Assessing the importance of demographic risk factors across two waves of SARS-CoV-2 using fine-scale case data.

For the long term control of an infectious disease such as COVID-19, it is crucial to identify the most likely individuals to become infected and the role that differences in demographic characteristics play in the observed patterns of infection. As high-volume surveillance winds down, testing data from earlier periods are invaluable for studying risk factors for infection in detail. Observed changes in time during these periods may then inform how stable the pattern will be in the long term. To this end we analyse the distribution of cases of COVID-19 across Scotland in 2021, where the location (census areas of order 500-1,000 residents) and reporting date of cases are known. We consider over 450,000 individually recorded cases, in two infection waves triggered by different lineages: B.1.1.529 ("Omicron") and B.1.617.2 ("Delta"). We use random forests, informed by measures of geography, demography, testing and vaccination. We show that the distributions are only adequately explained when considering multiple explanatory variables, implying that case heterogeneity arose from a combination of individual behaviour, immunity, and testing frequency. Despite differences in virus lineage, time of year, and interventions in place, we find the risk factors remained broadly consistent between the two waves. Many of the observed smaller differences could be reasonably explained by changes in control measures.

Evaluation of Tumor DNA Sequencing Results in Patients with Gastric and Gastroesophageal Junction Adenocarcinoma Stratified by TP53 Mutation Status.

BACKGROUND: Gastric cancer (GC) and gastroesophageal junction adenocarcinomas (GEJ) are molecularly diverse. TP53 is the most frequently altered gene with approximately 50% of patients harboring mutations. This qualitative study describes the distinct genomic alterations in GCs and GEJs stratified by TP53 mutation status. PATIENTS AND METHODS: Tumor DNA sequencing results of 324 genes from 3741 patients with GC and GEJ were obtained from Foundation Medicine. Association between gene mutation frequency and TP53 mutation status was examined using Fisher's exact test. Functional gene groupings representing molecular pathways suggested to be differentially mutated in TP53 wild-type (TP53WT) and TP53 mutant (TP53MUT) tumors were identified. The association of the frequency of tumors containing a gene mutation in the molecular pathways of interest and TP53 mutation status was assessed using Fisher's exact test with a P-value of <.01 deemed statistically significant for all analyses. RESULTS: TP53 mutations were noted in 61.6% of 2946 GCs and 81.4% of 795 GEJs (P < .001). Forty-nine genes had statistically different mutation frequencies in TP53WT vs. TP53MUT patients. TP53WT tumors more likely had mutations related to DNA mismatch repair, homologous recombination repair, DNA and histone methylation, Wnt/B-catenin, PI3K/Akt/mTOR, and chromatin remodeling complexes. TP53MUT tumors more likely had mutations related to fibroblast growth factor, epidermal growth factor receptor, other receptor tyrosine kinases, and cyclin and cyclin-dependent kinases. CONCLUSION: The mutational profiles of GCs and GEJs varied according to TP53 mutation status. These mutational differences can be used when designing future studies assessing the predictive ability of TP53 mutation status when targeting differentially affected molecular pathways.

Phase I study of the mTOR inhibitor everolimus in combination with the histone deacetylase inhibitor panobinostat in patients with advanced clear cell renal cell carcinoma.

Background Preclinical studies suggested synergistic anti-tumor activity when pairing mTOR inhibitors with histone deacetylase (HDAC) inhibitors. We completed a phase I, dose-finding trial for the mTOR inhibitor everolimus combined with the HDAC inhibitor panobinostat in advanced clear cell renal cell carcinoma (ccRCC) patients. We additionally investigated expression of microRNA 605 (miR-605) in serum samples obtained from trial participants. Patients and Methods Twenty-one patients completed our single institution, non-randomized, open-label, dose-escalation phase 1 trial. miR-605 levels were measured at cycle 1/day 1 (C1D1) and C2D1. Delta Ct method was utilized to evaluate miR-605 expression using U6B as an endogenous control. Results There were 3 dosing-limiting toxicities (DLTs): grade 4 thrombocytopenia (n = 1), grade 3 thrombocytopenia (n = 1), and grade 3 neutropenia (n = 1). Everolimus 5 mg PO daily and panobinostat 10 mg PO 3 times weekly (weeks 1 and 2) given in 21-day cycles was the recommended phase II dosing based on their maximum tolerated dose. The 6-month progression-free survival was 31% with a median of 4.1 months (95% confidence internal; 2.0-7.1). There was higher baseline expression of miR-605 in patients with progressive disease (PD) vs those with stable disease (SD) (p = 0.0112). PD patients' miR-605 levels decreased after the 1st cycle (p = 0.0245), whereas SD patients' miR-605 levels increased (p = 0.0179). Conclusion A safe and tolerable dosing regimen was established for combination everolimus/panobinostat therapy with myelosuppression as the major DLT. This therapeutic pairing did not appear to improve clinical outcomes in our group of patients with advanced ccRCC. There was differential expression of miR-605 that correlated with treatment response. Clinical trial information: NCT01582009.

