Chimeric hepatitis B surface antigen virus-like particles expressing the strep A epitope p*17 elicit a humoral immune response in mice.

To optimize immunogenicity, bacterial epitopes in putative vaccine constructs can be presented to immune cells as multiple repeated structures on a defined nanoparticle. Virus-like particles (VLPs) are viral capsid proteins that self-assemble to form compact and highly ordered nanoparticles that are within the optimal size range for uptake by dendritic cells. VLPs mimic the live virus in size and form but contain no viral genetic material, are therefore noninfective and are the basis of safe and effective vaccines against hepatitis B virus (HBV) and human papillomavirus (HPV). Due to their particulate nature, molecular stability, and expression of high density and repetitive antigen displays, recombinant cell culture-derived VLPs are ideal platforms for the delivery of small molecules, including bacterial epitopes. We developed a putative vaccine by expressing a minimal epitope from the bacterium Streptococcus pyogenes (Strep A) on the surface of a recombinant VLP comprising multiple copies of HBV small envelope protein (HBsAg-S). Strep A is responsible for a wide spectrum of human infections and postinfectious diseases that disproportionately affect children and young adults living in resource-poor communities. No vaccine is currently available to offer sufficiently broad protection from the numerous and diverse strains of Strep A endemic in these at-risk populations. The Strep A antigen targeted by our vaccine construct is p*17, a cryptic epitope from a highly conserved region of the Strep A M-protein with demonstrated enhanced immunogenicity and broad protective potential against Strep A. To ensure surface expression and optimal immunogenicity, we expressed p*17 within the immunodominant "a" determinant of HBsAg-S. The recombinant VLPs (VLP-p*17) expressed in HEK293T cells spontaneously formed 22 nm particles and induced the production of high titers of p*17-specific IgG in BALB/c mice immunized with three 0.5 µg doses of VLP-p*17 formulated with adjuvant.

Disruption of IL-17-mediated immunosurveillance in the respiratory mucosa results in invasive Streptococcus pyogenes infection.

Introduction: Streptococcus pyogenes is a Gram-positive pathogen that causes a significant global burden of skin pyoderma and pharyngitis. In some cases, infection can lead to severe invasive streptococcal diseases. Previous studies have shown that IL-17 deficiency in mice (IL-17-/-) can reduce S. pyogenes clearance from the mucosal surfaces. However, the effect of IL-17 on the development of severe invasive streptococcal disease has not yet been assessed. Methods: Here, we modeled single or repeated non-lethal intranasal (IN) S. pyogenes M1 strain infections in immunocompetent and IL-17-/- mice to assess bacterial colonization following a final IN or skin challenge. Results: Immunocompetent mice that received a single S. pyogenes infection showed long-lasting immunity to subsequent IN infection, and no bacteria were detected in the lymph nodes or spleens. However, in the absence of IL-17, a single IN infection resulted in dissemination of S. pyogenes to the lymphoid organs, which was accentuated by repeated IN infections. In contrast to what was observed in the respiratory mucosa, skin immunity did not correlate with the systemic levels of IL-17. Instead, it was found to be associated with the activation of germinal center responses and accumulation of neutrophils in the spleen. Discussion: Our results demonstrated that IL-17 plays a critical role in preventing invasive disease following S. pyogenes infection of the respiratory tract.

Efficacy of Alum-Adjuvanted Peptide and Carbohydrate Conjugate Vaccine Candidates against Group A Streptococcus Pharyngeal Infection in a Non-Human Primate Model.

Vaccine development against group A Streptococcus (GAS) has gained traction in the last decade, fuelled by recognition of the significant worldwide burden of the disease. Several vaccine candidates are currently being evaluated in preclinical and early clinical studies. Here, we investigate two conjugate vaccine candidates that have shown promise in mouse models of infection. Two antigens, the J8 peptide from the conserved C-terminal end of the M protein, and the group A carbohydrate lacking N-acetylglucosamine side chain (ΔGAC) were each conjugated to arginine deiminase (ADI), an anchorless surface protein from GAS. Both conjugate vaccine candidates combined with alum adjuvant were tested in a non-human primate (NHP) model of pharyngeal infection. High antibody titres were detected against J8 and ADI antigens, while high background antibody titres in NHP sera hindered accurate quantification of ΔGAC-specific antibodies. The severity of pharyngitis and tonsillitis signs, as well as the level of GAS colonisation, showed no significant differences in NHPs immunised with either conjugate vaccine candidate compared to NHPs in the negative control group.

