Androgen Deprivation, With or Without pTVG-AR, and With or Without T-Cell Checkpoint Blockade, in Patients With Newly Diagnosed, High-Risk Prostate Cancer

Inclusion Criteria: * Histologically confirmed adenocarcinoma of the prostate * Patients must be considered candidates for prostatectomy as per standard of care * High-risk patients for recurrent disease, with high risk defined based on one of the following criteria: * Gleason score 7 and baseline serum prostate specific antigen (PSA) \> 20 ng/mL * Gleason score \> 7 * Life expectancy of at least 12 months at screening * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Adequate hematologic, renal and liver function as evidenced by the following within 4 weeks of day 1: * Absolute neutrophil count (ANC) \> 1000 / mm3 * HgB \> 9.0 gm/dL independent of transfusion * Platelets \> 100,000 / mm3 * Creatinine \< 2.0 mg/dL * Aspartate aminotransferase (AST), Alanine transaminase (ALT) \< 2.5 x institutional upper limit of normal (ULN) * Total bilirubin \< 2x institutional ULN (NOTE: in subjects with Gilbert's syndrome, if total bilirubin is \>2x ULN, measure direct and indirect bilirubin and if direct bilirubin is within normal range, subject may be eligible) * No known history of HIV 1 and 2, HTLV-1, or active Hepatitis B or Hepatitis C * Must have adequate tissue (ten 5µm unstained formalin-fixed paraffin-embedded (FFPE) sections containing prostate cancer) remaining from pre-treatment diagnostic prostate biopsy for research purposes * Patients must be willing to undergo large-volume blood draws (up to 200mL per time point) for the investigational component of this trial * For those patients who are sexually active, they must be willing to use barrier contraceptive methods during the period of treatment on this trial * Patients must be informed of the experimental nature of the study and its potential risks, and must sign an IRB-approved written informed consent form indicating such an * Ability to comply with all study procedures and willingness to remain supine for 120 minutes during imaging Exclusion Criteria: * Small cell or other variant (non-adenocarcinoma) prostate cancer histology * Prior treatment for prostate cancer, including androgen deprivation therapy (ADT), orchiectomy, antiandrogens, ketoconazole, abiraterone acetate or enzalutamide * Prior radiation to the prostate * Patients may not be receiving other investigational agents or be receiving concurrent anticancer therapy other than the treatment-prescribed androgen deprivation therapy * Treatment with any of the following medications while on study is prohibited, washout period not required except as indicated: * Systemic corticosteroids (at doses over the equivalent of 10 mg prednisone daily) - not permitted within 3 months of registration; inhaled, intranasal or topical corticosteroids are acceptable * PC-SPES * Herbal supplements that have been shown to modulate testosterone or androgen signaling (e.g. Saw Palmetto) are not allowed while on study * Megestrol * Ketoconazole * 5-α-reductase inhibitors - patients already taking 5-α-reductase inhibitors prior to 28 days prior to registration may stay on these agents throughout the course of therapy, but these should not be started while patients are on study * Diethylstilbesterol * Any other non-study hormonal agent or supplement being used with the intent of cancer treatment * Major surgery within 4 weeks of registration is prohibited * Active cardiac disease defined as active angina, symptomatic congestive heart failure, or myocardial infarction within 6 months of registration * Patients with known psychological or sociological conditions, addictive disorders or family problems, which would preclude compliance with the protocol * Patients who have undergone splenectomy * Patients must not have other active malignancies other than non-melanoma skin cancers or superficial bladder cancer (this includes any non-muscle invasive bladder cancer including Ta, CIS and T1), that have been adequately treated. Subjects with a history of other cancers who have been adequately treated and have been recurrence-free for \> 3 years are eligible. * Any other medical intervention or condition, which, in the opinion of the principle investigator (PI) or treating physician, could compromise patient safety or adherence with the study requirements over the primary 3-6 month treatment period. * Patients who have concurrent enrollment on other phase I, II, or III investigational treatment studies cannot be actively receiving treatment and the last dose cannot be within 4 weeks. * Patients who have received a live vaccine within 14 days prior to the first dose of study treatment. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (eg, FluMist®) are live attenuated vaccines and are not allowed * Patients with a history of life-threatening autoimmune disease or active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Patients with a history of non-infectious pneumonitis that required corticosteroid treatment, or has current pneumonitis * Patients with a history of allergic reactions to the tetanus vaccine