Dose-Escalation and Efficacy Study of LAE001/Prednisone Plus Afuresertib Patients With m-CRPC

Inclusion Criteria: 1. Patients, males ≥18 years of age, must be able to provide written informed consent. 2. Patients must have documented histological or cytological evidence of adenocarcinoma of the prostate (excluding neuroendocrine differentiation or small cell histology). 3. Patients must have radiographic evidence of metastatic disease for mCRPC based on the 'Guideline of American Urological Association for Prostate Cancer' before study enrollment. (https://www.auanet.org/guidelines/prostate-cancer-castration-resistant11 guideline) 4. For PTEN and PIK3CA/AKT status test: Phase I: The PTEN/PIK3CA/AKT status test is optional and the result could be either positive, negative, undetermined or invalid. Phase II: Patients will be allowed to enroll regardless of the biomarker status, medical monitor review is necessary before enrollment. The biomarker status tests will be performed with the following order. The biomarker results of all enrolled patients will be used for retrospective analysis purposes. * Patients that have a documentation of "PTEN LOSS" and/or PTEN/PIK3CA/AKT alteration from a previous test on either tissue or liquid biopsy (e.g., IHC or next generation sequencing NGS), no further biomarker tests are needed in this study. * Patients who have PTEN or PI3KPIK3CA/AKT alteration status reported other than "PTEN LOSS", "PIK3CA/AKT alterations" or never completed any PTEN/PIK3CA/AKT test before, could either provide the archival tumor samples collected at any time before study enrollment or do a fresh core tumor biopsy. * As the last option, patients can perform a liquid biopsy for PTEN LOSS and PTEN/PIK3CA/AKT alteration tests by NGS of cfDNA if they have no archival tissue to provide, no tumor lesion for biopsy or a fresh biopsy is not feasible. 5. Patients must have progressive disease based on the PCWG3 criteria: * Patients who progressed based solely on total PSA rising, should have had a sequence of rising values on 3 consecutive occasions of at least 1-week intervals (if the third measurement is not greater than the second measurement, a fourth measurement at least a week apart must be taken and must be greater than the second measurement) and should have 2.0 ng/mL minimum level for entry. Note: Patient must have had a prior PSA response, followed by documented PSA progression on prior hormone treatment. * Patients who have documented disease progression per RECIST 1.1 are eligible independent of PSA. * Patients with bone only progression according to PCWG3 (i.e., bone scan showing appearance of ≥2 new lesions). 6. Patients must have castration levels of testosterone (\<50 ng/dL or 1.7 nmol/L). Note: Patients must have undergone androgen deprivation therapy (ADT), such as orchiectomy, or have been on luteinizing hormone releasing hormone (LHRH) agonists or antagonists, for at least 3 months prior to study enrollment. Patients on LHRH agonists/antagonists must remain on these agents for the duration of the study. 7. Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2. 8. Patients must have adequate hematopoietic function by local laboratory within the 28 days before enrollment, as evidenced by: * Absolute neutrophil count ≥1,500/μL * Platelet count ≥75,000/μL * Hemoglobin ≥9 g/dL 9. Note: Criteria must be met without growth factors or transfusion within 10 days prior to the screening lab tests. Total serum bilirubin ≤1.5 × ULN within the 28 days before enrollment (in patients with known Gilbert's syndrome, total bilirubin ≤3 × ULN with direct bilirubin ≤1.5 × ULN). 10. Aspartate aminotransferase and alanine aminotransferase ≤2.5 × ULN except for patients with tumor involvement of the liver who must have AST and ALT ≤5 × ULN within the 28 days before enrollment. 11. Patients must have adequate renal function as evidenced by a serum creatinine of ≤1.5 × ULN for the reference laboratory or creatinine clearance ≥30 mL/min within the 28 days before enrollment (calculated from Cockcroft-Gault formula or 24-hour urine collection). 12. Serum potassium ≥3.5 mmol/L and \< ULN within the 28 days before enrollment. 13. Fasting plasma glucose (fasting is defined as no caloric intake for at least 8 hours): * ≤126 mg/dL for those patients without a pre-existing diagnosis of Type 1 or Type 2 diabetes mellitus * ≤167 mg/dL for those patients with a pre-existing diagnosis of Type 2 diabetes mellitus AND glycosylated haemoglobin (HbA1C) ≤8% 14. Phase I: Patients who have mCRPC progressed or are intolerant after receiving at least 1 prior treatments of any anti-androgen (such as abiraterone, enzalutamide, apalutamide, or any other AR antagonists that are approved later), and/or chemotherapy. Patients must have at least 3 weeks of treatment of any antiandrogen and/or completed at least 4 Cycles of docetaxel or cabazitaxel treatment before their screening visit. Phase II: Patients who have mCRPC progressed or are intolerant after receiving 1-3 prior standard treatments for mCSPC, or nmCRPC, or mCRPC, including at least one second-generation antiandrogen treatment (i.e., abiraterone, enzalutamide, apalutamide, or darolutamide), and no more than one chemotherapy. Patients must have at least 3 weeks of treatment of any antiandrogen and/or completed at least 3 Cycles of docetaxel or cabazitaxel treatment and/or at least 3 injections of R223 and/or at least 2 injections of sipuleucel-T to be counted as one prior therapy. Patient's current diagnosis at screening must be mCRPC. 15. Concomitant use of bisphosphonates and other bone supportive agents is allowed if the dose and renal function have been stable for at least 12 weeks before enrollment and no related ≥Grade 2 side effects are present for at least 4 weeks prior to study drug treatment. The minimum washout period is 4 weeks for prostate cancer therapy (cytotoxic, biologics, antiandrogens, etc.) before enrollment, starting from the day the therapies were stopped. 