A CAF01-adjuvanted whole asexual blood-stage liposomal malaria vaccine induces a CD4+ T-cell-dependent strain-transcending protective immunity in rodent models.

IMPORTANCE: Malaria is a devastating disease that has claimed many lives, especially children <5 years of age in Sub-Saharan Africa, as documented in World Malaria Reports by WHO. Even though vector control and chemoprevention tools have helped with elimination efforts in some, if not all, endemic areas, these efforts have been hampered by serious issues (including drug and insecticide resistance and disruption to social cohesion caused by the COVID-19 pandemic). Development of an effective malaria vaccine is the alternative preventative tool in the fight against malaria. Vaccines save millions of lives each year and have helped in elimination and/or eradication of global diseases. Development of a highly efficacious malaria vaccine that will ensure long-lasting protective immunity will be a "game-changing" prevention strategy to finally eradicate the disease. Such a vaccine will need to counteract the significant obstacles that have been hampering subunit vaccine development to date, including antigenic polymorphism, sub-optimal immunogenicity, and waning vaccine efficacy.

Hiding in plain sight: an epitope-based strategy for a subunit malaria vaccine.

Recent data suggest that approaches to developing a subunit blood-stage malaria vaccine may be misdirected. While antigenic polymorphism is recognized as a challenge, efforts to counter this have primarily involved enhancing the quantity and quality of antibody with potent adjuvants, identifying conserved target proteins, or combining multiple antigens to broaden the immune response. However, paradoxically, evidence has emerged that narrowing, rather than broadening, the immune response may be required to obtain an immune response protective against multiple Plasmodium strains. Non-immunodominant, conserved epitopes are crucial. The evidence comes from studying the immune response to red cell surface-expressed antigens but should also be applicable to merozoite surface antigens. Strategies to define the targets of these highly focused immune responses are provided.

Malaria Vaccines: Progress to Date.

Malaria is a mosquito-borne disease caused by protozoan parasites of the genus Plasmodium. Despite significant declines in malaria-attributable morbidity and mortality over the last two decades, it remains a major public health burden in many countries. This underscores the critical need for improved strategies to prevent, treat and control malaria if we are to ultimately progress towards the eradication of this disease. Ideally, this will include the development and deployment of a highly effective malaria vaccine that is able to induce long-lasting protective immunity. There are many malaria vaccine candidates in development, with more than a dozen of these in clinical development. RTS,S/AS01 (also known as Mosquirix) is the most advanced malaria vaccine and was shown to have modest efficacy against clinical malaria in phase III trials in 5- to 17-month-old infants. Following pilot implementation trials, the World Health Organisation has recommended it for use in Africa in young children who are most at risk of infection with P. falciparum, the deadliest of the human malaria parasites. It is well recognised that more effective malaria vaccines are needed. In this review, we discuss malaria vaccine candidates that have progressed into clinical evaluation and highlight the most advanced candidates: Sanaria's irradiated sporozoite vaccine (PfSPZ Vaccine), the chemoattenuated sporozoite vaccine (PfSPZ-CVac), RTS,S/AS01 and the novel malaria vaccine candidate, R21, which displayed promising, high-level efficacy in a recent small phase IIb trial in Africa.

A Glycolipidated-liposomal peptide vaccine confers long-term mucosal protection against Streptococcus pyogenes via IL-17, macrophages and neutrophils.

Mucosally active subunit vaccines are an unmet clinical need due to lack of licensed immunostimulants suitable for vaccine antigens. Here, we show that intranasal administration of liposomes incorporating: the Streptococcus pyogenes peptide antigen, J8; diphtheria toxoid as a source of T cell help; and the immunostimulatory glycolipid, 3D(6-acyl) PHAD (PHAD), is able to induce long-lived humoral and cellular immunity. Mice genetically deficient in either mucosal antibodies or total antibodies are protected against S. pyogenes respiratory tract infection. Utilizing IL-17-deficient mice or depleting cellular subsets using antibodies, shows that the cellular responses encompassing, CD4+ T cells, IL-17, macrophages and neutrophils have important functions in vaccine-mediated mucosal immunity. Overall, these data demonstrate the utility of a mucosal vaccine platform to deliver multi-pronged protective responses against a highly virulent pathogen.

