This paper presents a qualitative analysis of COVID-19′s impact on the development, delivery, and uptake of “Favoring Myself”, a school-based interactive wellness program conducted via Zoom during 2020–2021. “Favoring Myself” targets resilience, self-esteem, body-esteem, self-care behaviors, and media literacy among 5th-grade preadolescents. Data were obtained from meetings, 23 semi-structured interviews with parents, teachers, and principals, and other modes of correspondence. All data were transcribed and thematically analyzed. The analysis highlighted the barriers faced when delivering external programs during COVID-19. Parents’ difficulties in cooperating with the program, distrustful relationships between parents and the education system, as well as teachers’ overload and stress, were identified as barriers to the external program’s sustainability. These challenges are discussed in light of previous studies of school-based programs, the psychological and social contexts of an ongoing crisis and the impact of neoliberalism on education. This study concludes that school-based prevention programs and accompanying research should be more flexible and focus on understanding and relating to parents’ and schools’ fears, uncertainties, and resistance. It is the hope of the authors that knowledge created through this exploration will be helpful in future coping vis-à-vis prevention program teams and recipients in times of unpredictable, unmanageable, and overpowering crises. This article explores parents’ and teachers’ engagement and difficulties in co-operating with the wellness program “Favoring Myself” and its accompanying research during the COVID-19 pandemic. “Favoring Myself”—a school-based resilience program—was integrated into the school curriculum in Israel four years ago. The program’s contents and face-to-face delivery effectiveness have been studied extensively see, for example, . When thThe following literature review explores the importance of cooperation between prevention program teams, teachers, and parents. Then, the literature on the influence of the COVID-19 pandemic on educational systems in general and mainly on remote learning is reviewed. Finally, a description of “Favoring Myself” follows, with its accompanying research, and the modifications this program has undergone to make it relevant to current conditions.The socio-ecological scientific prevention method, as well as other universal, and multimethod programs advocate approaching multiple levels, with the understanding that promoting the strengths of children, parents, and schools may lead to multiple positive outcomes ,4,5. In The recent COVID-19 outbreak has challenged youth’s ability to continue to perform tasks, develop, and achieve goals under conditions of vulnerability, helplessness, uncertainty, and a relative lack of control over outcomes . During In terms of COVID-19′s influence on relationships, it has been found that students and their parents who are confined to their homes feel stressed and anxious and that relationships between the parents and schoolteachers become strained . Consequ“Favoring Myself” is an interactive, school-based, wellness program that has been integrated into the school curriculum in Israel as part of a module on life skills initiated by the National Ministry of Education in primary schools. The program highlights key protective factors to increase resilience and well-being, reduce risk behaviors and prevent internalizing unrealistic sociocultural norms. The program consists of ten 90-min weekly sessions ,2 with eA.A unique community coordinator assisted with recruiting and addressing the difficulties caused by COVID-19.B.Duration of sessions was reduced from 90 to 60 min. Lengthy discussions were replaced by interactive activities.C.Each class was divided into two sub-groups that attended the program during different hours to enable their class teacher to participate in both.D.School-team collaboration: (1) An introductory Zoom conversation was conducted with each school team. (2) To facilitate supervision of instructors by teachers, as well as communication among all members of the program team, a computerized form was implemented. (3) Each school principal was advised to request that the head of the parents’ committee support the program.E.Engagement strategies for the 5th-grade participants included the following: (1) Two pupils were chosen in each class to assist the facilitators, motivating the group to attend and complete assignments. (2) A competition was planned between classes, measuring attendance, cooperation rate, and task submission. (3) Facilitators reached out to the fifth-grade participants before and after the program sessions, sending humorous messages as reminders to practice the skills taught in class.F.Parental component: (1) Parents received information about the program content, structure, and previous outcomes, along with a link to a short video describing the program. (2) Consenting parents received weekly updates about the topic discussed and its importance, and one or two shared assignments to be practiced with their children. (3) Two reminders were sent to participants who did not complete the weekly assignment. (4) An assignment delivered by both the child and a parent received two stars, while those produced only by the child received one star.G.Evaluative research modification: (1) A Kahoot simulation questionnaire was created to prepare pupils to answer the research questionnaire. (2) The program facilitators discussed the various feelings participants might experience when they faced questions, they were not sure of how to answer or felt embarrassed about. (3) Each subgroup of 12 to 14 participants was divided into two Zoom breakout rooms, and additional research assistants were present in each room to assist pupils who had difficulties in understanding the questionnaire.With the outbreak of COVID-19, it was clear that some modifications would have to be made in order to implement preventive strategies , includiThe current article is based on a qualitative study, aimed to understand the perceptions and opinions of parents and school teams to the implementation of “Favoring Myself” and its accompanying effectiveness research during the COVID-19 pandemic.Choosing a qualitative approach stemmed from the search for an interpretive, subjective manner of studying people’s own perceptions of events to understand and interpret reality from their points of view, highlight and explain life experiences, and give them meaning. Qualitative research allows us to deeply explore different perspectives and to discover the complexities of situations through a holistic framework ,25,26. QThe four educational institutions in which the program was conducted are in the north of Israel, serving a financially comfortable population. Since data included protocols of meetings, phone calls, and WhatsApp contacts, all the people involved in the program from 2020 to 2021 are considered as participants in this study. In addition, twenty-three people agreed to be interviewed at the program’s completion. The school principals were asked to invite all the teachers and parents who were involved in the project to contact the researchers if they were willing to be interviewed regarding their experiences with “Favoring Myself”. Initially, only two school principals, three teachers, and six parents contacted the researchers. Using a snowball method, additional interviewees were recruited. Finally, two school principals, five 5th grade teachers, and sixteen parents were interviewed. The interviewed parents represented various attitudes and behavioral responses to the program that year: Six were highly engaged with the parental component of the intervention, four refused to consent to their child’s participation in the study, and six withdrew their consent for their child’s participation and involvement in the parental component.This study received approval from the College Institutional Review Board . Parents and school teams received information about the program and the qualitative study and provided their informed consent via computerized links. All the procedures involved in this study comply with the ethical standards of the 1975 Helsinki Declaration and Consort 2010 guidelines and regulations.1.Data from meetings of the research team with the schools to set shared objectives, build trust, and discuss ways to address participants’ engagement.2.WhatsApp messages and telephone calls: Some parents who had concerns regarding the program sent messages to the teachers and researchers. These messages were saved. Phone calls from parents were documented by teachers, facilitators, and researchers as soon as possible after their completion.3.Zoom meeting: To avoid the escalation of parents’ agitation in one of the schools, the first author suggested that the school principal host a Zoom meeting with interested parents and school team members. A 1.5-h discussion with 30 volunteering parents and the school’s fifth-grade teachers was conducted via Zoom by the first author and the school principal, during the second week of the program. This meeting, in which parents expressed a great deal of anger and frustration, was recorded, with the consent of all participants, and then transcribed.4.Interviews: At the program conclusion, twenty-three in-depth, semi-structured personal interviews (see Data were obtained from the program’s participants and collaborators: school principals, teachers, and parents using the following methods:Data from all resources were analyzed using the thematic analysis approach. Reading and re-reading the texts was initially performed, and side notes were taken. Then, the researchers identified recurring key themes that shed light on interviewees’ experiences and attitudes. Stories of different participants which seemed to have common motives were connected, in order to represent processes  and undeThis analysis gave us profound insight into school principals’, teachers’, and parents’ reactions toward the program as well as a deeper understanding of the relationship between the parents and the education system in times of persistent crisis.A thematic analysis of data obtained from preparatory