Pediatric to Adult Transition in Sickle Cell Disease: Survey Results from Young Adult Patients.

BACKGROUND/AIMS: We surveyed sickle cell disease (SCD) patients who transitioned from pediatric care at Texas Children's Hematology Center (TCHC) to adult care to determine the characteristics of patients with an adult SCD provider, continuation rates of pre-transition therapies, and patient perceptions of the transition process. METHODS: A cross-sectional study was conducted by telephone survey of 44 young adults with SCD, aged 19-29 years, who transitioned from TCHC to adult care within the last 15 years. RESULTS: Findings of the 23-item questionnaire revealed that transitioned patients with current adult providers (68.2%) were more likely to have seen a provider within 6 months of transition (p = 0.023) and to have been on hydroxyurea and/or monthly blood transfusions pre-transition (p = 0.021) than transitioned patients without a provider; 83% of patients on pre-transition hydroxyurea reported continuing hydroxyurea after transition. Transition challenges included inadequate preparation, difficulty finding knowledgeable adult providers, and lack of healthcare insurance/coverage. CONCLUSION: Transition to adult providers is predicted by establishing care with an adult SCD provider within 6 months of transition and being on pre-transition disease-modifying therapy. Transition may be improved if pediatric hematology centers assist and verify adult provider contact within 6 months of transition and engage patients of all disease severity during transition.

Antiviral potency of long-acting islatravir subdermal implant in SHIV-infected macaques.

Treatment nonadherence is a pressing issue in people living with HIV (PLWH), as they require lifelong therapy to maintain viral suppression. Poor adherence leads to antiretroviral (ARV) resistance, transmission to others, AIDS progression, and increased morbidity and mortality. Long-acting (LA) ARV therapy is a promising strategy to combat the clinical drawback of user-dependent dosing. Islatravir (ISL) is a promising candidate for HIV treatment given its long half-life and high potency. Here we show constant ISL release from a subdermal LA nanofluidic implant achieves viral load reduction in SHIV-infected macaques. Specifically, a mean delivery dosage of 0.21 ± 0.07 mg/kg/day yielded a mean viral load reduction of -2.30 ± 0.53 log10 copies/mL at week 2, compared to baseline. The antiviral potency of the ISL delivered from the nanofluidic implant was higher than oral ISL dosed either daily or weekly. At week 3, viral resistance to ISL emerged in 2 out of 8 macaques, attributable to M184V mutation, supporting the need of combining ISL with other ARV for HIV treatment. The ISL implant produced moderate reactivity in the surrounding tissue, indicating tolerability. Overall, we present the ISL subdermal implant as a promising approach for LA ARV treatment in PLWH.

Empirical distributions of time intervals between COVID-19 cases and more severe outcomes in Scotland.

A critical factor in infectious disease control is the risk of an outbreak overwhelming local healthcare capacity. The overall demand on healthcare services will depend on disease severity, but the precise timing and size of peak demand also depends on the time interval (or clinical time delay) between initial infection, and development of severe disease. A broader distribution of intervals may draw that demand out over a longer period, but have a lower peak demand. These interval distributions are therefore important in modelling trajectories of e.g. hospital admissions, given a trajectory of incidence. Conversely, as testing rates decline, an incidence trajectory may need to be inferred through the delayed, but relatively unbiased signal of hospital admissions. Healthcare demand has been extensively modelled during the COVID-19 pandemic, where localised waves of infection have imposed severe stresses on healthcare services. While the initial acute threat posed by this disease has since subsided with immunity buildup from vaccination and prior infection, prevalence remains high and waning immunity may lead to substantial pressures for years to come. In this work, then, we present a set of interval distributions, for COVID-19 cases and subsequent severe outcomes; hospital admission, ICU admission, and death. These may be used to model more realistic scenarios of hospital admissions and occupancy, given a trajectory of infections or cases. We present a method for obtaining empirical distributions using COVID-19 outcomes data from Scotland between September 2020 and January 2022 (N = 31724 hospital admissions, N = 3514 ICU admissions, N = 8306 mortalities). We present separate distributions for individual age, sex, and deprivation of residing community. While the risk of severe disease following COVID-19 infection is substantially higher for the elderly and those residing in areas of high deprivation, the length of stay shows no strong dependence, suggesting that severe outcomes are equally severe across risk groups. As Scotland and other countries move into a phase where testing is no longer abundant, these intervals may be of use for retrospective modelling of patterns of infection, given data on severe outcomes.

