiplication of active or catalytic centers in the time course of the reactions, a feature that makes these processes similar to the autocatalytic reactions (Fig. 1). In a simplified expression, the reaction rate is determined by the multiplication coefficient (r), which is proportional to the probability of generating new active/catalytic centers divided by the probability of their loss or quenching. Depending upon the rate of multiplication versus quenching, the reactions may switch between auto-acceleration and decay modes. When multiplication exceeds quenching (r > 1), the reaction proceeds with self-acceleration. If the rate of quenching is higher than the rate of multiplication (r < 1), the reaction decays. When r is equal to 1.00, the number of active centers remains constant during the reaction time; therefore, the kinetics of such reactions follow the formal mechanism of enzyme catalysis (Fig. 1). However, apparently negligible changes in experimental parameters, such as the presence of microimpurities or a change in the shape of the reaction vessel, may alter the r-value and switch the reaction to decay mode or to auto-acceleration mode. The branched-chain reactions have been known to be unusually ‘sensitive’ to slight changes in experimental parameters that might be seen as stochastic behavior, in which the reaction follows the ‘all or nothing’ rule.
It is important to indicate that the branched-chain mechanism is consistent with the sigmoidal kinetics of fibrillation, which has been previously referred to as ‘nucleation-elongation’ kinetics (Fig. 2). According to the nucleation-polymerization model, the lag-phase in the fibrillation process corresponds to the nucleation step, a stage when mature fibrils are not yet formed (Fig. 2A). By contrast to this prediction, we found that mature fibril were present at the lag-phase of rPrP fibrillation [16,19]. This observation is consistent with the branched-chain mechanism that attributes the lack of an observable signal during the second part of the lag-phase to the limitations in detecting small amounts of the final reaction products (i.e. in this case, fibrils) (Fig. 2B). As soon as the final reaction products are formed even in miniscule amounts, the reaction rate is accelerated due to the branched-chain mechanism of multiplication of active centers. Therefore, in a branched-chain mechanism, the length of the lag-phase is regulated by the rate of multiplication of active centers. The higher the rate of multiplication, the shorter is the lag-phase (Fig. 2C). The branched-chain mechanism predicts that the rate of fibril fragmentation controls the length of lag-phase and the cooperativity of sigmoidal kinetics (Fig. 2C). In our yet unpublished studies, we, indeed, observed substantial differences in the length of the lag-phase and polymerization rate of PrP fibrillation reactions that were carried out under identical solvent conditions, but subjected to different fragmentation intensities (O. V. Bocharova & I. V. Baskakov, unpublished results).
The mechanism of the branched-chain reaction predicts three potential outcomes for prion disease. Depending on the dynamic balance between the rate of multiplication versus clearance, prion disease could: (a) progress very quickly to the clinical form (if >> 1, the kinetics of PrPSc (Sc-scrapie) accumulation follow the formal mechanism of branched-chain reactions); (b) develop very slowly and exist at subclinical level for a long period of time (r = 1, the kinetics of PrPSc formation follow the formal mechanism of enzyme catalysis), or (c) never progress (r < 1, PrPSc is cleared, the rate of clearance follow apparent first order kinetics). It has been shown that the concentration of PrPSc in the brain of experimental animals drops substantially in the first week after intracerebral inoculation [20,21], indicating that the rate of clearance may exceed the rate of multiplication during the initial stage of prion transmission. Despite substantial resistance to proteolytic digestion, the life-time of PrPSc was found to be relatively short (only 28 h) [22,23]. Therefore, for the disease to progress to the clinical stage, the rate of PrPSc multiplication should eventually exceed the rate of clearance. If the process of multiplication of the active PrPSc form is slower than the degradation, PrPSc will be cleared throughout an animal's lifetime.
The critical role of the multiplication of active centers is reflected by the history of the development of an experimental procedure for cell-free prion replication. Successful amplification of prion infectivity in vitro was not achieved until the repetitive steps of fibril fragmentation were introduced as a part of the experimental protocol. In 1995, Caughey and coworkers demonstrated that PrPC (C-cellular) can be converted into the proteinase K (PK)-resistant form, referred to as PrP-res, in the presence of PrPSc in a cell-free system [24,25]. In these studies, however, only small amounts (approximately 20%) of PrPC supplied to the reaction mixtures were converted into the PrP-res form despite a 50-fold molar excess of PrPSc used as a seed. In subsequent studies, unlimited amplification of PrPSc was achieved in the conversion reactions referred to as misfolding cyclic amplification by introducing repetitive cycles of elongation and fragmentation, where fragmentation was induced by short pulses of sonication [26–28]. Without sonication, substantially lower levels of PrPSc amplification were reported, illustrating that sonication is critical for multiplication of active replication centers [29,30].