meetings, emails, WhatsApp messages, interviews, and the Zoom meeting, identified themes, which are presented hereby divided into school reactions, parent reactions, and parent–school relationships.The reactions in the educational systems can be divided into school’s ambivalence, teachers’ difficulties in co-operating with facilitators, and principals’ reactions.due to the uncertainty regarding the reopening of the schools, the teaching methods, and handling of the schools’ competing needs”. They said, “It is not the right time for these decisions.” Finally, four schools chose to enroll, providing their consent only in October 2020, but only three of them adhered to the program’s agreed schedule. The fourth school slated the program time to the afternoons, which resulted in the absence of pupils who had joined a basketball class. The school’s coordinating teacher was quite upset: “I failed to convince the principal that changing the program’s schedule would decrease participants’ motivation”, and also noted that no one considered that changing the time of the program imposed personal challenges: “I had to be present during these sessions after my teaching day had ended.”Unlike in previous years, schools were reluctant to commit to the program, which manifested itself from the onset in principals’ inconsistent responsiveness to the program’s community coordinator’s calls. After receiving information letters with a link to a three-minute video highlighting the program’s importance, objectives, and novelty, only seven out of the seventeen approached schools expressed their interest. During the initial months of recruitment, principals were not ready to commit ““a lack of gratitude from the participants’ parents, which made it hard to remain involved and motivated”. One of them said: “I understand that it is an important program, and I see the facilitators’ efforts, but I cannot supervise them thoroughly. I am always in a rush to my next class.”Although introductory Zoom meetings were attended by the vast majority of teachers of eligible classes, and most of them expressed enthusiasm towards the program and agreed to the research demands, eventually many of them had a hard time maintaining their ongoing collaboration with the program’s facilitators. While some teachers provided helpful feedback to the group facilitators after sessions, many failed to do so consistently. In the interviews, these teachers self-confessed that they were exhausted after having experienced “didn’t want to fuel the fire” and that the parents were too upset for them to “confront them over an external program” or that “the parents overreacted, even violently, to the program, and to protect myself, I took a step back and maintained a cordial relationship with them.”In addition, only one teacher out of the four classes in which parents mounted resistance to the program, attempted to mediate and negotiate with these parents. The other teachers confessed that they The following quote from one of the teachers seems to express the complexity of their experience: “I have gone above and beyond to recruit participants to attend these lessons, stayed after my working hours. And combined with the emotional burden of my students and the lack of privacy, ‘Favoring Myself’ was not prioritized”. This teacher’s experience demonstrates how, despite good intentions, cooperation became almost impossible.School principals varied in the way they coped with the challenges surrounding the program’s delivery during the COVID-19 pandemic.“The questionnaire and the program relate to complex and latent topics that are not discussed in most households… the child’s teacher and school counselor attend the sessions and explain the research topics to participants. Our objective is to educate a mature, aware, and resilient generation”.One of the principals sent out a clarification letter to the parents, in which she explained the importance of the program as part of a mandatory lesson, and the choice of “Favoring Myself” due to its excellent reputation. Relating to parents’ concerns regarding sensitive issues she explained: In his interview, another principal explained, “Dealing with our parents is complicated, which we know from experience. Now they are more antagonistic than ever before”. A third school principal asserted, “Despite the good intentions of the program’s facilitators and the class teacher, this year, introducing the program was an incorrect decision. It is a wonderful program with great objectives. Still, such sessions lose their effectiveness over a Zoom platform where participants’ privacy is compromised, and implementation is problematic due to the exhaustion of the system and the teachers, and the sacrifices that have been made this year.”Parents’ reactions are divided into their reactions to the program itself and their experiences with the accompanying study.“the program includes intimidating topics that should be discussed delicately and not by young students as facilitators.” Thus, for example, a mother praised one of the assignments but objected to uploading a picture of her and her son exercising on the class WhatsApp group: “I do not understand why I should share our activities with others. It bothered me.”Parents’ views of the sessions varied. Some appreciated the opportunity, while others felt that “if I do not like to perform the shared assignments, I am the ‘bad guy’ who causes my child’s class to receive fewer stars.” One of the mothers stated, “It bothered me when I heard my daughter tell her friend that if they do not complete the assignments, their group will not get the stars. This is social pressure,” or: “If this is a positive challenge, why bribe them?”As mentioned earlier, one of the modifications to the program due to the pandemic was adding a competition game component in order to encourage attendance and performance of assignments by the child or the family. Competition between classes was perceived by some parents as harmful because Our children sit in front of the screen for so many hours a day as it is. We may say we are in control, but the truth is we are not.” On the other hand, and potentially as a reaction, the Zoom classes were perceived and presented by parents as an opportunity to observe teachers’ and facilitators’ conduct. One of the mothers said, “I sat and watched many of these lessons. Some are nice, but sometimes you hear the facilitator pushing the children into a corner.” One of the mothers stated, “You are using our children for a damaging experiment, and I say so because this program has never been delivered on Zoom.”Interestingly the delivery of the program over the Zoom was experienced as two-folded. On the one hand, it was perceived as problematic, as one mother stated: ““existing load of assignments”, or feeling that “such a study should not be conducted during the COVID crisis”, and ending with extreme reactions, such as saying that they did not want their child to be “treated as a guineapig” or to be “forced to participate in the study”. “It is not acceptable that our children are obligated to answer personal questions,” said one of the fathers.Parents’ reactions to the research were overall quite negative, varying from passive non-cooperation, such as forgetting to turn in forms they agreed to sign, to moderate complaints focusing on the burden of filling out questionnaires by their child, who already had difficulties with his/her “wake up sleeping dogs.” For example, a mother who felt that her daughter “never worried about her body, and as a person who suffered from eating disorders in the past, I do not want her to answer these questions.” A somewhat more practical and moderate approach was expressed by parents who suggested that “if the whole questionnaire and the program protocols had been sent to parents earlier, we might have felt differently.”.Some parents were worried that specific themes appearing in the questionnaires would from my point of view, clear boundaries were crossed here and under the roof of our local school.” In relation to the study, one of the parents wondered, “Who in our school permitted the research process?” Other parents were more concerned with their child’s confidentiality and addressed their school’s management with questions such as “How do you secure our children’s privacy?” Teachers also had their own reactions to being distrusted and criticized by parents. One of the teachers commented on the parents’ protest, saying, “The class teachers accompanied this process. You talk as if we were not there. We were there to mediate.” A school principal described the parents as “opinionated and suspicious”.Some parents expressed anger towards the school or the school’s management. A parent wrote, “The current research addresses some of the barriers faced when attempting to establish academic–school–parent collaboration for the application of a wellness program during the COVID-19 pandemic.According to the results, parents expressed ambivalence toward the program. Initially, they agreed to their children’s participation, and some of them were pleased with certain activities or sessions. But when they were expected to perform assignments with their children and consequently were exposed to the program’s more personal and sensitive themes, various parents reacted with anger and criticism. In response to parents’ concerns that research on body image might precipitate body or eating problems in their child, it was explained that previous research has shown a very low prevalence of distress due to children’s participation in body image research . NeverthMany parents were also opposed to the use of incentives to encourage attendance and performance of assignments. They talked about “bribing” and “social pressure”. General resistance was elicited, mainly when a few parents, quarantined at home, saw their children struggling to complete the research questionnaire. They saw the questionnaire as a sign of exploitation of their children by the program, the facilitators, and the researcher. Consequently, they condemned the school and program staff for damaging their children’s well-being. They were not appeased by the calming statements from the class teachers, school counselor, principal, and the first