Exploring the landscape of Babesia bovis vaccines: progress, challenges, and opportunities.

Bovine babesiosis, caused by different Babesia spp. such as B. bovis, B. bigemina, B. divergens, and B. major, is a global disease that poses a serious threat to livestock production. Babesia bovis infections are associated with severe disease and increased mortality in adult cattle, making it the most virulent agent of bovine babesiosis. Babesia bovis parasites undergo asexual reproduction within bovine red blood cells, followed by sexual reproduction within their tick vectors, which transmit the parasite transovarially. Current control methods, including therapeutic drugs (i.e., imidocarb) have been found to lead to drug resistance. Moreover, changing environmental factors add complexity to efficient parasite control. Understanding the fundamental biology, host immune responses, and host-parasite interactions of Babesia parasites is critical for developing next-generation vaccines to control acute disease and parasite transmission. This systematic review analyzed available research papers on vaccine development and the associated immune responses to B. bovis. We compiled and consolidated the reported vaccine strategies, considering the study design and rationale of each study, to provide a systematic review of knowledge and insights for further research. Thirteen studies published since 2014 (inclusive) represented various vaccine strategies developed against B. bovis such as subunit, live attenuated, and viral vector vaccines. Such strategies incorporated B. bovis proteins or whole live parasites with the latter providing the most effective prophylaxis against bovine babesiosis. Incorporating novel research approaches, such as "omics" will enhance our understanding of parasite vulnerabilities.

Reasons for Optimism About Academic Medicine's Actions Against Climate Change.

Since the first mention of climate change in Academic Medicine in 2009, the pace of the climate crisis has accelerated, its impacts on every facet of planetary health have grown more severe, and the urgency for humans to act has become more dire. Medical schools, teaching hospitals and health systems, universities, affiliated organizations, and the millions of people who traverse the halls of these institutions as leaders, physicians, scientists, educators, learners, patients and families, and community members have an obligation to respond. In this commentary, the authors describe 3 reasons they are optimistic that academic medicine will continue to act against climate change. First, the mission of academic medicine, inherently aligned with climate action, propels teaching hospitals and health systems to address climate change to improve the health of patients, families, and communities. Second, younger generations of learners, faculty, and staff who populate the workforce increasingly desire, and often demand, to work at institutions that are aligned with their personal values for climate action. Third, broader forces are pushing academic medicine forward in action against climate change. Economic factors will continue to reduce the cost and increase the return on investment of climate-smart facilities, purchased goods and services, fuel, transportation, food systems, and waste management. The authors are optimistic but not complacent. Current levels of climate action in academic medicine are not nearly enough. Faculty, staff, learners, leaders, patients and families, and community partners can and must apply a "climate lens" to everything they do: weave climate solutions into education, patient care, research, community collaborations, operations, and supply chain and facility management; integrate climate actions into strategic thinking, planning, and doing; address health inequities and climate injustice; and leverage their trusted voices to press for climate action and climate justice in the health sector and in society.

Polymeric epitope-based vaccine induces protective immunity against group A Streptococcus.

Group A Streptococcus (Strep A) is a life-threatening human pathogen with no licensed vaccine. Here, we used a biopolymer particle (BP) approach to display repeats of Strep A vaccine candidate peptides p*17 and K4S2 derived from M and non-M protein, respectively. BPs densely displaying both peptides (BP-p*17-S2) were successfully assembled in one-step inside an engineered endotoxin-free Escherichia coli strain. Purified BP-p*17-S2 showed a spherical core-shell morphology with a biopolymer core and peptide shell. Upon formulation with aluminum hydroxide as adjuvant, BP-p*17-S2 exhibited a mean diameter of 2.9 µm and a positive surface charge of 22 mV. No cytotoxicity was detected when tested against HEK-293 cells. Stability studies showed that BP-p*17-S2 is ambient-temperature stable. Immunized mice showed no adverse reactions, while producing high titers of peptide specific antibodies and cytokines. This immune response could be correlated with protective immunity in an animal model of infection, i.e. intranasal challenge of mice with Strep A, where a significant reduction of >100-fold of pathogen burden in nose-associated lymphoid tissue, lung, and spleen was obtained. The cost-effective scalable manufacture of ambient-temperature stable BPs coated with Strep A peptides combined with their immunogenic properties offer an attractive alternative strategy to current Strep A vaccine development.