What factors regulate the clearance and multiplication of active PrPSc centers? Multiple effects may contribute to the clearance of PrPSc: strain-specific intrinsic stability of PrPSc[31,32]; species and tissue-specific variations in proteolytic activity [33,34]; interactions of PrPSc with cellular cofactors such as glycosaminoglycans [35–37] or polysaccharides  that stabilize PrPSc. Removal of active PrPSc centers could also occur due to aggregation of PrPSc into large plaques or oxidative modification of amino acid residues on the PrPSc surface that are involved in prion replication. Our previous studies revealed that sorption of self-propagating amyloid fibrils to walls of reaction vessels may account for deactivation of active seeds in vitro, resulting in dramatic volume-dependent threshold effects [15,16]. For the majority of branched-chain reactions, the multiplication coefficient r depends on the ratio of surface to volume of the reaction vessel . Vessel surfaces may either catalyze or deactivate active centers, thus having a significant impact on the lag-phase and final yield of the reactions. The volume-dependent threshold is consistent with the scenario that self-propagating forms of rPrP are adsorbed and deactivated by the vessel surface. As the reaction volume decreases, the surface-to-volume ratio grows. Therefore, the threshold may be reached when the rate of surface-dependent deactivation exceeds the rate of multiplication of self-propagating forms. Indeed, we found that amyloid fibrils have high propensity to adsorb to walls of the reaction tubes made from different materials . Binding of fibrillar rPrP to surfaces is reminiscent of that of PrPSc. It is known that prion diseases can be efficiently transmitted through wires and surgical instruments contaminated with PrPSc[39–42]. Although sorption of the active amyloid seeds seems to be a peculiar property of in vitro fibrillization, it may, in fact, mimic the clearance of the PrPScin vivo, and therefore provide mechanistic insight into prion replication mechanisms.
With regards to the multiplication of active centers, both external cofactors and the intrinsic fragility of PrPSc fibrils should control the rate of multiplication. It is important to note that the fibril elongation does not result in multiplication of the active or catalytic centers, unless fibril fragmentation occurs (Fig. 1). Cellular chaperones were found to be involved in fragmentation of yeast prion fibrils . Cellular cofactors participating in fragmentation of mammalian prion fibrils have yet to be identified. The intrinsic fragility (i.e. the ability of fibrils to fragment into shorter pieces) seems to be controlled by the conformational stability of amyloid fibrils and, specifically, by the stability of the cross-β-fibrillar structure  (Y. Sun & I. V. Baskakov, unpublished data). Recent studies have revealed a strong link between conformational stability and the intrinsic infectivity of fibrils formed by the yeast prion protein Sup35 . The amyloid fibrils that displayed low conformational stability exhibited a high efficiency of infection with the large majority of colonies showing a strong phenotype. Vice versa, fibrils that had high conformational stability displayed low infectivity and produced ‘weak’ strains that disappeared fast or that could be easily cured. A similar correlation between conformational stability and infectivity was observed for synthetic mammalian prions [45,46]. Both yeast and mammalian prion studies indicated that the intrinsic infectivity of fibrils might be controlled, at least in part, by the conformational stability of the cross-β-sheet core, an unexpected lesson that we have learned . If the intrinsic fragility of PrPSc aggregates does dictate the rate of prion propagation, this property could account for substantial differences in the incubation times produces by different strains of PrPSc. Future studies will determine whether conformational stability proves to be the missing link in our search for the physical determinants of prion fibril infectivity. Elucidating the relationship between conformational stability and infectivity may help us to answer the intriguing questions as to why are some but not all amyloidogenic proteins capable of forming infectious fibrils, and why are some but not all types of amyloid fibrils made of the same protein infectious.
Ulstrastructure of PrP amyloid fibrils
In recent years, there has been considerable debate as to whether small nonfibrilar oligomeric particles are more pathogenic or infectious than amyloid fibrils [47,48]. A discussion regarding a plausible role for fibrillar or nonfibrillar PrP aggregates in the pathological process is meaningless unless the physical properties of β-structures and their origin are specified. The key criterion in our classification of variable β-sheet rich forms should be their substructure, and not size. Our judgment as to whether PrP aggregates are fibrillar or nonfibrillar is often made solely base on techniques with poor spatial resolution such as light microscopy. Light microscopy has been utilized historically for neuropathological studies and used often for classification of prion aggregates. Using light microscopy only, it is easy to confuse nonfibrillar oligomers with small fibrillar fragments (Fig. 3). In fact, the size distribution of fibrils is very broad and, at any given time, includes very small or short fibrillar fragments. Short fibrils or their fragments can be generated at the initial stages of fibril elongation, but also produced as a result of fibril fragmentation. In addition to small fragments, fibrils might form aggregates of various shapes and densities (Fig. 3). Although fibrillar aggregates or plaques are believed to be less pathogenic, they might serve as repositories of more pathogenic small fibrillar fragments and therefore are equally important. Regardless of the fibril size and shape, the key feature of fibrils is cross-β-sheet structure, which is essential for the prion self-propagating activity. Moreover, the cross-β-sheet structure of amyloid fibrils is substantially more stable kinetically and thermodynamically than the structure of nonfibrillar oligomeric species, ensuring that fibrils remain assembled and preserving their physical properties even at low biologically relevant concentrations of PrP.