author.Some parents were annoyed by the facilitators’ and researchers’ expectations that they would join their children’s assignments. COVID-19 has changed teaching and learning processes , puttingParents’ rageful comparisons of their children to laboratory animals, may be a reflection of worldwide disputes around the COVID-19 vaccine. Skepticism about vaccine development , fear ofTheir resentment and worries resemble the findings of other studies regarding the general mood during the pandemic. Current research shows that many people experienced distress, including anxiety, depression, and over-excitement ,23. It s“over an external program”.Teachers’ reactions to the program were characterized by frustration and even a sense of helplessness. This finding is consistent with Carlson’s  study shRegarding parent–school relationships, the results resemble previous studies, which have demonstrated strained relations between parents and schoolteachers during the pandemic ,20. An iThis parental response also resonates with neo-liberal education policies which promote parental educational rights, responsibilities, and involvement, while encouraging them to express their choices, and legitimizing their refusal to obey school instructions. Hornby et al.  have she“this year the initiation of the program was an incorrect decision” may have articulated the experiences of the program’s team as well. Indeed, many school-based wellness interventions have been suspended during the pandemic [Finally, building on studies and theories supporting the effectiveness of socio-ecological prevention methods , “Favoripandemic .It, therefore, seems important to suggest ways in which prevention program teams and developers may cope with future unpredictable crises. Fornaro, Struloeff, and Flowers  who studFornaro, Struloeff, and Flowers  also sugThis research provides essential information about the barriers faced in prevention programs during times of crisis. Twenty-three interviews, a group meeting, WhatsApp messages, and emails are regarded as a small sample, to draw general conclusions. Qualitative research, however, does not demand bigger samples since its reliability and validity are achieved through a deeper analysis of an existing sample with its multiplicity of voices ,48. In a“Favoring Myself” is rooted in the socio-ecological scientific prevention approach  and is d


Dear EditorWe recently read an article written by Leo Nherera et al. . The autFirst, the research conducted by Yu et al.  was actuSecond, in the “Study selection and eligibility criteria” section, the inclusion criteria were described as “Adults with intertrochanteric hip fractures with subtrochanteric extension or subtrochanteric fractures,” which did not correspond to the purpose of this article, because subtrochanteric fractures are much different from intertrochanteric fractures, not to mention that this leads to a greater heterogeneity.Third, only 188 patients were recruited in 2 RCTs and these cases were far from enough, given this meta-analysis involved 987 cases and 6 researches. Furthermore, although the authors claimed RCTs were assessed with the Cochrane Collaboration's risk of bias tool, the risk of bias graph was not found in this study. Meanwhile, the Newcastle–Ottawa Scale  was usuaFourth, the included researches were either conducted in Turkey or China; however, the authors did not mention ethnic bias which could be critical to the conclusion. Also, only 2 or 3 included researches were applied in some subgroup analysis.The controversies above may weaken the reliability of this meta-analysis. As a result, more studies need to be carried out to clarify these issues.


There are a variety of governance mechanisms concerning the ownership and use of patents. These include government licenses, compulsory licenses, march-in rights for inventions created with federal funding, government use rights, enforcement restrictions, subject-matter restrictions, and a host of private governance regimes. Each has been discussed in various contexts by scholars and policymakers and some, in some degree, have been employed in different cases at different times. But scholars have yet to explore how each of these choices are subject to—or removed from—democratic control. Assessing the range of democratic implications of these patent governance choices is important in understanding the social and political implications of controversial or wide-ranging technologies because their use has a significant potential to affect the polity. This paper seeks to unpack these concerns for genome editing, such as CRISPR, specifically. Patents covering genome editing make an interesting case because, to date, it appears that the polity is concerned less with certain kinds of access, and more with distribution and limits on the technology’s particular uses, such as human enhancement and certain agricultural and environmental applications. Here, we explore what it means for patents to be democratic or non-democratically governed and, in so doing, identify that patents covering many of the most controversial applications—that is, ones most likely to gain public attention—are effectively controlled by either non- or anti-democratic institutions, namely, private restrictions on licensing. This may be effective—for now—but lawmakers should be wary that such restrictions could rapidly reverse themselves. Meanwhile, other choices, like compulsory licenses, more broadly touch on democratic deliberation but, as currently structured, are aimed poorly for particular applications. Insofar as the public wants, or perhaps deserves, a say in the distribution and limits of these applications, illuminating the ways in which these governance choices intersect—or fail to intersect—with democratic institutions is critical. We offer some concluding thoughts about the nature of patents and their relationship with democratic governance as distributed claims to authority, and suggest areas for scholars and policymakers to pay close attention to as the genome editing patent landscape develops. Few technologies are recognized as revolutionary immediately upon their invention. CRISPR—a form of altering DNA sequences inside living cells, or “genome editing”—stands out among those . Like otCRISPR is a form of genome editing, the ability to alter the constituent DNA of a living cell (its “genome”), at will using an engineered—and infinitely malleable—bacterial immune system . It is cAs a powerful, commercially valuable technology, CRISPR is subject to a broad patent estate. Foundational patents covering a basic iteration of the technology are owned by the Broad Institute in Cambridge, Massachusetts (a joint effort between MIT and Harvard University) and the University of California, Berkeley, among other collaborating academic institutions . Beyond While certainly not ignored—and indeed, explicitly mentioned by the WHO’s recent report on governing human genome editing —patents These licensing regimes—despite all ultimately being forms of technology control—have differing intersections with democratic theory. Some are receptive to the usual instruments of representative democracy, such as the polity’s support for research funding for certain applications and not others. Other regimes are one step removed, those where legislative representatives have petitioned patent holders to change their licensing practices. At other end these examples lies private licensing regimes, like those from the Broad Institute, that seem, at first blush, entirely undemocractic. But they are likely similarly receptive to faces of lay, participatory democracy, the populous demanding measures from private actors wielding significant amount of power.Understanding all of this should be important to theorists and policymakers alike. For theorists, it brings patent licensing as a democratic mechanism of technology control, however successful, to the fore. It also suggests that patent licensing—long thought of as an elitist business—has more nuanced democratic implications, especially for controversial technologies like genome editing. This should similarly be useful to policymakers and advocacy groups seeking legally salient mechanisms to control technology in manners responsive to broader constituencies. This paper examines these features—patentsas technology governance, and patent licensing as democratic instrument—in two parts.exclude others from making, using, selling, or importing particular inventions (35 U.S.C. § 271(a))—not, as is commonly misunderstood, an affirmative right to use them.Patents are one form, among many, of intellectual property. They are legal instruments that protect inventions from being copied by others without permission of the patent holder. In this way, patents operate as a right to This right to exclude is a limited right and only operates for a limited time: all patents expire, currently 20 years from the date when their underlying applications are filed. While international treaties harmonize a variety of the world’s patents laws—including this expiration period —patents Moving from a patent application to a government-issued patent is nontrivial. Around the world patents undergo a substantive examination to assess whether the claimed invention is worthy of protection. Inventions sought to be patented must meet a variety of statutory requirements; in particular, that the underlying invention is new, useful, and—as the concept is articulated in US law—“nonobvious,” i.e., a significant improvement over the prior state of the art (35 U.S.C. § 103). The patent document itself must also properly disclose inventions to the world, broadly enabling those with skill in the art to make and use and invention; describing the invention fully and with particularity; and noting that the invention has some nontrivial use (35 U.S.C. § 112(a)). In addition, patents conclude with claims—single sentence recitations of the underlying invention—that define the specific contours of the patent right (35 U.S.C. § 112(b)). Claims, too, must be sufficiently specific and intelligible to those with skill in the patent’s art.Patents are also not self-enforcing; they must be policed by their owners. This is typically accomplished through litigation, i.e., suits