Changes in local tissue microenvironment in response to subcutaneous long-acting delivery of tenofovir alafenamide in rats and non-human primates.

Several implantable long-acting (LA) delivery systems have been developed for sustained subcutaneous administration of tenofovir alafenamide (TAF), a potent and effective nucleotide reverse transcriptase inhibitor used for HIV pre-exposure prophylaxis (PrEP). LA platforms aim to address the lack of adherence to oral regimens, which has impaired PrEP efficacy. Despite extensive investigations in this field, tissue response to sustained subcutaneous TAF delivery remains to be elucidated as contrasting preclinical results have been reported in the literature. To this end, here we studied the local foreign body response (FBR) to sustained subdermal delivery of three forms of TAF, namely TAF free base (TAFfb), TAF fumarate salt (TAFfs), and TAFfb with urocanic acid (TAF-UA). Sustained constant drug release was achieved via titanium-silicon carbide nanofluidic implants previously shown to be bioinert. The analysis was conducted in both Sprague-Dawley (SD) rats and rhesus macaques over 1.5 and 3 months, respectively. While visual observation did not reveal abnormal adverse tissue reaction at the implantation site, histopathology and Imaging Mass Cytometry (IMC) analyses exposed a local chronic inflammatory response to TAF. In rats, UA mitigated foreign body response to TAF in a concentration-dependent manner. This was not observed in macaques where TAFfb was better tolerated than TAFfs and TAF-UA. Notably, the level of FBR was tightly correlated with local TAF tissue concentration. Further, regardless of the degree of FBR, the fibrotic capsule (FC) surrounding the implants did not interfere with drug diffusion and systemic delivery, as evidenced by TAF PK results and fluorescence recovery after photobleaching (FRAP).

Inferior Outcomes of EU Versus US Patients Treated With CD19 CAR-T for Relapsed/Refractory Large B-cell Lymphoma: Association With Differences in Tumor Burden, Systemic Inflammation, Bridging Therapy Utilization, and CAR-T Product Use.

Real-world evidence suggests a trend toward inferior survival of patients receiving CD19 chimeric antigen receptor (CAR) T-cell therapy in Europe (EU) and with tisagenlecleucel. The underlying logistic, patient- and disease-related reasons for these discrepancies remain poorly understood. In this multicenter retrospective observational study, we studied the patient-individual journey from CAR-T indication to infusion, baseline features, and survival outcomes in 374 patients treated with tisagenlecleucel (tisa-cel) or axicabtagene-ciloleucel (axi-cel) in EU and the United States (US). Compared with US patients, EU patients had prolonged indication-to-infusion intervals (66 versus 50 d; P < 0.001) and more commonly received intermediary therapies (holding and/or bridging therapy, 94% in EU versus 74% in US; P < 0.001). Baseline lactate dehydrogenase (LDH) (median 321 versus 271 U/L; P = 0.02) and ferritin levels (675 versus 425 ng/mL; P = 0.004) were significantly elevated in the EU cohort. Overall, we observed inferior survival in EU patients (median progression-free survival [PFS] 3.1 versus 9.2 months in US; P < 0.001) and with tisa-cel (3.2 versus 9.2 months with axi-cel; P < 0.001). On multivariate Lasso modeling, nonresponse to bridging, elevated ferritin, and increased C-reactive protein represented independent risks for treatment failure. Weighing these variables into a patient-individual risk balancer (high risk [HR] balancer), we found higher levels in EU versus US and tisa-cel versus axi-cel cohorts. Notably, superior PFS with axi-cel was exclusively evident in patients at low risk for progression (according to the HR balancer), but not in high-risk patients. These data demonstrate that inferior survival outcomes in EU patients are associated with longer time-to-infusion intervals, higher tumor burden/LDH levels, increased systemic inflammatory markers, and CAR-T product use.