Because the infectious form of PrP has been often referred to as nonfibrillar in nature, it is important to evaluate the validity of such claims. First, if infectious prions are indeed nonfibrillar, the question of how could oligomeric nonfibrillar species be infectious in the absence of the self-propagating cross-β structure needs to be answered. Second, the vast majority of experimental procedures used for extraction and purification of PrPSc involved sonication, treatment with detergents and, sometimes, freezing and thawing [49–51]. All of these steps cause severe fragmentation of fibrils. In our experience, sonication for only 1 min is sufficient to fragment fibrils into small fibrillar fragments that could easily be confused with nonfibrillar particles (Fig. 3B).
In our search for physical properties that are essential for prion infectivity it is important to gain information about the substructure of PrP fibrils. What regions of PrP molecule adopt cross-β-sheet conformation within amyloid fibrils? Can we control the conformational stability of cross-β-sheet core?
The large size of PrP molecules in combination with the highly aggregated, heterogeneous and insoluble nature of PrP fibrils precluded application of NMR and other high-resolution techniques. In the absence of methods to solve structure of PrP fibrils in the near future, we employed several alternative approaches for elucidating ultrastructure of fibrils. High resolution atomic force microscopy revealed that fibrils produced in vitro from the full-length rPrP consisted of several laterally assembled filaments . In our recent studies, we found that the fibrils produced under single growth conditions varied with respect to the number of constitutive filaments and the manner in which the filaments were assembled. The high-order fibrils formed through a highly hierarchical mechanism of lateral assembly. At each step, filaments were found to associate in pairs in a pattern resembling dichotomous coalescence (Fig. 4) [19,52]. Because of alternative modes of lateral assembly, fibrils produced under a single growth condition were heterogeneous with respect to the width, height and twisting morphology.
How many PrP molecules are packed per 1 nm within an amyloid fibril? As judged from atomic force microscopy (AFM) measurements and atomic volume calculations, a single full-length rPrP polypeptide occupied a distance of approximately 1.2 nm within a single filament (Fig. 5A) . The amyloid fibrils are known to be build of β-strands oriented perpendicular to the fibrillar axis with the distance between two neighboring β-strands of approximately 4.8 Å. Therefore, the axial distance occupied by one rPrP molecule should be equivalent to approximately 2.5 layers of β-strands. Our studies using PK digestion assay revealed that the PK resistant core of the amyloid fibrils consisted of residues 138/141–230, 152/153–230 and 162–230, where the fragment 162–230 was the most resistant to PK digestion (Fig. 5) [53,54]. Upon treatment with PK, the 152/153–230 and 162–230 PK-resistant fragments maintained fibrillar structure and preserved a high β-sheet context with strong intermolecular hydrogen bonds. Remarkably, the β-sheet rich fibrillar cores encompassed by residues 152/153–230 and 162–230 were found to maintain high seeding activity in vitro despite cleavage of the N-terminal and central regions [53,55]. Consistent with these studies, the rPrP regions 159–174 and 224–230 were observed to be buried in the fibril interior and were the most resistant to GdnHCl-induced denaturation as judged from the newly developed dual color immunofluorescence microscopy assay (Fig. 5) . The 132–156 segment was cryptic under native conditions and solvent-exposed under partially denaturing conditions, whereas region 95–105 was solvent-accessible regardless of the solvent conditions . In fibrils formed from truncated rPrP 90–230, the residues 169–230 showed the slowest hydrogen exchange rate confirming that the C-terminal part is involved in the β-sheet structure . Site-specific conformational studies revealed that the C-terminal region accounts for the high conformational stability of amyloid fibrils . As judged from the C1/2 values, the conformational stability of the residues within the region 127–230 were found to be similar to the global stability of the amyloid structure, whereas the stability of residue 98 was substantially lower than the global stability, but approached that of natively folded proteins .
Taken together, the data accumulated to date have indicated that the C-terminal part of the rPrP molecule encompassing residues 152–230 and 162–230, and possibly 169–230, acquires cross-β-sheet self-propagating core in amyloid fibrils [53,54,56–58]. These regions account for the high conformational stability and structural integrity of fibrils. The central regions encompassing residues 90–150 are likely to be involved in forming the fibrillar interface that participates in lateral interactions between filaments within mature fibrils. Whether the PrPSc infectious particle has a substructure similar to that of rPrP fibrils generated in vitro remains to be determined in future studies.
I.V.B. is supported by a National Institute of Health grant, NS045585.