for patent infringement. Generally speaking, an entity infringes a patent where they use the claimed technology in some manner without the permission of the patent holder (35 U.S.C. § 271). The remedy, if there is a finding of infringement, is often either a measure of damages to compensate the patent holder  or a court-ordered injunction, stopping the infringer from the accused activity.Despite these limitations, patents are powerful instruments. Patent infringement, while not a crime, can bring with it serious financial penalties. In the United States, damages for major patent infringement disputes now routinely eclipse $1 billion USD . Further1 For purposes of this paper, we focus less on those decisions as effectuated through substantive patent law—that is, laws concerning which inventions get patented in the first instance, like the nonobviousness requirement—and turn our attention instead to policies surrounding patent licensing and their relationship to democratic or nondemocratic institutions of power. While we focus primarily on United States licensing practices, we note that many of the licensing policies described here have close analogues around the globe—or, in other cases, are harmonized by treaty. Licensing restrictions, potentially more than substantive patent law, have potential to speed or hinder technological development, to place it in the hands of a select few or many, and to decide which applications can be broadly used and under what conditions. Government policies on technology licensing are, too, policies of technological governance and have implications for democratic oversight.Whatever role patents play in technology development—a hotly contested area of scholarly debate—government policies concerning patent licensing have the potential to ultimately affect access, distribution, and conditions of use on particular technologies. Patent licenses are permissions from patent holders to use a given piece of technology. Like other property rights, patent licenses are subject to a variety of government policies regarding when, whether, and to what extent they can be used. Those policies, the most significant of which are catalogued here, further bring with them important choices about democracy and polity—who, ultimately, has rights to access the technology and under which conditions.Through extramural grants and other programs, governments often fund a substantial amount of research and development within their borders—globally, about $2 trillion USD per year . In the Taken broadly, this regime—that public funding grants the government the right to freely use a patented invention—can be construed as a mixed public-private governance mechanism for the development and use of technologies. At the outset, governments must choose which technologies to fund, decisions that are ideally responsive to the desires of the underlying polity. Cancer research, for example, receives a substantial amount of government funding because combatting cancer is politically popular . PickingRelated to the Bayh-Dole Act’s government license provisions are the Act’s rules regarding “march-in rights.” March-in rights allow a government funding agency to “march in” and forcibly grant others a patent license for a funded technology if the funding recipient has not sufficiently commercialized the invention. As set forth in the relevant statute, march-in can occur if the patented invention has not “achieve[d] practical application” or is needed to “alleviate health or safety needs,” among other cases (35 U.S.C. § 203(a)). Notably, while threats of exercising march-in rights occur from to time, no U.S. agency has ever formally used the provision .Like government licenses, march-in rights, too, can be viewed as a mixed public-private governance mechanism for the distribution of technologies. Again, the public chooses which broader area of technology to fund, while private funding recipients largely direct which implementation of that technology gets developed and whether it will be patented. The benefit of this bargain, in theory, is that the public will have practical, commercial access to the technology, once developed. But where the funding recipient or later patent holder has not commercialized the underlying technology to make it available to the public, government  has authority to wrest it from private hands. In theory, at least, such governance is a balance between private rights and public benefits from the technology it, itself, has funded. And indeed, recent march-in threats have been couched in just such terms. A 2016 march-in petition directed to the National Institutes of Health and signed by 51 members of Congress requested the agency use its march-in authority “to respond to the soaring cost of pharmaceuticals” by licensing patents “developed with taxpayer funds, [that] are keeping those in need from being able to access care” . March-in, is consequently, a governance mechanism over government funded research “intended to distribute the fruits of those labors to the public” .Apart from licensing those inventions which it funds, the government also possesses the right to use inventions owned and patented by private entities. In the United States, one statute, 28 U.S.C. § 1498(a), allows the government to use or manufacture a patented invention “without license of the owner thereof.” Unlike government licenses or march-in rights, however, such a use is not free: the government, after a trial, must pay the patent owner a “reasonable and entire compensation for such use and manufacture.” (28 U.S.C. § 1498(a)). This provision, colloquially referred to as § 1498, has, in fact, been used in the United States in the past, most notably, in the late 1950s when the Military Medical Supply Agency used the provision to cut costs on tetracycline, a popular antibiotic, for personnel . More reSection 1498, consequently, can also be viewed as an instrument of technology governance, a public restriction on private ownership of patented technology. It essentially removes the right of patent holders to forbid the government from using the claimed technology, irrespective of the technology’s development history or its genesis from the coffers of government. The public—faced with outsized expenses regarding a particular technology or some other pressing need—can move patented technology from behind private walls into the public sphere, so long as the government pays the patent owner compensation for its use. This larger conflict regarding access to privately owned technology sounds in various aspects of democratic theory concerning the public’s right to safety, health, and welfare and its power to use purely private property to effectuate such ends .Analogous to § 1498, are compulsory patent licenses, the requirement a private patent holder license the claimed technology to another private entity. While compulsory licenses are essentially unheard of in American law, they are well defined by international treaty, such as the 1994 TRIPS Agreement. Compulsory patent licenses have recently been used in Brazil, Ecuador, India, South Africa, and Thailand, among other countries . Other cCompulsory licenses, in this way, present many of the same governance choices as does § 1498, i.e., a public restriction on private ownership of patented technology. While they have largely been used in the public health context—to lower drug costs, for example—compulsory licenses occupy a broader institutional power. They can be used, under article 31 of the TRIPS Agreement, for cases of “national emergency or other circumstances of extreme urgency”—a readily pliable standard. Compulsory licenses are, therefore political choices concerning the distribution of private property in cases of extremis—when too few own too much of a beneficial good, and the government’s rights in expanding access. And, like other political choices, they are a resolution a societal tensions between the government’s role in respecting private property and democratic process concerning its distribution. One analysis of compulsory patent licenses in Canada—and their diminishment following the North American Free Trade Agreement—characterized this tension in compulsory licenses as just that: between “subjecting domestic law to corporate-led agreements…[and] democratic process in Canada” .Whereas compulsory licenses allow the government to compel patent license to others—that is, without the permission of the patent-holder—the government also has the power to restrict patent licenses if the underlying license agreements violate public policy. There are a variety of circumstances under which such restrictions arise, although they mainly center on various aspects of promoting market competition. One particularly prevalent example concerns “reverse payment agreements,” the practice of patent-holders paying others to take licenses to their technologies, often because the underlying patents are of questionable validity or it is a cost-effective way at keeping others out of the market for a given period of time . There aRestrictions on patent licensing govern circumstances under which private agreements regarding access to technology. Unlike some of the other cases described above, these do not immediately concern the public’s use of the technology or, as with § 1498 or compulsory licensing, the government picking winners and losers to use technology. Instead, they center on platting a level (and broad) playing field for private participation in a given technology. This is layered on an already substantial literature exploring the relationship between democratic ideals and the antitrust laws. Recently, for example, Lina M. Kahn drew a deep connection between the market power of online platform services, such as Amazon, and their potential to diminish democratic values, even in absence of traditional antitrust concerns like consumer welfare . Patent Beyond these public patent licensing governance regimes, there is a wealth of private ones. Private patent holders largely possess the right to license their patents to whom they want to on, and on a variety of financial and practical terms. The largest divide, perhaps (at least in terms of access and distribution to a given patented