Maximizing the positive and minimizing the negative: Social media data to study youth mental health with informed consent.

Social media usage impacts upon the mental health and wellbeing of young people, yet there is not enough evidence to determine who is affected, how and to what extent. While it has widened and strengthened communication networks for many, the dangers posed to at-risk youth are serious. Social media data offers unique insights into the minute details of a user's online life. Timely consented access to data could offer many opportunities to transform understanding of its effects on mental wellbeing in different contexts. However, limited data access by researchers is preventing such advances from being made. Our multidisciplinary authorship includes a lived experience adviser, academic and practicing psychiatrists, and academic psychology, as well as computational, statistical, and qualitative researchers. In this Perspective article, we propose a framework to support secure and confidential access to social media platform data for research to make progress toward better public mental health.

Anatomic patterns of recurrence in biliary tract cancers: does primary tumor site matter?

Background: Recommendations for postoperative surveillance and adjuvant therapy following curative-intent resection for biliary tract cancers-including intrahepatic and extrahepatic cholangiocarcinoma (IHCCA and EHCCA) and primary gallbladder cancer (GBC)-are uniform across primary tumor site. However, these tumors may have distinct patterns of recurrence. Methods: A retrospective observational cohort study was performed at a specialty cancer center. Patients undergoing resection of IHCCA, EHCCA, and GBC were identified (2005-2020). Recurrence-free survival (RFS) was estimated using Kaplan-Meier and Cox proportional hazard methods. Anatomic patterns of initial site of recurrence were described and compared. Results: There were 142 patients included; 50 IHCCA, 32 EHCCA, and 60 GBC. Median RFS was 30.8 months, which was not significantly different between IHCCA, EHCCA, or GBC in univariate analysis or after adjustment. Nodal positivity was significantly associated with poor RFS (HR 3.92, P≤0.001). The most common initial site of recurrence overall was intrahepatic (n=49/64, 77%), in isolation (n=32) or synchronous with other site of recurrence (n=17). Significant differences in anatomic pattern of recurrence were observed (P=0.049) with IHCCAs more commonly recurring with simultaneous hepatic-pulmonary disease (n=5/22, 23%; EHCCA n=2/19, 10%; GBC n=1/23, 4%), GBC more commonly recurring within the porta (n=7/23, 30%; IHCCA n=0; EHCCA n=1/19, 5%), and EHCCA more commonly recurring within the peritoneum (n=5/19, 26%; IHCCA n=2/22, 9%, GBC n=2/23, 9%). Conclusions: Patterns of initial recurrence appear to differ between primary tumor site, likely reflecting underlying differences in anatomy and biology. These data could help inform future studies for adjuvant therapy as well as timing and anatomic focus for surveillance imaging.

Local SARS-CoV-2 Peptide-Specific Immune Responses in Lungs of Convalescent and Uninfected Human Subjects.

Multi-specific and long-lasting T cell immunity have been recognized as indicators for long term protection against pathogens including the novel coronavirus SARS-CoV-2, the causative agent of the COVID-19 pandemic. Functional significance of peripheral memory T cells in individuals recovering from COVID-19 (COVID-19 + ) are beginning to be appreciated; but little is known about lung resident memory T cells (lung TRM) in SARS-CoV-2 infection. Here, we utilize a perfused three dimensional (3D) human lung tissue model and identify pre-existing local T cell immunity against SARS-CoV-2 proteins in lung tissues. We report ex vivo maintenance of functional multi-specific IFN-γ secreting lung TRM in COVID-19 + and their induction in lung tissues of vaccinated COVID-19 + . Importantly, we identify SARS-CoV-2 peptide-responding B cells and IgA + plasma cells in lung tissues of COVID-19 + in ex vivo 3D-tissue models. Our study highlights the importance of balanced and local anti-viral immune response in the lung with persistent induction of TRM and IgA + plasma cells for future protection against SARS-CoV-2 infection. Further, our data suggest that inclusion of multiple viral antigens in vaccine approaches may broaden the functional profile of memory T cells to combat the severity of coronavirus infection.

Outcomes of CD19-Targeted Chimeric Antigen Receptor T Cell Therapy for Patients with Reduced Renal Function Including Dialysis.