16. Patients with a female partner of childbearing potential must agree to use condoms plus an additional contraceptive method to avoid conception until the end of relevant systemic exposure plus 90 days following the Clinical Trial Facilitation Group contraception guideline from September 2014. 17. Patient should be suitable for oral medication and should not have any known gastrointestinal diseases that may interfere with drug absorption. 18. Life expectancy of at least 6 months. Exclusion Criteria: 1. Major surgery within 28 days before study treatment and/or have not adequately (Grade 1) recovered from the adverse effects of any major surgical procedures before study treatment. 2. Patients that received other second-line ADT (including but not limited to ketoconazole and amino glutethimide) within 6 weeks before enrollment. 3. Patients who have completed sipuleucel-T (Provenge®) treatment within 6 weeks of enrollment. 4. Patients who have received antiandrogens such as flutamide (EULEXIN®), bicalutamide (CASODEX®), or nilutamide (NILANDRON®) for \>3 months must be off treatment for 6 weeks prior to enrollment and should demonstrate a continued rise in PSA after withdrawal. 5. Patients who have received Radium Ra 223 dichloride (XOFIGO®) must be off therapy for 7 weeks prior to enrollment or Samarium Sm 153 lexidronam (QUADRAMET®) must be off therapy for at least 2 weeks prior to enrollment. 6. Patients that are currently receiving increasing or chronic treatment (\>5 days) with corticosteroids or another immunosuppressive agent, other than the following: daily use of up to 10 mg prednisone (or equivalent) or low-dose steroid for the control of nausea and vomiting, topical steroid, or inhaled steroid use. 7. Patients who require potassium-wasting diuretics. 8. Patients who have received any investigational agent beyond those indicated for the treatment of prostate cancer within 5 half-lives of the agent; if the half-life of the agent is not known, the patients must be off investigational therapy for 4 weeks prior to enrollment (whichever is shorter of the two should be preferred). 9. Patients who have received palliative and other radiotherapy for the target lesion within 4 weeks of study enrollment. 10. Patients with symptomatic or known central nervous system metastases from prostate cancer or who are at high risk for spinal cord compression, per investigator's judgment. 11. Patients with a history of hypothalamus, pituitary or adrenal insufficiency. 12. Patients with \>grade 2 neuropathy at study enrollment. 13. History of another primary malignancy that is currently clinically significant or currently requires active intervention. 14. Inadequately controlled hypertension (eg, systolic blood pressure ≥160 mmHg or diastolic blood pressure ≥95 mmHg) or hypotension (eg, systolic blood pressure ≤ 80 mmHg or diastolic blood pressure ≤50 mmHg) after up to 3 measurements with at least 5 minutes apart during 28 days before study enrollment. 15. Patients with active cardiac disease or a history of cardiac dysfunction including any of the following: * Severe or unstable angina pectoris or acute coronary syndrome or stroke within 6 months prior to study enrollment. * Symptomatic pericarditis. * Documented myocardial infarction or arterial thrombotic events within 6 months prior to study enrollment. * History of documented congestive heart failure (New York Health Association functional classification III to IV). * Documented history of cardiomyopathy. * Known left ventricular ejection fraction \<50% as determined by multiple gated acquisition scan or echocardiogram within 28 days prior to enrollment. * History of clinically significant cardiac arrhythmias unsuitable to participate, as determined by the investigator. 16. Patients with a Fridericia-corrected QT (QTcF) interval of \>470 msec on the screening ECG (using the QTcF formula), has a short/long QT syndrome, or history of QT prolongation/Torsades de Pointes, unless prolonged QTc interval is due to (right or left) bundle branch block and/or pacemaker rhythm. If wide QRS complex is present, cardiology consultation is required to assess the risk for Torsade de Pointes. 17. Patients with a history of an active infection (viral, bacterial, or fungal) requiring systemic therapy within 10 days before enrollment, including but not limited to tuberculosis. 18. Patients who have active human immunodeficiency virus (HIV), hepatitis B, or hepatitis C infections. 19. Patients that are currently receiving treatment with drugs known to be moderate or strong inhibitors or inducers of isoenzyme CYP1A (including but not limited: α-Naphthoflavone, Furafylline, Omeprazole, Lansoprazole) and isoenzyme CYP3A (including but not limited: Itraconazole, Ketoconazole, Azamulin, Troleandomycin, Verapamil, Rifampicin). The patients must have discontinued moderate or strong inducers for at least 2 weeks prior to study enrollment and must have discontinued moderate or strong inhibitors for at least 1 week before study enrollment. Spironolactone Strong bile salt export pump (BSEP) inhibitors, grapefruit juice, herbal medicines such as St. John's wort, Kava, ephedra, gingko biloba, dehydroepiandrosterone, yohimbe, saw palmetto and ginseng should be discontinued. 20. Sexually active males not willing to use a condom during the whole course of the study and for 16 weeks after stopping treatment. Male patients must not father a child in this period. A condom is required to be used also by vasectomized men as well as during intercourse with a male partner in order to prevent delivery of the drug via seminal fluid. 21. Patients with any other medical, psychiatric, or social condition, including substance abuse, which in the opinion of the investigator, would preclude participation in the study. 22. Patients with a history of upper gastrointestinal bleeding or uncontrolled peptic disease in the previous 3 months which in Investigator's opinion may impact patient's participation in the study. 23. Patients have previously received AKT or PI3 kinase pathway or mTOR inhibitors