technology) is whether the license is exclusive or nonexclusive—that is, whether the technology will be licensed exclusively to a single other entity or broadly licensed among a variety of market participants. But there are, to be sure, various gradations in between .This right to license brings with it a right to establish licensing conditions governing specific uses or development restrictions over a particular technology, i.e., barring licensees from engaging in particular veins of research or development. This occurred most recently with a suite of genome editing patents owned by the Broad Institute. The Broad Institute, for its patents covering its CRISPR technologies, established a tiered regime system for its licenses concerning whether they were used for academic research, tool development, or commercial products . In addiThese private license restrictions are themselves a form of private governance, here, a profit-seeking company’s autonomy to determine how a technology gets developed and on what terms. In some instances, they are commendable and dovetail with governance values centered around attention and expertise. Oftentimes, private licensors are experts in the technology’s field and know most about a given technology’s societal dangers and technical pitfalls . But sucSince CRISPR genome-editing technology was first described in 2012 , governmBeyond these patents, the number of CRISPR patents and patent applications has exploded since the technology’s invention. A seminal 2016 paper by Egelie et al. catalogued the patent landscape for CRISPR technologies through 2014, finding hundreds of patent applications distributed across the globe. Since then, others have landscaped CRISPR patents in China, India, and South Africa, among other countries, and reached similar conclusions .Meanwhile, the CRISPR technology itself has significantly evolved, beyond the Cas9 enzyme and basic forms of genomeediting, to synthetic forms of CRISPR enzymes and powerful, precise applications to make a variety of manipulations to the genome . In addiThere is a strong expectation CRISPR technology will continue to be improved and continue to be patented. The academic literature demonstrates that CRISPR technology will continue evolve; new applications of CRISPR are announced frequently. As a consequence, there will be more patents covering various forms of CRISPR, held by many more players, in more than countries than current patent landscape analyses suggest. Much of this is a consequence of the technology’s susceptibility to “democratization,” i.e., its ability to be cheap, powerful, flexible, and easy to use . At the What is democratic governance? What do we mean when we say a government or system is democratic? Defining or identifying key markers of democracy help illuminate its qualities and evaluate how or why its absence is deleterious to society, to the public (as opposed to private) interest, or to general welfare. With respect to the patent licensing as an instrument of governance, two broader principles of democratic theory are worth exploring: The first is an understanding of democracy as an equalizing political power, redistributing power away from elites and toward a greater majority or group . The secIn the case of CRISPR, one of the primary concerns is that its powerful effects will be used to benefit some groups disproportionately and create discriminatory outcomes for others. Patent licenses have the ability to maintain the high cost of therapies, to consequently affect the availability of insurance coverage, and to stymie competition. In addition, patent licenses often shape which diseases are studied for commercial development . That is, “it is precisely the novelty and power of CRISPR—and the potential effects of its patent landscape on the public health—that counsel us to solve these problems before it is too late for patients” . To be cYet this is not to say that such choices should primarily focus on equal access as an end in itself. Given the nature of patent licensing—almost always with at least one private actor involved—these benefits should be primarily evaluated instrumentality. Do they get us what the public wants, even if achieved by private actors? Democracies are not only desirable descriptively, but legitimate insofar as a broader distribution of power creates the conditions for bettering public welfare . This maThis may have implications for private licensing insofar as greater government reliance on private licensing to regulate technology means that the government becomes more and more accountable to private interests, and less so to the public’s interest. This is, in some ways, concerning with respect to ethical licensing restrictions as imposed by the Broad Insitute on its CRISPR patents. Relying too much on this model risks corrupting democratic institutions regarding technology distribution by eroding their ability to distribute resources equitably. In other words, efforts to correct such reliances after the technology has expanded becomes stymied as they become increasingly captured by private interests, giving sway to their desire to earn a profit or thrive above considerations of the public .global distribution efforts have faltered and remain vastly unequal  their constituents. Recent threats of government use rights, for example, were born from the wellspring of constituent demands . And yetWithin this context, therefore, it is notable that it is the legislature—rather than, say, an elitist judiciary—that has become the principal site of patent licensing policy and nuance. In the modern age, democratic rule typically means electoral democracy, with the mark of a “healthy” or “stable” democracy one in which there are frequent and fair elections of representatives . “MirrorThe relationship between profit-maximizing capitalism and representative democracy is comple. While we do not pretend to fully untangle and resolve it here, we do note that patent governance has the potential to be responsive to such democratic interests or remove them from the public entirely. This is analogous, perhaps, to regulatory agencies mandate to protect the public from private interests’ cost-cutting, a bulwark protecting safe, reliable, and healthy products for consumption. Increasing the distance from the sight of decision-making runs the risk of making representative legislatures less democratically accountable even as it serves an important function in the system.What role then do or should the populous have in engaging directly in democratic institutions? While there is good precedent in including people through deliberative opportunities in one-off events, what would democratic engagement in patent license governance look like if it were institutionalized? Does this governance construct even make sense given that most people may not even know what patents are, how CRISPR works, or what impacts this intersection may have on their lives?There are roughly two ways of thinking about public engagement through deliberation: One is through creating or carving out systems of inclusion, such as town halls or participatory budgeting. The other is through allowing groups to participate by creating collective power that acts on institutions from the outside, such as patient advocacy groups that organize to pressure rightsholders to understand their views and push for resources (or object to such work). Beyond these formal collectives, there is renewed interest in creating randomly selected bodies of lay people, like a citizens jury, to assess public perceptions of new technologies . If giveFor genome editing technologies like CRISPR, deliberative forums are likely to include a variety of disability rights groups and environmental protection organizations who are certain to have, for some use cases, diverging views. A number of groups, for example, have advocated for patent holders to turn their attention to particular, oft-neglected diseases, including Duchenne muscular dystrophy . Some ofAt the same time, few of these groups or their allies have considered ways in which patent licensing could effectuate their goals, either through representative government or directly, to patent holders. One notable exception is MIT professor Kevin Esvelt’s proposal to use patent licensing (and the threat of infringement) to police CRISPR “gene drive” technology—a strategy that has been noted by some advocacy groups . In thisGiven these conditions, political theorists interested in using patent licensing as a form of democratic technology governance should consider ways to reduce the democratic deficit of these spaces of power and decision-making authority. And in conjunction, those interested in patent governance should consider ways in which deliberative forums like mini-publics are being included in governance decisions around the world . IncludiThese kinds of deliberative forums, also known as mini-publics, have varied in kinds, sizes, and selection mechanism and could be convened by institutions responsible for patent licensing decisions, including private entities or, in the case of public licensing, Congress. Similarly, the question of patent governance could included on the agenda of broader deliberative events about technology governance, such as the Australian Citizens Jury. While most mini-publics currently play an advisory role, it is conceivable that, as they gain traction, their instrumental value in risk-governance and modes of engagement becomes more politically acceptable. If licensors grant them increasing levels of authority, they stand to actually impact the law.Whereas many people consider the lay public less capable of reaching certain decisions on such technical issues, evidence from such mini-publics as Deliberative Polls and other assemblies shows that mini-publics actually have good capacity for learning and understanding technical material, and weighing risk in ways that are helpful value-based perspectives . Given tOnce the province of the arcane, patents should become a larger part of the conversation concerning technology governance, like that surrounding genome editing, for they are a powerful form of technology governance. Licenses, that is, permissions to use patented technologies, determine who, what