Streptolysin O Deficiency in Streptococcus pyogenes M1T1 covR/S Mutant Strain Attenuates Virulence in In Vitro and In Vivo Infection Models.

Mutation within the Streptococcus pyogenes (Streptococcus group A; Strep A) covR/S regulatory system has been associated with a hypervirulent phenotype resulting from the upregulation of several virulence factors, including the pore-forming toxin, streptolysin O (SLO). In this study, we utilized a range of covR/S mutants, including M1T1 clonal strains (5448 and a covS mutant generated through mouse passage designated 5448AP), to investigate the contribution of SLO to the pathogenesis of covR/S mutant Strep A disease. Up-regulation of slo in 5448AP resulted in increased SLO-mediated hemolysis, decreased dendritic cell (DC) viability post coculture with Strep A, and increased production of tumor necrosis factor (TNF) and monocyte chemoattractant protein 1 (MCP-1) by DCs. Mouse passage of an isogenic 5448 slo-deletion mutant resulted in recovery of several covR/S mutants within the 5448Δslo background. Passage also introduced mutations in non-covR/S genes, but these were considered to have no impact on virulence. Although slo-deficient mutants exhibited the characteristic covR/S-controlled virulence factor upregulation, these mutants caused increased DC viability with reduced inflammatory cytokine production by infected DCs. In vivo, slo expression correlated with decreased DC numbers in infected murine skin and significant bacteremia by 3 days postinfection, with severe pathology at the infection site. Conversely, the absence of slo in the infecting strain (covR/S mutant or wild-type) resulted in detection of DCs in the skin and attenuated virulence in a murine model of pyoderma. slo-sufficient and -deficient covR/S mutants were susceptible to immune clearance mediated by a combination vaccine consisting of a conserved M protein peptide and a peptide from the CXC chemokine protease SpyCEP. IMPORTANCE Streptococcus pyogenes is responsible for significant numbers of invasive and noninvasive infections which cause significant morbidity and mortality globally. Strep A isolates with mutations in the covR/S system display greater propensity to cause severe invasive diseases, which are responsible for more than 163,000 deaths each year. This is due to the upregulation of virulence factors, including the pore-forming toxin streptolysin O. Utilizing covR/S and slo-knockout mutants, we investigated the role of SLO in virulence. We found that SLO alters interactions with host cell populations and increases Strep A viability at sterile sites of the host, such as the blood, and that its absence results in significantly less virulence. This work underscores the importance of SLO in Strep A virulence while highlighting the complex nature of Strep A pathogenesis. This improved insight into host-pathogen interactions will enable a better understanding of host immune evasion mechanisms and inform streptococcal vaccine development programs.

Streptococcus pyogenes vaccine candidates do not induce autoimmune responses in a rheumatic heart disease model.

We have developed a candidate vaccine to protect against multiple strains of Streptococcus pyogenes infections. The candidate vaccine contains two synthetic peptides derived from S. pyogenes proteins: the M-protein epitope, p*17 and the IL-8 degrading S. pyogenes Cell-Envelope Proteinase (SpyCEP) epitope, K4S2. In this study we utilise a rat autoimmune valvulitis model that displays both the cardiac and neurobehavioural pathology associated with post-streptococcal sequelae, to assess if the vaccine candidate antigens induce autoimmune complications and inflammatory pathology. Each antigen was conjugated to carrier protein diphtheria toxoid (DT) and independently assessed for potential to induce autoimmune pathology in female Lewis rats. Rats were administered three subcutaneous doses, and one intranasal dose over a four-week study with a two-week recovery period. A positive control group received recombinant S. pyogenes M5 (rM5) protein, and the negative control group received PBS. Rats that received rM5 developed significant cardiac and neurological pathologies. There was no evidence of these pathologies in the PBS control group, or the rats administered either P*17-DT or K4S2-DT. This study provides further preclinical evidence of the safety of the vaccine candidates p*17 and K4S2 and their appropriateness as candidates in human clinical trials.

Assembly of Immunogenic Protein Particles toward Advanced Synthetic Vaccines.

