Study to Examine the Cytokine Levels, Gene Expression and Safety of a Single Nasal Dose of JNJ-43260295, in Healthy Participants, and Atopic Participants With Mild to Mild-Persistent Asthma

Inclusion Criteria: A. Healthy Participants and Atopic Mild to Mild-Persistent Asthmatic Participants: * Participants must be non-smokers or non-regular smokers (1 to 2 cigarettes on the weekend as part of social gathering) for at least 3 months prior to Screening, according to the participant's self-reported medical history. Participants should be willing to (continue to) abstain from smoking from Screening until completion of the last study related activity * Participants must have a body mass index (BMI: weight in kilogram \[kg\] divided by the height in square meter \[m\^2\]) of 18.0 to 30.0 kg/m\^2, extremes included * Participants must have a normal 12-lead electrocardiogram (ECG) at Screening including normal sinus rhythm (heart rate between 40 and 100 beats per minute \[bpm\]); QT interval corrected for heart rate according to Fridericia (QTcF) interval less than and equal to (\<=) 450 milliseconds (ms); QRS interval lower than 120 ms; and PR interval \<=220 ms * Participants must be healthy, with the exception of findings related to asthma and allergy in atopic mild to mild-Persistent asthmatic participants, on the basis of a medical evaluation that reveals the absence of any clinically relevant abnormality and includes a physical examination, medical history, vital signs (Systolic Blood Pressure \[BP\], Diastolic BP, pulse rate, respiratory rate, and body temperature), and the results of blood biochemistry and hematology tests performed at Screening * Participants must be willing/ able to adhere to the prohibitions and restrictions specified in the protocol and study procedures B. Atopic Mild to Mild-Persistent Asthmatic Participants: * Participants with Investigator-diagnosed mild to mild-persistent asthma based on the Guidelines for the Diagnosis and Management of Asthma * Participants having a well-established allergen profile (participants have been previously skin tested and, by history, have allergic responses to specific allergens) * Participants with forced expiratory volume in 1 second (FEV1) greater than (\>) 70 percent (%) of predicted at Baseline Exclusion Criteria: A. Healthy Participants and Atopic Mild to Mild-Persistent Asthmatic Participants: * Participants having a significant (by the assessment of the Investigator) nasal abnormality and/or has a history of nasal or sinus surgery within 12 months of enrollment * Participants having an upper or lower respiratory tract infection within 4 weeks of enrollment * Participants with a history or evidence of use of alcohol, barbiturates, amphetamines, recreational or narcotic drug use within the past 1 year, which in the Investigator's opinion would compromise participant's safety and/or compliance with the study procedures * Participants with a known history of human immunodeficiency virus type 1 (HIV-1) or HIV-2 infection, or with a known history of hepatitis A, B, or C virus infection at study Screening * Female participants who are breastfeeding at Screening or having a positive urine pregnancy test at Screening B. Atopic Mild to Mild-Persistent Asthmatic Participants: * Hospitalization or treatment in an emergency care facility for asthma during the last 3 years * Participants using nasal corticosteroids on a daily basis in the 4 weeks prior to enrollment * Participants who have received allergen immunotherapy in the last 2 years