extent, and under what terms others than can use them. These include a variety of government set licensing regimes that do just that, including licensing regimes sought by the government itself, march-in rights, government-use rights for others’ patented technologies, compulsory licenses, and restrictions on licenses, to say nothing of private governance regimes with ethical limitations. These licenses are themselves a form of democratic oversight that gives the public the capacity to preventing purely private interests from superseding their own, especially in ways that are dominating, oppressing, or otherwise harmful or unjust.These patent licensing regimes also often intersect and have different democratic purchase. Some, like march-in rights, are effectuated only through the filter of representative democracy, and even then are rarely, if ever, acted upon. Others are subject to non or even antidemocratic norms in a variety of exclusionary ways. At the same time, participatory democracy has the potential to shape patent licensing regimes according to popular will (or whim), an effort to control the development and distribution of technology in ways small enough to be effective, both at the level of government, down to individual patent holders.This a critically important mechanism for a technology like CRISPR, one with such heated public interest and with such intense calls for public accountability. The technology’s applications have grown tremendously alongside increased calls for public engagement. There are serious concerns that certain forms of technology, as released to the wider public, will be permanent facets of society foisted on it without its deliberative input. Meanwhile, the CRISPR patent estates, although once held in the hands of few, are rapidly expanding.Facilitating and incorporating public input for such an expansive technology will likely be a long and difficult task. It is further unclear what, exactly, the public wants for such a wide-ranging technology that has so captured its imagination. Previous efforts, like public commissions, community representatives on government panels, may not be successful to garner a definitive view. Smaller, piecemeal efforts at public engagement over licensing regimes, both public and private, may contribute to better digestible—and more effective—forms of democratic technology governance both because they can be asked a more targeted policy question and because they are situated upstream of further distribution policy questions. Using the patents allows the public to better control technology under currently established legal regimes and do so in a way the public deems equitable. The public is better armed to mitigate the domination of private interests.Whether this is viable remains to be seen. Scholars should look to see whether patent licensing regimes are, in fact, being used by government to control genome editing technology and whether the public, through the procedures of deliberative or participatory democracy or otherwise, is interested in using patent restrictions as a governance mechanism. Scholars may also further examine licensing restrictions to see what the terms are and how they are generated.The power of CRISPR, as a technology, ultimately has strongly democratic features insofar as it is the most equitably distributed gene editing tool. It can be used by almost anyone, anywhere in the world, with minimal training and inexpensive reagents. Yet, the technology’s commercial development—and some of its most egregious applications, real and, to date, fictional—have sailed over many democractic controls otherwise taken for granted. Democracy, like CRISPR, can be a powerful corrective technology for the ills of society.


Curcuma longa), is a yellowish polyphenol that has been used traditionally in Asian countries as a medicinal herb for various types of disease and pathological conditions caused by inflammation and oxidative stress. In the present review, we conducted a comprehensive literature search for evidence that shows the effect of curcumin on factors influencing exercise performance, including muscle damage, muscle soreness, inflammation, and oxidative stress. During exercise, reactive oxygen species and inflammation are increased. Thus, if there is no balance between endogenous and exogenous antioxidants and increases in oxidative stress and inflammation, which is important for maintaining redox homeostasis in skeletal muscle, it can lead to muscle soreness and muscle damage and ultimately result in reduced exercise performance. Due to the anti‐oxidant and anti‐inflammatory properties of curcumin, it can increase exercise performance and decrease exercise‐induced muscle soreness and muscle damage. It appears that curcumin supplementation can have positive effects on exercise performance and recovery, muscle damage and pain, inflammation, and oxidative stress. However, there is still a need to precisely evaluate factors to more accurately assess/quantify the beneficial therapeutic effects of curcumin with regard to enhancing exercise performance and recovery.Curcumin, as the main natural compound in the turmeric plant ( Curcumin, by functioning as an antioxidant, may reduce oxidative stress to cells, and especially mitochondria, in the long‐term, as well as positively impact exercise endurance, strength, and recovery to improve overall health. Furthermore, it has been reported that curcumin administration can increase exercise performance due to its anti‐inflammatory and antioxidant properties, as well as through mitochondrial biogenesis , or placebo, for 28 days. The authors reported that curcumin did not affect the plasma total antioxidant capacity (TAC), TNF‐α, and MDA concentration in participants after exercise‐induced muscle damage. However, curcumin supplementation reduced muscle soreness and muscle damage as measured by a visual analog scale (VAS) and plasma CK concentrations, respectively, compared to these same parameters for participants that received placebo ; (2) 7 days after exercise . The results showed that curcumin did not affect TNF‐α, IL‐8, joint range of motion (ROM), and the BAP compared to the placebo when consumption of curcumin occurred after exercise (experiment 2), whereas, it was able to mediate a reduction in elevated IL‐8 levels 12‐h after exercise when it was consumed before exercise (experiment 1). Also, this study indicated a reduction in CK and muscle soreness and an increase in joint range of motion and isometric maximal voluntary contraction (MVC) torque in experiment 2 only , and IL‐8 (up to 2 days) after exercise when compared to these same parameters in the participants who took the placebo, and there were no significant differences in either muscle soreness resulting from normal activities of daily living (ADL's), or IL‐6 and IL‐10, despite a similar response in IL‐8 and TNF‐α . These authors attributed the lack of statistical difference in MRI and immunohistochemcial results to the short duration of the study and the small number of samples used , or placebo (b.i.d), for 4 days (initiated from 48‐h before to 24‐h after moderate aerobic activity). The results showed a lower level of IL‐8 in the curcumin group compared to the subjects in the placebo group; however, despite a slight increase in high‐sensitivity C‐reactive protein, monocyte chemoattractant protein‐1, catalase, GPx, ferric reducing ability of plasma, and CK (as a marker of muscle damage) in the curcumin group compared to the placebo, none of these measurements reached statistical significance between the two groups. In addition, muscle damage was assessed using both MRI and histological analyses 48‐h after the exercise. Results from MRI showed a reduction in muscle damage in the posterior or medial compartment of the right and left thigh in the treatment group compared to the placebo, while immunohistochemical staining did not show any change in sarcolemmal damage between the two groups  and the expression of TNF‐α, IL‐6, and IL‐1β, as well as inhibited TLR4‐mediated NF‐KB signaling pathways , joint range of motion (ROM)  may have a negative effect on exercise. In our previous study, we provided a comprehensive review of the hormetic behavior of curcumin under different conditions (Moghaddam et al., oxidative stress, while those participants that engaged in regular exercise of moderate intensity had lower levels of oxidative stress (Radak et al., Finally, as mentioned previously, it is essential to consider the intensity, duration, and type of exercise, as well as the appropriate dose of curcumin, when evaluating the positive effects of curcumin on exercise performance. Numerous studies have shown that curcumin and exercise both have a hormetic effect, which is defined as a 2We reviewed the existing evidence for the effects of curcumin administration on exercise performance in preclinical studies and clinical trials. The preclinical studies in this review strongly support the beneficial effects of curcumin administration in reducing exercise‐induced complications, including muscle damage and muscle pain, which are thought to occur due to a reduction in inflammation and oxidative stress. Accordingly, this results in better exercise performance and a faster recovery. While the clinical evidence has shown promising results for curcumin supplementation to mediate a reduction in muscle damage and pain, inflammation, and oxidative stress, it is not overwhelmingly convincing. In general, it appears that curcumin supplementation can have positive effects on exercise performance and recovery, muscle damage and pain, inflammation, and oxidative stress, especially when taken after the exercise. However, there is still a need to further examine factors such as bioavailability, dosage, frequency of curcumin administration, time of curcumin supplementation relative to the time at which the exercise occurs, and the type and intensity of the exercise, as well as the age and gender of the athlete. Finally, curcumin, via its antioxidant properties, may be effective in reducing cellular oxidative stress, especially in mitochondria over the long term, as well as positively impacting exercise endurance, strength, and recovery to improve overall health.None.