Immunogenic carrier proteins such as the non-toxic diphtheria toxin variant, cross-reacting material 197 (CRM197), are widely used in subunit vaccine formulations to boost immunogenicity of chemically conjugated antigens. Conjugate vaccines are inherently expensive due to laborious manufacturing steps. Here, this work develops a particulate vaccine platform based on using engineered Escherichia coli to assemble CRM197-antigen fusion proteins into discrete submicron-sized particles. This approach enables precise loading of diverse antigens and epitopes enhancing their immunogenicity. A cost-effective, high-yield, and scalable biomanufacturing process is developed. Purified particulate CRM197-antigen vaccines are ambient-temperature stable. CRM197 particles incorporating pathogen-specific antigens or epitopes from SARS-CoV-2, Streptococcus pyogenes (group A), and Mycobacterium tuberculosis induced cell-mediated and humoral immune responses mediating protective immunity in respective animal models of infection. The CRM197 particle vaccine platform is versatile, enabling co-delivery of selected antigens/epitopes together with immunogenic CRM197 as discrete stable particles avoiding laborious manufacture of soluble CRM197 and antigen followed by chemical conjugation.

Extreme Electron Acceleration with Fixed Radiation Energy.

We examine the extreme situation of radiation from an electron that is asymptotically accelerated to the speed of light, resulting in finite emission energy. The analytic solution explicitly demonstrates the difference between radiation power loss and kinetic power loss (null).

A vaccine for human babesiosis: prospects and feasibility.

Babesiosis is a tick-borne disease caused by intraerythrocytic Babesia parasites. It is a well-known illness in companion animals and livestock, resulting in substantial economic losses in the cattle industry. Babesiosis is also recognized as an emerging zoonosis of humans in many countries worldwide. There is no vaccine against human babesiosis. Currently, preventive measures are focused on vector avoidance. Although not always effective, treatment includes antimicrobial therapy and exchange transfusion. In this review, we discuss the host's immune response to the parasite, vaccines being used to prevent babesiosis in animals, and lessons from malaria vaccine development efforts to inform the development of a human babesiosis vaccine. An effective human vaccine would be a significant advance towards curtailing this rapidly emerging disease.

Investigation of liposomal self-adjuvanting peptide epitopes derived from conserved blood-stage Plasmodium antigens.

Malaria is a vector born parasitic disease causing millions of deaths every year. Despite the high mortality rate, an effective vaccine against this mosquito-borne infectious disease is yet to be developed. Up to date, RTS,S/AS01 is the only vaccine available for malaria prevention; however, its efficacy is low. Among a variety of malaria antigens, merozoite surface protein-1(MSP-1) and ring-infected erythrocyte surface antigen (RESA) have been proposed as promising candidates for malaria vaccine development. We developed peptide-based Plasmodium falciparum vaccine candidates that incorporated three previously reported conserved epitopes from MSP-1 and RESA into highly effective liposomal polyleucine delivery system. Indeed, MSP-1 and RESA-derived epitopes conjugated to polyleucine and formulated into liposomes induced higher epitope specific antibody titres. However, immunized mice failed to demonstrate protection in a rodent malaria challenge study with Plasmodium yoelii. In addition, we found that the three reported P. falciparum epitopes did not to share conformational properties and high sequence similarity with P. yoelii MSP-1 and RESA proteins, despite the epitopes were reported to protect mice against P. yoelii challenge.

Vaccinating Children against COVID-19: Commentary and Mathematical Modeling.

With the recent licensure of mRNA vaccines against COVID-19 in the 5- to 11-year-old age group, the public health impact of a childhood immunization campaign is of interest. Using a mathematical epidemiological model, we project that childhood vaccination carries minimal risk and yields modest public health benefits. These include large relative reductions in child morbidity and mortality, although the absolute reduction is small because these events are rare. Furthermore, the model predicts "altruistic" absolute reductions in adult cases, hospitalizations, and mortality. However, vaccinating children to benefit adults should be considered from an ethical as well as a public health perspective. From a global health perspective, an additional ethical consideration is the justice of giving priority to children in high-income settings at low risk of severe disease while vaccines have not been made available to vulnerable adults in low-income settings. IMPORTANCE Countries have recently begun implementation of childhood vaccination against SARS-CoV-2 with the Pfizer/BioNTech mRNA vaccine in children 5 to 11 years of age. Because SARS-CoV-2 disease severity is remarkably age dependent, vaccinating children may have modest public health benefits, relative to the unequivocal benefit of vaccinating vulnerable older adults. Furthermore, vaccinating children to "altruistically" increase herd immunity should be considered from an ethical as well as a public health perspective. An additional question is related to global social justice: should priority be given to vaccinating children in high-income settings while older adult populations in low-resource settings have limited access to vaccine? To address the risks and benefits of childhood vaccination, we provide a balanced commentary, supported by a mathematical epidemiological model, using Australia and Alberta, Canada, as case studies. We give highlights of the modeling findings in the commentary and include details in the supplemental materials for interested readers.