Patients with renal impairment (RI) are typically excluded from trials evaluating chimeric antigen receptor (CAR) T cell therapies. We evaluated the outcomes of patients with RI receiving standard of care (SOC) CAR T cell therapy for relapsed/refractory (R/R) diffuse large B cell lymphoma (DLBCL). In this retrospective, single-center cohort study of patients with R/R DLBCL treated with SOC axicabtagene ciloleucel (axi-cel) or tisagenlecleucel (tisa-cel) after 2 or more prior lines of therapy, renal and survival outcomes were compared based on RI and fludarabine dose reduction (DR) status. RI was defined by an estimated glomerular filtration rate <60 mL/min/1.73 m2 as determined by the Modification of Diet in Renal Disease equation using day -5 creatinine (Cr) values. Acute kidney injury (AKI) was identified and graded using standard Kidney Disease: Improving Global Outcomes criteria. Renal recovery was considered to occur if Cr was within .2 mg/mL of baseline by day +30. Fludarabine was considered DR if given at <90% of the recommended Food and Drug Administration label dose. Among 166 patients treated with CAR T cell therapy were 17 patients (10.2%) with baseline RI and 149 (89.8%) without RI. After CAR T cell infusion, the incidence of any grade AKI was not significantly different between patients with baseline RI and those without RI (42% versus 21%; P = .08). Similarly, severe grade 2/3 AKI was seen in 1 of 17 patients (5.8%) with baseline RI and in 11 of 149 patients (7.3%) without RI (P = 1). Decreased renal perfusion (28 of 39; 72%) was the most common cause of AKI, with cytokine release syndrome (CRS) contributing to 17 of 39 AKIs (44%). Progression-free survival (PFS) and overall survival (OS) did not differ between patients with RI and those without RI or between those who received standard-dose fludarabine and those who received reduced-dose fludarabine. In contrast, patients with AKI had worse clinical outcomes than those without AKI (multivariable PFS: hazard ratio [HR], 2.1; 95% confidence interval [CI], 1.2 to 3.7; OS: HR, 3.9; 95% CI, 2.1 to 7.4). Notably, peak inflammatory cytokine levels were higher in patients who experienced AKI. Finally, we describe 2 patients with end-stage renal disease (ESRD) on dialysis who received lymphodepletion and CAR T cell therapy. Baseline renal function did not affect renal or efficacy outcomes after CAR T cell therapy in DLBCL. On the other hand, patients with AKI went on to experience worse clinical outcomes. AKI was commonly related to CRS and high peak inflammatory cytokine levels. CAR T cell therapy is feasible in patients with ESRD and requires careful planning of lymphodepletion.

Investigational PARP inhibitors for the treatment of biliary tract cancer: spotlight on preclinical and clinical studies.

Introduction: Alterations in DNA damage repair (DDR) genes are observed in up to 60% of biliary tract cancer (BTC) patients. Patients with advanced/metastatic BTC have few therapeutic options, so there is a demand for the development of new and innovative treatment approaches. The use of poly-adenosine diphosphate-ribose polymerase (PARP) inhibitors (PARPis), either as a monotherapy or in combination, is being extensively studied in clinical trials.Areas Covered: This review examines the targeting of the DDR pathway with PARPis as a potential novel treatment option for the management of BTCs. The rationale behind the use of PARPis and current clinical experience is discussed. Moreover, further insights into potential future directions concerning the applicability of PARPis in the treatment of BTCs are proposed.Expert Opinion: Prospective clinical data with PARPis in the treatment of BTCs are limited. The potential combination of PARPis and IDH1 inhibitors or immune checkpoint inhibitors in clinical trials is interesting because of the potential synergistic preclinical data. There are other possible combinations including those drugs that target the angiogenesis or STAT3 pathways. An enhanced understanding of acquired resistance to PARPis is necessary to progress the use of these agents in clinical trials.

Extracellular Vesicle Mediated Tumor-Stromal Crosstalk Within an Engineered Lung Cancer Model.