The evolution of diverse phenotypes both involves and is constrained by molecular interaction networks. When these networks influence patterns of expression, we refer to them as gene regulatory networks (GRNs). Here, we develop a model of GRN evolution analogous to work from quasi-species theory, which is itself essentially the mutation–selection balance model from classical population genetics extended to multiple loci. With this GRN model, we prove that—across a broad spectrum of selection pressures—the dynamics converge to a stationary distribution over GRNs. Next, we show from first principles how the frequency of GRNs at equilibrium is related to the topology of the genotype network, in particular, via a specific network centrality measure termed the eigenvector centrality. Finally, we determine the structural characteristics of GRNs that are favoured in response to a range of selective environments and mutational constraints. Our work connects GRN evolution to quasi-species theory—and thus to classical populations genetics—providing a mechanistic explanation for the observed distribution of GRNs evolving in response to various evolutionary forces, and shows how complex fitness landscapes can emerge from simple evolutionary rules. But, l states ,13.et al. [Over the past two decades, several models of gene regulatory network (GRN) evolution have been proposed –19, whicet al.  showed cet al.  demonstrMore recently, studies integrating empirical data with computational models have hypothesized how an expanded set of evolutionary forces may shape the structure of GRNs –35. The When genotypes are expanded to more complicated sets of genes, the long-term stationary solution for a population genetic model describing their evolution can be studied with quasi-species theory ,45. UsinHere, we derive analytical conclusions for models of GRN evolution using an approach similar to those taken in population genetics and quasi-species theory . However. 2. 2.1We begin with a quasi-species model that incorporates selection, asexual reproduction and mutation such that the viable individuals in the current generation reproduce and generate their offspring, which experience mutation and undergo selection to form the next generation  be its genotype and It is viable. Here It survives, and It−1 → It the event that the randomly sampled individual at generation t − 1, namely It−1, reproduced and generated the randomly sampled individual at generation t, namely It. We use More formally, suppose that tafter selection. In other words, we would like to know the probability that we observe a randomly sampled individual at generation t with genotype g, given that the sampled individual is viable. Applying Bayes’ theorem, this focal conditional probability becomesviability of genotype g, and the average viability at generation t.For any genotype gbefore selection. The derivation of It depends on the unique genotype of its parent and any subsequent mutation; second, this parent individual must be viable. The event g(It) = g is hence partitioned1 by the joint events mutational probability from genotype g′ to genotype g.What we have left in equation  is the pt has genotype g′. Applying Bayes’ theorem once more, this probability becomesreproductivity of genotype g′, and t − 1. Note that, instead of defining reproductivity as the number of offspring an individual has, the probabilistic formulation describes reproductivity as—when sampling from the infinitely sized next generation—how likely is one to observe an offspring of the focal genotype.Finally, equation  is the pt − 1, a randomly sampled individual has genotype g′ given that it is viable. Combining t − 1, a . 2.2pathway framework, to describe how the structure of GRNs varies due to genetic changes and how they respond to a given selective pressure [In the existing literature on quasi-species theory, the model parameters are usually arbitrarily tunable or follow an assumed distribution for simplicity. Hypothetically, these parameters depend on the resultant phenotypes of the genotypes, and any genotype–phenotype mapping reflects constraints and provides information on the model parameters. In previous work, we proposed a modelling approach, termed the pressure ,19 .possibly appear in the organisms, and the state of a protein is binary, which indicates whether the protein is present or absent in an organism. Second, assuming that any gene’s expression is activated by a single protein and produces a single protein product, the allele of the gene becomes the ordered pair of protein activator/product. If the protein activator is in the present state, the allele of the gene turns the state of the protein product to present. Third, there is a fixed collection of genes In this work, we focus on a minimal pathway framework of GRNs which relies on a few additional assumptions. First, we assume there is a constant collection of proteins Under these assumptions, a GRN can be transformed from its conventional notion, where nodes in the network represent genes and the edges show regulation among them, into a more compact format such that the nodes are exactly the constant collection of proteins, and the directed edges describe the expression behaviour of alleles of genes see . HereaftThe pathway framework provides an approach to model various evolutionary forces, such as random mutation and natural selection, through graphical operations and structural characteristics on the GRNs. Mutation at a gene changes its allele stochastically, which is essentially a random process over all possible pairs of protein activators/products in the constant collection . 2.3genotype network of GRNs is a undirected network of networks, where every possible GRN becomes a mega-node, and two mega-nodes are connected if the two corresponding GRNs differ only by an allele at a single locus. In other words, an edge between two mega-nodes in the genotype network represents a single-locus mutation between GRNs  and/or recombination ,60,61. Heen GRNs . Instead network ,61, whicWe emphasize two important properties of a genotype network of GRNs and its induced sub-graphs under the pathway framework. First, because the underlying collections of proteins and genes are fixed, and a mutation at any gene can lead to a mutant allele that points from any protein activator to any protein product, each GRN has the same number of mutational neighbours. As a result, the genotype network of GRNs is in fact a regular graph. Second, for any phenotypic constraint, we show that the resulting induced sub-graph of the genotype network is connected. In other words, there always exists a sequence of single-locus mutations between two GRNs such that the involved GRNs all satisfy the arbitrarily given constraint on their phenotype. The guaranteed connectedness also applies to the neutral network of GRNs, where the phenotypic constraint corresponds to protein states leading to the same viability and reproductivity.gs and gt satisfying the phenotypic constraint. This trajectory consists of three segments—between gs and a naive GRN g′, between g′ and another naive GRN g″, and finally between g″ and gt—and all GRNs traversed by the mutational trajectory also satisfy the given phenotypic constraint.We leave to electronic supplementary material, appendix C the detailed proof for the connectedness of a sub-graph of the genotype network induced from arbitrary phenotypic constraint, but provide a brief outline here. The proof is based on a few observations of the pathway framework of GRNs. Under the assumption of binary protein states, there naturally exist some protein activator/product pairs that are ‘redundant’ in terms of the resulting phenotype. Such redundancy manifests when the product is simply the activator itself, or when multiple genes share the same activator/product pair. Furthermore, given a phenotypic constraint, one can come up with a family of ‘naive’ GRNs that satisfy the constraint. Specifically, such a ‘naive’ GRN is constructed by (i) for each required-present protein, assigning it as the product of a gene with an external stimulus as the activator and (ii) assigning the rest of genes with redundant activator/product pairs. Our proof in electronic supplementary material, appendix C systematically finds a mutational trajectory between two GRNs . 3. 