Population Health at the Academic Health Center: An Interactive, Multipart, Case-Based Session for Executives, Faculty, and Administrators.

INTRODUCTION: Academic health centers (AHCs) play critical roles in population health by providing health care, conducting population health research, and providing population health training and education. This publication describes an interactive, multipart, case-based session targeted at AHC executives, faculty, and administrators about population health initiatives at AHCs and how the AHC structure can be leveraged to promote population health. METHODS: This 90-minute virtual session was conducted during the Association of Academic Health Centers' 2020 annual meeting. The session opened with 5-minute, Ignite-style presentations showcasing population health innovations. Next, in small groups, participants discussed a case introducing a fictional AHC charged with assisting its local government's population health efforts. Participants self-selected into one of four small groups (analytics, education and training, community engagement, and implementation) and were provided additional case content and tailored prompts. In the large group, participants debriefed their discussions. Participants completed a postsession survey. RESULTS: Forty-six individuals from 31 AHCs participated. Eighteen participants completed the survey. Sixteen respondents (89%) agreed the session was valuable and provided ideas for implementation at their AHC. Fifteen participants (83%) indicated that they planned to follow up with their colleagues regarding how to leverage the AHC structure to improve population health. DISCUSSION: This session provides an interactive forum to discuss population health in the context of an AHC and examine how its structure can facilitate population health. While offered at a conference, the session can also be implemented at a single AHC to foster local understanding of population health and inform future initiatives.

Ambient Temperature Stable, Scalable COVID-19 Polymer Particle Vaccines Induce Protective Immunity.

There is an unmet need for safe and effective severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccines that are stable and can be cost-effectively produced at large scale. Here, a biopolymer particle (BP) vaccine technology that can be quickly adapted to new and emerging variants of SARS-CoV-2 is used. Coronavirus antigen-coated BPs are described as vaccines against SARS-CoV-2. The spike protein subunit S1 or epitopes from S and M proteins (SM) plus/minus the nucleocapsid protein (N) are selected as antigens to either coat BPs during assembly inside engineered Escherichia coli or BPs are engineered to specifically ligate glycosylated spike protein (S1-ICC) produced by using baculovirus expression in insect cell culture (ICC). BP vaccines are safe and immunogenic in mice. BP vaccines, SM-BP-N and S1-ICC-BP induced protective immunity in the hamster SARS-CoV-2 infection model as shown by reduction of virus titers up to viral clearance in lungs post infection. The BP platform offers the possibility for rapid design and cost-effective large-scale manufacture of ambient temperature stable and globally available vaccines to combat the coronavirus disease 2019 (COVID-19) pandemic.

CGHS Black Hole Analog Moving Mirror and Its Relativistic Quantum Information as Radiation Reaction.

The Callan-Giddings-Harvey-Strominger black hole has a spectrum and temperature that correspond to an accelerated reflecting boundary condition in flat spacetime. The beta coefficients are identical to a moving mirror model, where the acceleration is exponential in laboratory time. The center of the black hole is modeled by the perfectly reflecting regularity condition that red-shifts the field modes, which is the source of the particle creation. In addition to computing the energy flux, we find the corresponding moving mirror parameter associated with the black hole mass and the cosmological constant in the gravitational analog system. Generalized to any mirror trajectory, we derive the self-force (Lorentz-Abraham-Dirac), consistently, expressing it and the Larmor power in connection with entanglement entropy, inviting an interpretation of acceleration radiation in terms of information flow. The mirror self-force and radiative power are applied to the particular CGHS black hole analog moving mirror, which reveals the physics of information at the horizon during asymptotic approach to thermal equilibrium.