Tumor-stromal interactions within the tumor microenvironment (TME) influence lung cancer progression and response to therapeutic interventions, yet traditional in vitro studies fail to replicate the complexity of these interactions. Herein, we developed three-dimensional (3D) lung tumor models that mimic the human TME and demonstrate tumor-stromal crosstalk mediated by extracellular vesicles (EVs). EVs released by tumor cells, independent of p53 status, and fibroblasts within the TME mediate immunomodulatory effects; specifically, monocyte/macrophage polarization to a tumor-promoting M2 phenotype within this 3D-TME. Additionally, immune checkpoint inhibition in a 3D model that included T cells showed an inhibition of tumor growth and reduced hypoxia within the TME. Thus, perfused 3D tumor models incorporating diverse cell types provide novel insights into EV-mediated tumor-immune interactions and immune-modulation for existing and emerging cancer therapies.

Lersivirine, a nonnucleoside reverse transcriptase inhibitor with activity against drug-resistant human immunodeficiency virus type 1.

The nonnucleoside reverse transcriptase inhibitors (NNRTIs) are key components of highly active antiretroviral therapy (HAART) for the treatment of human immunodeficiency virus type 1 (HIV-1). A major problem with the first approved NNRTIs was the emergence of mutations in the HIV-1 reverse transcriptase (RT), in particular K103N and Y181C, which led to resistance to the entire class. We adopted an iterative strategy to synthesize and test small molecule inhibitors from a chemical series of pyrazoles against wild-type (wt) RT and the most prevalent NNRTI-resistant mutants. The emerging candidate, lersivirine (UK-453,061), binds the RT enzyme in a novel way (resulting in a unique resistance profile), inhibits over 60% of viruses bearing key RT mutations, with 50% effective concentrations (EC(50)s) within 10-fold of those for wt viruses, and has excellent selectivity against a range of human targets. Altogether lersivirine is a highly potent and selective NNRTI, with excellent efficacy against NNRTI-resistant viruses.

Pyrazole NNRTIs 1: design and initial optimisation of a novel template.

The design and synthesis of a novel series of non-nucleoside HIV reverse transcriptase inhibitors (NNRTIs) based on a pyrazole template is described. These compounds are active against wild type reverse transcriptase (RT) and retain activity against clinically important mutants.

Pyrazole NNRTIs 4: selection of UK-453,061 (lersivirine) as a development candidate.

We prepared three discreet cohorts of potent non-nucleoside HIV reverse transcriptase inhibitors (NNRTIs) based on the recently reported 3-cyanophenoxypyrazole lead 3. Several of these compounds displayed very promising anti-HIV activity in vitro, safety, pharmacokinetic and pharmaceutical profiles. We describe our analysis and conclusions leading to the selection of alcohol 5 (UK-453,061, lersivirine) for clinical development.

Pyrazole NNRTIs 3: optimisation of physicochemical properties.

Our efforts to reduce overall lipophilicity and increase ligand-lipophilicity efficiency (LLE) by modification of the 3- and 5-substituents of pyrazole 1, a novel non-nucleoside HIV reverse transcriptase inhibitor (NNRTI) prototype were unsuccessful. In contrast replacement of the substituted benzyl group with corresponding phenylthio or phenoxy groups resulted in marked improvements in potency, ligand efficiency (LE) and LLE.

The design and discovery of novel amide CCR5 antagonists.

The synthesis of a range of novel amine-containing structures and their primary potency as inhibitors of HIV-1 fusion via blocking of the CCR5 receptor is described. The development of the medicinal chemistry strategy and SAR's which led to the identification of the piperidine amide compounds 33 and 36 as excellent leads for further evaluation is described, along with key physicochemical data which highlighted their lead potential.

Solvable model of a many-filament Brownian ratchet.

We construct and exactly solve a model of an extended Brownian ratchet. The model comprises an arbitrary number of heterogeneous, growing and shrinking filaments which together move a rigid membrane by a ratchet mechanism. The model draws parallels with the dynamics of actin filament networks at the leading edge of the cell. In the model, the filaments grow and contract stochastically. The model also includes forces which derive from a potential dependent on the separation between the filaments and the membrane. These forces serve to attract the filaments to the membrane or generate a surface tension that prevents the filaments from dispersing. We derive an N-dimensional diffusion equation for the N filament-membrane separations, which allows the steady-state probability distribution function to be calculated exactly under certain conditions. These conditions are fulfilled by the physically relevant cases of linear and quadratic interaction potentials. The exact solution of the diffusion equation furnishes expressions for the average velocity of the membrane and critical system parameters for which the system stalls and has zero net velocity. In the case of a restoring force, the membrane velocity grows as the square root of the force constant, whereas it decreases once a surface tension is introduced.