3.1g with a zero viability, i.e. g from a randomly sampled individual that has survived selection is also zero. Formally speaking, denoting those GRNs with a non-zero viability by t. Second, we denote the GRNs with a zero reproductivity by t, we have Our goal now is to prove the convergence of the quasi-species model  under tht into a column vector pt). Next, we must show that the mutation probability μg′g is positive as well. Recall that, when constructed through the pathway framework of GRNs, the sub-graph of the genotype network induced by any phenotypic constraint is connected . More formally, the connectedness among GRNs constrained by a non-zero viability and reproductivity implies that, for any g′ to g through GRNs in g′ to mutate to g within one generation,2 i.e. μg′g > 0. As a result, we observe that T is a positive matrix.The matrix equation , and it T is symmetric and provide the proof for a non-symmetric T in electronic supplementary material, appendix D. In this case, the eigenvectors T are linearly independent and form a basis of n-dimensional vectors, where Tpt) and consequentlyv1 and λ1 are the leading eigenvector and the leading eigenvalue of T, respectively. Since T is a positive matrix, by the Perron–Frobenius theorem, we have |λ1| > |λi| for every i > 1, which guarantees the convergence of equation . Therefore, under the pathway framework of GRNs, the master equation  is the number of genes with different expression behaviour between g′ and g.Third, given the underlying collection of proteins T into a seriesigth row and the ig′th column of matrix Tk is ρμg′ g if d = k and 0 otherwise. Observe that T0 is proportional to the identity matrix I (of a proper size), and T1 is proportional to the adjacency matrix3 of the neutral network of GRNs (see §2.3), which we denoted by A. Writing μ, equation  = d, the theory of eigenvalue perturbation [T converges to the leading eigenvector4 of A,the probability distribution of viable GRNs converges to a stationary distribution that is proportional to their eigenvector centrality in the neutral network.We further consider the scenario that mutations are rare events, specifically, under the limit urbation ,63 ensurequation , we haventrality ,65 of th7 parallel populations. The simulations are parametrized with the constant sets of input proteins. We also assume that at least one protein only has direct physiological effects and cannot activate any of the genes in the network, which we call the output proteins. Under this minimal set-up, there are a total of To validate the predicted probability distribution of GRNs under mutation–selection balance, we simulate the evolution of 105 and given a current generation, the next generation is generated through randomly choosing viable GRNs from the current generation with replacement followed by potential mutations with a per-locus mutation probability μ = 0.1. We begin with 10 000 different initial populations where the GRN of every individual is chosen uniformly at random from all possible GRNs 7 parallel populations are evolved for a constant number of generations, and we randomly sample one viable GRN from each of them to form the simulated distribution of GRNs. This fixed length of evolution is determined through the temporal lower bound such that the resulting GRN distribution is theoretically close enough to the stationary distribution within a given level of error tolerance . In electronic supplementary material, figure S7, we show that our approximation holds for population sizes of 1600 and in electronic supplementary material, figure S8 with larger population sizes and much lower mutation rates (μ = 0.001).We simulate the evolution of parallel populations using a Wright–Fisher model . Specifi7 independent samples from the predicted distribution , the most prevalent GRNs are the ones where several redundant genes are directly activated by an external stimulus and produce the essential protein (group (i)). When redundant genes are excluded (group (vi)), the prevalent GRNs have multiple parallel paths between the external stimuli and the essential proteins. When constrained such that genes activated by the external stimuli cannot produce the essential protein (group (vii)), the prevalent GRNs similarly show multiple pathways that share the same intermediate genes. Jointly imposing the two constraints mentioned above (group (viii)) results in prevalent GRN structures that maintain multiple, distinct regulatory pathways within the same GRN.Finally, when both essential and fatal proteins exist (environment 7) and GRNs are unconstrained, the most probable networks only contain redundant genes that are directly activated by the stimulus and synthesize the essential target (groups (i), (ii) and (iv)). When we constrain GRNs such that they cannot have redundant genes, the prevalent regulatory structures typically only have a single pair of connected genes, one that is activated by the external stimuli and whose protein product activates a second gene that produces the essential protein (groups (iii) and (vi)). If we further require the activation of genes or exclude direct selection on individual genes (groups (v), (vii) and (viii)), we again see multiple pathways emerge in the prevalent GRNs.. 4In this work, we analyse the evolutionary dynamics of GRNs under a quasi-species model with selection, mutation and asexual reproduction. Integrating this model with the pathway framework of GRNs, we analytically show that the population dynamics always converge to a stationary distribution of GRNs given any arbitrary viability function. This stationary distribution characterizes the ensemble of regulatory networks under mutation–selection balance, and it reveals the structural features of GRNs predicted to be favourable under long-term evolution. Next, we investigate a case study assuming binary viability, identical reproductivity and rare mutation, and find that the stationary distribution of GRNs can be derived from the topology of the genotype network alone. Specifically, the probability of observing a GRN under mutation–selection balance is proportional to each GRN’s eigenvector centrality in the neutral network, which—in this simplified model—is a sub-graph of the genotype network consisting of all viable GRNs. Using this approximation, we identify the network structures which are most likely to evolve in response to various selective regimes and regulatory constraints.et al. [Our primary contribution to the broader field of quasi-species theory (and hence population genetics) is a mechanistic explanation for the key assumption of irreducible transition matrices –48. As wet al.  concludeet al. . Despiteet al. .Our result that a GRN’s eigenvector centrality in the neutral network is proportional to its fitness sheds light on how we may interpret the prevalence of GRNs under rare mutation and strong selection. When first introduced by Bonacich , the eiginviable neighbours. In other words, the observed GRNs under various environmental conditions represent a balance between survival, reproduction and the number of viable neighbours in the neutral network. We emphasize that this concept of robustness emerges naturally from our mechanistic, quasi-species model of GRN evolution rather than an a prior assumption about important properties of GRNs.The observed prevalent structures of GRNs in our analyses also provide an alternative explanation for evolutionary robustness. We inductively find that prevalent GRNs are those with a minimal number of inviable mutational neighbours (see §3.3). Since the genotype network is a regular graph under the pathway framework of GRNs , i.e. every GRN has the same number of mutational neighbours, GRNs with equal viability and reproductivity can still have different fitness if they have different numbers of et al. [et al. [et al.’s [degree instead of the eigenvector centrality in the neutral network [Previous work has also found that the topological features of genotype networks can be related to evolutionary processes of interest. For example, evolvability has been approximated by the size of the genotype network of a given phenotype , as wellet al.  adopted  [et al.  were theet al.’s  conclusi network .The current scope of this work is not without limitation. First, we assume a constant, static environment in which the population evolves, whereas populations certainly experience shifting or alternating environmental conditions –74. ConsAcross a broad range of models, our work demonstrates that the neutral network of GRNs is always connected  and tha